multimodal green logistics network design of urban...

Research ArticleMultimodal Green Logistics Network Design of UrbanAgglomeration with Stochastic Demand

Jiehui Jiang 1 Dezhi Zhang 12 Shuangyan Li 3 and Yajie Liu 4

1 School of Traffic amp Transportation Engineering Central South University Changsha Hunan 410075 China2Key Laboratory of Traffic Safety on Track of Ministry of Education Central South University Changsha Hunan 410075 China3College of Logistics and Transportation Central South University of Forestry and Technology Changsha Hunan 410004 China4College of System Engineering National University of Defense Technology Changsha Hunan 410073 China

Correspondence should be addressed to Yajie Liu liuyajienudteducn

Received 23 April 2019 Revised 1 July 2019 Accepted 24 July 2019 Published 7 August 2019

Guest Editor Juneyoung Park

Copyright copy 2019 Jiehui Jiang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study investigates a multimodal green logistics network design problem of urban agglomeration with stochastic demand inwhich different logistics authorities among the different cities jointly optimize the logistics node configurations and uniform carbontaxes over logistics transport modes tomaximize the total social welfare of urban agglomeration and consider logistics usersrsquo choicebehaviorsThe usersrsquo choice behaviors are captured by a logit-based stochastic equilibrium model To describe the game behaviorsof logistics authorities in urban agglomeration the problem is formulated as two nonlinear bilevel programming models namelyindependent and centralized decision models Next a quantum-behaved particle swarm optimization (QPSO) embedded witha Method of Successive Averages (MSA) is presented to solve the proposed models Simulation results show that to achieve theoverall optimization layout of the green logistics network in urban agglomeration the logistics authorities should adopt centralizeddecisions construct a multimode logistics network and make a reasonable carbon tax

1 Introduction

The logistics network design problem (LNDP) has beenwidely studied [1ndash3] Generally this problem comprises twosubproblems (i) a location problem namely how to decidethe locations of logistics nodes (such as logistics parksdistribution centers and logistics terminals) and (ii) anallocation problem namely how to route the flow of goodsto originndashdestination (O-D) Since the construction of urbanlogistics nodes has the characteristics of a large investmentlong period an great risk the rationality and feasibility of theplan need to be ensured with the objective guidance of theoryand method Meanwhile with the development of societyand the improvement of peoplersquos living standards traffic con-gestion and transportation-related environmental issues havebecome the focus of attention for scholars and governments[4ndash6] Against this unsettling backdrop the traditional singlemode of transport does not meet the needs of modern citiesTherefore how to design amultimodal logistics network withhigh efficiency safety and environmental friendliness is an

important issue to be solved urgently in the development ofurban agglomeration logistics

To locate logistics nodes as addressed in the conventionalfacility location problem (FLP) [7] the multimodal logisticsnetwork design problem (MLNDP) of urban agglomerationneeds to address the rational allocation of limited resourcesbetween different cities in urban agglomerations Becauseof the limited resources in urban agglomerations there is agreat game among each local government in the resources(eg politics economy and population) and this game willderive many game-disordered problems under the restrictionof the governmentrsquos political and economic behavior Localgovernments usually establish the logistics network based onthe situation of their own precinct to fit the regional devel-opment with little coordination and communication withother surrounding regions resulting in the lack of effectiveintegration of the basic logistics resources [8] Thereforegame theory is used to analyze the game relationship amongcity governments in urban agglomeration which is of greatsignificance to the rational allocation of resources

HindawiJournal of Advanced TransportationVolume 2019 Article ID 4165942 19 pageshttpsdoiorg10115520194165942

2 Journal of Advanced Transportation

To route the flow of goods multimodal transporta-tion is a hybrid of transportation that involves two classictransportation services the single mode of transport andcombined transport [9] Compared with the single trans-portation mode the multimodal transportation can makefull use of existing logistics networks of infrastructure andthe advantage of various modes of transport integratingtransport capacity resources meeting the transport demandand achieving the target (eg time cost and profit) [1011] In the multimodal transportation there is no effectiveconnection between each mode of transportation and thedesign of the multimodal transportation plan needs to befurther improved and optimized [12] However urban trafficcongestion and transportation-related environmental issues(eg carbon dioxide (CO2) nitrogen oxide and sulfur oxide)are the bottlenecks that restrict the sustainable developmentof cities [13 14] Consequently there is an inevitable trendtoward the future development of urban agglomeration greenlogistics systems to develop multimodal and integrativetransportation networks

11 Literature Review We classify the literature related to ourresearch into three branches (1) urban agglomeration logis-tics (2) green logistics network design for facility locationand (3) logistics network design with choice behaviors

111 Urban Agglomeration Logistics The urban agglomer-ation logistics system is an important part of the urbanagglomeration economy as it plays an important and sup-porting role in the sustainable development and evolution ofthe urban agglomeration Mullen and Marsden [15] exploredthe adaptive adjustment mechanism of regional logistics andregional economy Li et al [16] emphasized the relationshipbetween traffic investment and traffic efficiency in urbanagglomeration Jiang et al [17] analyzed the bidirectionalrelationship between multimodal transportation investmentand economic development However some scholars studiedthe spatial and temporal distribution characteristics of urbanagglomeration logistics [18 19] Lindsey et al [20] studiedthe relationships among freight transport economic marketdrivers and industrial space demand Kumar et al [21] inves-tigated spatial patterns of transportation and logistics clusterin the US regions applying spatial cluster and econometricanalyses The above studies mainly focus on the linkagemechanism between logistics and economy demand andspatial and temporal distribution and few focus on the greenlogistics system of urban agglomeration Table 1 summarizesthe main features of the proposed models in the reviewedstudies

112 Green Logistics Network Design for Facility LocationGreen logistics aims to restrain the environmental dam-age (eg greenhouse gas emissions noise and accidents)caused by logistics activity and develop a sustainable balancebetween economic social and environmental objectives [22]Facility location modeling is a strategic planning designapproach that selects the optimal set of facilities from a setof potential facilities [23] As a branch of network design

the green logistics network design problem originates fromthe classic facility location problem (FLP) [7 24] and thenextends it to the location-allocation problem (LAP) [25ndash27]

In the background of the vigorously developing greeneconomy Turken et al [24] investigated the impact of carbontax on plant capacity and location decisions of a firmYang et al [26] studied the low-carbon network designproblem of the third-party logistics distribution system Tosolve location-allocation problem with a carbon emissionsconstraint Rezaee et al [2] developed a two-stage stochasticprogrammingmodel and Gao et al [28] proposed five multi-dimensional mixed-integer nonlinear programming modelsIn practice the urban agglomeration logistics network maycomprise multiple urban logistics networks which are inde-pendently and separately managed by local governments (orlogistics authorities) with different targets Nevertheless theliterature always supposed that the network is totally designedby a single management body which may not suit the designof the logistics network in urban agglomeration

113 Green Logistics Network Design under Route ChoiceModels In general route choice models should evaluate theutility of each route and route the flow of passengers or goodsfrom origin to destination Although they have been widelyused to solve urban passenger transportation problems byresearchers and engineers [29ndash33] using these models tosolve urban cargo transportation problems has received littleattention in the literature

The logistics network design problem based on routechoice behavior can be characterized as a bilevel program-ming model or an equivalent mathematical program withequilibrium constraints (MPEC) model At the upper levelthe logistics authority determines the number location andcapacity of logistics facilities (nodes) At the lower levelshippers and carriers follow the user equilibrium (UE)principle or stochastic user equilibrium (SUE) principle [34ndash36] Yamada et al [37] presented a bilevel programmingmodel to simulate the multimodal freight transport networkdesign problem where the lower-level model is a multimodalmulticlass user equilibrium model To address the inter-modal hub-and-spoke network design problem for multiplestakeholders and multitype containers Meng and Wang [38]established anMPECmodel and used a variational inequalityto describe the operatorsrsquo route choice behavior Wang andMeng [39] extended the research work of Meng and Wang[38] by considering congestion effects and piecewise linearcost functions and solved it with a solution algorithm basedon nonlinear optimization and branch-and-bound globaloptimization

However the route choice models of these studies didnot consider the carbon emissions cost perception errorand elastic demand In addition they mainly focus on staticdetermined network design issues As strategic decision plan-ning the design of a logistics network in urban agglomerationinvolves long-term planning of a between 5- and 20-yeartimeline where the logistics demand is often uncertain withthe development of urban evolution and industrial structureoptimization Hence it is more realistic and reasonable to

Journal of Advanced Transportation 3

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Research

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Transportm

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Dem

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Choice

behaviors

Num

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Type

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Routing

Carbo

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Exact

Heuris

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MS

MS

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Utility

SM

Xion

gandWang[12]

--

Costtim

e

MOGA

Harris

etal[25]

--

CostCO

2em

issions

SEAMO2

Yang

etal[26]

--

Cost

Cplex

Turken

etal[24]

--

Cost

FLAA

Rezaee

etal[2]

--

Cost

Cplex

Gao

etal[28]

--

Cost

Cplex

Yamadaetal[37]

UE

Costtim

e

Benefitndashcostratio

GAGLS

MengandWang[38]

UE

Costtim

e

Cost

GA

WangandMeng[39]

UE

Costtim

e

Cost

BampB

Zhangetal[35]

UE

Costtim

e


GA+FW

ATh

isstu

dy

SU

ECosttim

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ission

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ultip

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edeterm

inisticStsto

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FWFrank

ndashWolfeAlgorith

mQ

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behavedParticleSw

arm

Optim

ization

andMSA

Metho

dof

Successiv

eAverages


design the logistics network with demand uncertainty andstochastic route choice

12 Objectives and Contributions In view of the above-mentioned realistic problems and specific characteristics oflogistics development in urban agglomerations the objectiveof this paper is to coordinate the distribution of various typesof logistics nodes (eg logistics parks distribution centersand logistics terminals) in the urban agglomeration logisticsnetwork from the overall perspective of urban agglomerationand fully consider the low carbon requirement together withdemand uncertainties The main contributions of this paperare as follows First to characterize different decision-makingbehaviors among multiple local authorities the multimodallogistics network design problem is formulated as two non-linear bilevel programming models At the upper level thelogistics authority of each city attempts tomaximize the socialwelfare including producer surplus and consumer surplusAt the lower level the logistics usersrsquo route choice decisionsfollow logit-based stochastic user equilibrium (SUE) withelastic demand under logistics demand scenario Second aheuristic solution algorithm that is a combination of quantumbehaved particle swarm optimization (QPSO) and Methodof Successive Averages (MSA) is developed to solve theproposed bilevel programming model Third the optimalnumber scale and location of logistics nodes analysis of theimpact on the distribution of city group logistics networkof infrastructure investment budget and carbon tax areillustrated with an example

The remainder of this article is arranged as followsThe basic considerations of this paper including generalassumptions and network representation are described inSection 2 A nonlinear bilevel programming formulationis proposed in Section 3 and the solution methods arepresented in Section 4 A numerical example is presentedto illustrate the availability of previous models in Section 5Finally the conclusion and future studies are discussed inSection 6

2 Basic Considerations

21 General Assumptions To facilitate the presentation ofessential ideas without the loss of generality the followingbasic assumptions are made

A1 For the simplicity of expression the urban agglomerationis assumed to be a city that is a set of all single cities and theplanning period is assumed to be one week

A2 In the urban logistics system the logistics nodes invest-ment and subsidy are determined by the logistics authority

A3 The disutility of each service route is measured bytransport time transport cost and CO2 emission taxes (ifany) Logistics users select their logistics service routes whichare associated with their own perceptions of service disutility

A4 The urban agglomeration comprises several citiesand each city has one logistics authority In decentralized

decision-making the decision-making of logistics depart-ments in urban agglomeration is completely independent

22 Network Representation Tomodel logistics service of theurban agglomeration we first represent the demand networkmultimodal logistics physical network andmultimodal logis-tics service network

Demand Network Let 119874 isin 1198730 be the set of logistics demandorigin nodes and let 119863 isin 1198730 be the set of logistics demanddestination nodes where 1198730 is the set of logistics nodes(or transfer nodes) including existing and potential logisticsparks distribution centers and logistics terminals Denote by119882 sub 119874 times 119863 the set of logistics demand origin-destination(OndashD) pairs For a given logistics O-D pair Figure 1(a) showsthe different types of logistics demands such as industrialdemand (K1) commercial demand (K2) and agriculturaldemand (K3) These demands are served by the multimodallogistics network as shown in Figures 1(b)ndash1(e)

Multimodal Logistics Physical Network Suppose that a multi-modal logistics physical network needs to be designed whichismade up of a set of logistics nodes and a set of logistics linksor arcs of different transport modes Each logistics node orlink is provided by a logistics operator

We denote the multimodal logistics physical network asa directed network 1198660 = (1198730 1198600) where 1198730 is the set oflogistics nodes and1198600 is the set of logistics links Let119873119905 sub 1198730

denote the set of logistics transfer nodes and let 1198720 be theset of modes Each link 119886 isin 1198600 is represented by a triplet(119904119886 119890119886 119898119886) where 119904119886 119890119886 isin 1198730 are the starting point andending point of link 119886 respectively and 119898119886 isin 1198720 is thetransportation mode on the link

Analogously for any logistics transfer node 119894 isin 119873119905 let119860 119894119899(119894) denote the set of logistics links pointing into transfernode 119894 and let 119860119900119906119905(119894) denote the set of logistics linksstemming out of transfer node 119894 For each logistics link 119886 isin119860 119894119899(119894) we make a copy of transfer node 119894 as its ending pointLet119873119894119899(119894) denote the set of heads (copies) of all logistics arcsin 119860 119894119899(119894) after copying Similarly For each logistics link 119886 isin119860119900119906119905(119894) we make a copy of transfer node 119894 as its ending pointLet119873119900119906119905(119894) denote the set of tails (copies) of all logistics arcsin119860119900119906119905(119894) after copyingThus the set of virtual arcs at transfernode 119894 is denoted by119860 119905(119894) = ((119895 119896) 119895 isin 119873119894119899(119894) 119896 isin 119873119900119906119905(119894))and the virtual subnetwork of logistics transfer node 119894 can berepresented by a directed graph 119866119894 = (119873119894119899(119894) cup119873119900119906119905(119894) 119860 119905(119894))

Figure 1(b) shows an example of a multimodal logisticsphysical network 1198660 = (1198730 1198600) where 1198730 = OD 1 2 3and 1198600 = 119886119894 | 119894 = 1 2 6We suppose119873119905 = 1 2 3 and119872 = Railway Expressway Then the virtual subnetworksat each logistics transfer node 119894 isin 119873119905can be generatedFigure 1(c) shows the example of the virtual subnetwork1198661 = (119873119905(1) 119860 119905(1))at logistics transfer node 1 where119873119905(1) =1a 1b 1c and 119860 119905(1) = 1198867 1198868Multimodal Logistics Service Network A hypernetwork 119866 =(1198720 119873119860119892 119860 119905) is used to construct a multimodal logisticsservice network where 1198720 represents the type of routetransport modes 119873 = ⋃119894isin119873119905

(119873119894119899(119894) cup 119873119900119906119905(119894)) cup 119873119894isin1198730119873119905


DO

K1

K2

K3

(a) Logistics user demand network 119866119889 = (119873119889119860119889)

3 D21Oa1 = ( 1 ＲＪＬＭＭＱＳ)

a2 = (1 2 ２ＣＦＱＳ)

a3 = (1 2 ＲＪＬＭＭＱＳ)

a4 = (2 3 ２ＣＦＱＳ)


a6 = (3 ＄ＲＪＬＭＭＱＳ)

(b) Multimodal logistics physical network 1198660 = (1198730 1198600)

2a1b1aO

2b1c

a1 = ( 1 ＲＪＬＭＭＱＳ)

a2 = (1 2 ２ＣＦＱＳ)


a8 = (1 1＝)

a7 = (1 1＜)

Ain (1) = a1Aout (1) = a2 a3G1

(c) Representation of the virtual subnetwork of logistics transfer node 1

1aO 2a 2c 3a 3c D1c

2b 2d 3b1b

Expresswayservice subnetwork

Railway servicesubnetwork

a1 a7 a3

a8 a10

a9 a5 a13 a6

a4a12

a11a2

a14

(d) Multimodal logistics service supernetwork 119866 = (119872119873119860119892 119860119905)

1aO 2a 2c 3a 3c D1csingle mode

combinedmode 1aO 2b 2d 3b 3c D1b

a1

a1

a7 a3

a8

a9a5 a13

a6

a6a4a12a2 a14

(e) Logistics service route

Figure 1 Multimodal logistics network representation

denotes the set of nodes after transfer node copies 119860119892 =119860119901 denotes the set of logistics links and 119860 119905 = ⋃119894isin119873119905119860 119905(119894)

denotes the set of transfer arcs Based on the example ofmultimodal logistics physical network in Figure 1(b) and thevirtual transfer subnetworks the logistics service supernet-work 119866 = (1198720119873 119860119892 119860 119905) is then generated and containshighway subnetworks and railway subnetworks (Figure 1(d))

Feasible Sets of Route Although in the multimodal logisticsservice supernetwork there are some routes from the logisticsdemand origin to the destination only the routes that satisfycertain conditions such as cost time or CO2 emissionsare called feasible routes Thus for any logistics O-D pair119908 isin 119882 let 119877119908 denote the set of logistics feasible serviceroutes connecting 119908 in the multimodal logistics servicesupernetwork and let 120575119903119898119908 be one if service route 119903 isin 119877119908 usestransport mode119898 isin 119872 and zero otherwise

3 Model Formulation

31 e General Stochastic Bilevel Programming ModelStochastic bilevel programming combines the characteristicsof stochastic programming and bilevel programming andintroduces random scenarios to describe the uncertaintiesinvolved in the model The most commonly used stochastic

bilevel programming model is the expected bilevel program-ming model which is described in the following mathemati-cal form [40]

(1198800) minx 119864 [119865 (x y (120585) 120585)]119904119905 119864 [119866 (x y (120585) 120585)] le 0 (1)

where response function y = y(x) is implicitly defined by

(1198710) miny 119891 (x y (120585) 120585)119904119905 119892 (x y (120585) 120585) le 0 (2)

Obviously the expected bilevel programming modelcomprises two submodels (U0) which is defined as an upperlevel and (L0) which is a lower level x 119865(x y(120585) 120585) and119866(x y(120585) 120585)denote the decision vector objective functionand constraint set of the upper-level decision-makers or sys-tem managers respectively 119864[sdot] is the expectation operatorwith respect to random scenarios 120585 y(120585) 119891(x y(120585) 120585) and119892(x y(120585) 120585)denote the decision vector objective functionand constraint set of the lower-level decision-makers or usersrespectively

Assume that the random scenarios 120585 have a finite numberof statesΨ = (120590119904 119904 isin Ω) Let 119904 = 1 2 |Ω| index


Logistics authority

Shippers(demand) Given the logistics service

fare and time

Carriers (supply)

Logistics service path choice

Capacities forlogistics node

Carbon tax onservice link

User equilibrium flow assignment

Upper decision modeltotal social welfare

Lower decision modellogit-based stochastic

user equilibrium

Figure 2 Decision framework of green logistics system

be its possible realizations and let 119901119904 be their respectiveprobabilities Then we can now express the extensive formof the stochastic bilevel program as follows

(1198801) minx sum119904isinΩ

119901119904119865 (x y119904 (120590119904) 120590119904)119904119905 sum

119904isinΩ

119901119904119866 (x y119904 (120590119904) 120590119904) le 0 (3)


(1198711) miny119904 119891 (x y119904 (120590119904) 120590119904)119904119905 119892 (x y119904 (120590119904) 120590119904) le 0 (4)

32 Decentralized Decision inMultiple Cities Since the urbanlogistics system is exclusivelymanaged by a logistics authoritybut serves for all logistics users (ie shippers and carriers)equally the urban logistics network design is typically for-mulated as a Stackelberg game that can well characterize theinteractions between the logistics authority and users

As shown in Figure 2 a bilevel program is used to modelthe leader-follower behaviors between logistics authority andusers At the upper level the logistics authority attemptsto maximize the social welfare by planning the investmentcapacity of logistics nodes and determining the carbon tax ontransportation service links At the lower level the logisticsusersrsquo reactions and choice decisions to the urban logisticsnetwork design scheme will be assumed to follow logit-based stochastic user equilibrium (SUE) under the logisticsdemand scenario Moreover the main notations are providedin Appendix A

321 Upper-Level Model of Green Logistics Network Design fora Single City As the upper-level decision maker the logisticsauthority aims to maximize the total social welfare of its owncity It iswell known that the total social welfare comprises theconsumer surplus and producer surplus in scenario 119904 isin Ωwhich can be expressed as

SW119904119896 (X119896 119910119896V119896) = 119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962 (5)

where

119862119878119904119896 = sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908 minus sum119908isin119882119896

119902119904119896119908120582119904119896119908forall119896 isin 119870 119904 isin Ω

(6)

1198751198781199041198961 = sum119894isin119868119896

(119862119896119894 minus 120578119896119894) 119891119904119896119894

+ sum119894isin119875119896

max (119909119896119894 minus 119911119896119894 0) 119878119906119887119896119894minus sum

119894isin119868119896

1198620119896119894 (119909119896119894)120588 forall119896 isin 119870 119904 isin Ω

(7)

1198751198781199041198962 = sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886 (119888119898119896119886 minus 120591119898119896119886)

+ sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886119890119898119886 119910119896 forall119896 isin 119870 119904 isin Ω (8)

Eq (6) formulates the consumer surplus and 119863minus1119908 (119908)

is the inverse function of the logistics demand functionConsumer surplus is the extra benefit logistics usersrsquo gainswhen the costs they actually pay are less than what theywould be prepared to pay Eqs (7) and (8) formulate theproducer surplus of all logistics nodes and logistics arcsrespectively Producer surplus is a measure of producerwelfare Taking (7) as an example the first term is transferprofits the second term is subsidy revenues and the last ispark construction costsThen the upper-levelmodel of greenlogistics network design in single city 119896 isin 119870 is formulatedas

maxX119896119910119896

SW (X119896 119910119896V119896) = sum119904isinΩ

119901119904119896 (119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962) (9)


subject to

0 le 119909119896119894 le 119878max119896119894 forall119894 isin 119875119896 (10)

0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)

where V119896(X119896 119910119896) can be obtained by solving the upper-levelmodel

The objective function (9) formulates the expected socialwelfares Constraint (10) represents the establishment orexpansion capacity restraint of the logistics nodes constraint(11) denotes the constraint of carbon tax and constraint(12) represents the construction investment constraint of thelogistics nodes

322 Lower-Level Model of Green Logistics Network Design

TravelTransfer Time To capture the difference in attributes ofdifferent modes of transport for each transport link 119886 isin 119860119892

119896we consider the following service time function

119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)

where 1199051198980119886 is the link free-flow transport service time and119905119889119896119898 is the average transport time interval For HGVs or

LGVs the Bureau of Public Roads-type (BPR) function canbe adopted to estimate transport service time For railways orwaterways we consider service time function as a function oflink free-flow transport service time and departure intervaltime [11 35] Similarly for each virtual transfer arc we usethe following service time function

119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0

+infin 119909119896119894 = 0forall119896 isin 119870 119894 isin 119868119896 119886 isin 119860119905

119896 119904 isin Ω(14)

where 1199051198940119896119886

is the arc free-flow transfer service time and 1205720 and1205730 are impedance parameters

RouteUtility and Flow According toA3 each logistics serviceroute is associated with a given actual cost (disutility) whichcan be expressed as

119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908

forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω (15)

where 120591V119900119905 is the value of time 119862119903119904119896119908 119879119903119904

119896119908 and 119866119903119904119896119908 represent

the transportation cost logistics service time and CO2

emission cost on service route 119903 between O-D pair 119908 in city119896 isin 119870 under logistics demand scenarios 119904 respectively whichare expressed as

119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119888119894119896119886120575119894119903forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω

(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903

forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119898 isin 119872 119904 isin Ω(17)

119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119890119898119897119896119886119910119896120575119898119886119903forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119898 isin 119872 119904 isin Ω

(18)

It is worth noting that the transportation cost (time) ofeach route includes the transport cost (time) on links and thetransfer cost (time) at parks Due to variations in perceptionthe route service disutility is perceived differently by eachlogistics user and thus the perceived disutility of each routeis treated as a random variable If the random variable canbe considered to obeyGumbel distribution [41] then the pathflow 119891119903119904

119896119908on route 119903 isin 119877119908 between O-D pair119908 isin 119882119896 in single

city 119896 isin 119870 and scenario 119904 isin Ω can be given by

119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)

sum119903isin119877119908exp (minus120579119906119903119904

119896119908)

forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω(19)

where 120579 represents the sensitivity of route selection disutilityand 119902119904119896119908 denotes the logistics demand function Eq (19) is themost widely used flow assignment method in traffic planningand represents the flow assigned to each feasible route foreach logistic demand [41] To capture the logistics usersrsquoresponses to logistics service disutility we assume that theelastic demand function between a generic O-D pair 119908 isin 119882119896

is a monotonically decreasing function of the O-D servicecost 119906119903119904119896119908 between this O-D pair The generic elastic demandfunction [42] is expressed as follows

119902119904119896119908 = 119863119908 (120582119904119896119908) = 119902119904119896119908 exp (minus120573120582119904119896119908) forall119896 isin 119870 119908 isin 119882119896 119904 isin Ω (20)

where 120573 represents the sensitivity to the expected service costand 120582119904119896119908 is the expected minimum perceived service costbetween O-D pair 119908 isin 119882119896 in single city 119896 isin 119870 and scenario119904 isin Ω In the case of stochastic user equilibrium (SUE)assignment with elastic demand [42] the expected minimumservice cost between an O-D pair under logistics demandscenario 119904 isin Ω in city 119896 isin 119870 could be expressed as

120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)


Equivalence Model According to the above analysis for anygiven logistics authority decision (X119896 119910119896) the lower-levelmodel of green logistics network design in a single city 119896can be formulated as the following equivalent minimizationprogram

min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896

119902119904119896119908 (ln 119902119904119896119908 minus 1) minus sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908

119891119903119904119896119908 = 119902119904119896119908 forall119896 isin 119870 119908 isin 119882119896 119904 isin Ω (23)

119891119903119904119896119908 gt 0 forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω (24)

where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903 forall119896 isin 119870 119894 isin 119868119896 119904 isin Ω (26)

Constraint (23) is the flow conservation constraint Con-straint (24) is the nonnegativity constraints of service routeflows Constraint (25) defines the relationship between theroute flow and path flow Constraint (26) defines the rela-tionship between the route flow and logistics nodes flowrespectively

Proposition 1 eminimization program (22)-(26) is equiva-lent to the logit-based stochastic user equilibrium (SUE) assign-ment with elastic demand under logistics demand scenario119904 isin Ω in city 119896 isin 119870 e proof of Proposition 1 is given inAppendix B

33 Centralized Decision in Urban Agglomeration In theprevious subsection we study the problem that severallogistics authorities perform logistics network design deci-sions independently However such independence might beadverse to the overall benefit of urban agglomeration sinceit does not explore the full potential of the investment toimprove the need of all logistics users on the entire logisticsnetwork We propose a centralized decision model in whichlogistics authorities cooperate with each other to maximizethe total social welfare in urban agglomeration

The upper-level model of green logistics network designin urban agglomeration is formulated as

maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)

subject to0 le 119909119894 le 119878max

119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)

The lower level program is still the traffic assignmentproblem described in Section 322

4 Solution Methods

41 e Quantum Behaved Particle Swarm Optimization(QPSO) The QPSO was introduced by Sun et al [43]combining quantum theory based on the particle swarmoptimization (PSO) Different from that in PSO particlesin QPSO have no velocity vectors in addition parametersthat need to be adjusted are far fewer It has been widelyused in theory and engineering practice because of its globalconvergence together with comparative simplicity In theQPSO the particles are updated with the four followingequations119898119887119890119904119905 (119905119906) = (1198981198871198901199041199051 (119905119906) 1198981198871198901199041199052 (119905119906) 119898119887119890119904119905|119863| (119905119906))

= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)

119901119895119889 (119905119906) = 120593119895119889 sdot 119875119895119889 (119905119906) + (1 minus 120593119895119889) sdot 119875119892119889 (119905119906) forall119895 isin 119872119876 119889 isin 119863 120593119895119889 sim 119880 (0 1) (32)

120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)

119883119895119889 (119905119906 + 1) = 119901119895119889 (119905119906) plusmn 120572 (119905119906) sdot 10038161003816100381610038161003816119898119887119890119904119905119889 (119905119906)minus 119883119895119889 (119905119906)10038161003816100381610038161003816 sdot ln( 1120583119895119889 (119905119906))

forall119895 isin 119872119876 119889 isin 119863 120583119895119889 sim 119880 (0 1)(34)

where the119883 denotes the particlersquos position 119898119887119890119904119905 denotes themean best position of all the particlesrsquo best positions The 119875119895and 119875119892 are the particlersquos personal best position and the globalbest position respectively 120572(119905119906) is the expansion-contractioncoefficient where 119905 is the current iteration number and 119879 isthe maximum number of iterations in general 1199060 = 1 1199061 =05


Begin the program

Step 1 External loop initializationQPSO parameters maximum iteration (T) external loop iteration

Step 2 Inner loop operation(solve the lower-level flow assignment by MSA)

Step 3 Calculate the mean of the personal best (pbest) positions

Step 4 Update the expansion-contraction coefficient

Step 5 For each particle calculate the personal fitness value

Step 7 For each particle generate the new local attractor point

Step 8 For each particle update the particlersquos position

Step 10 Output the final optimal solutions

End the program

Step 9 Checkthe termination

criterion

Yes

No

Step 21 Inner loop initialization

Step 22 Calculate the link flow and nodeflow by using (25) and (26)

Step 23 Calculate the transport time andtransfer time by using (13) and (14)

Step 24 Calculate the disutility

Step 25 Calculate the auxiliary route flow

Step 26 Update route flow by using methodof successive average (MSA)

Step 28 Return the inner loop optimal


criterion

Yes

No

QPSO algorithm MSA algorithm

counter tu = 0 particlersquos initial position Xkj(tu)

mbestk(tu) by using (31)

k(tu) by using (33)

F (Xkj (tu)) Vk (Xkj (tu))) and pbest position Pkj (tu)

pkjd (tu) by using (32)

Xkjd(tu + 1) by using (34)

determine Rw iteration counter tl = 1

solutions Vk (Xkj (tu))

Step 6 Update the global best (gbest) position Pkj (tu)

umswr by using (15)(tl)

fms

wr by using (19)(tl)

sa (0) = calculating fmswr (0)Initialize

Figure 3 Flow chart of QPSO and MSA hybrid algorithm

42 Hybrid QPSO Algorithm for Bilevel Decision ProblemTo penalize the candidate solutions violating constructioninvestment constraints (12) we first define the evaluationfunction as the sum of the objective function and penaltyterms as follows

119865 (X119896 119910119896V119896)= SW (X119896 119910119896V119896)minus 119903119890 (max(sum

119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)

subject to (10)(11)(13)-(26) and 119896 isin 119870where 119903119890 is the positive variable penalty coefficient

The above model can then be solved by a solutionalgorithm based on the QPSO and Method of SuccessiveAverages (MSA) hybrid algorithm (Figure 3) The detailedprocess of the above hybrid algorithm is described as follows

Step 1 External Loop Initialization

(1) Set the QPSO parameters population size (|119872119876|) andrelated parameters(1205720 1205721)

(2) Set the termination criterion for the external loopoperation maximum iteration (T)

(3) Set the external loop iteration counter 119905119906 = 0 andrandomly generate particlersquos initial positionX119896119895(119905119906) =[X119896119895(119905119906) 119910119896119895(119905119906)] forall119895 isin 119872119876 119896 isin 119870 in which


Carbon tax

x1 x2 middot middot middot x|P| yk

Investment capacity xi isin [0 SＧＲi ] yk isin [0 CℎＧＲ]

Figure 4 Representation of individual particle

X119896119895(119905119906) is sampled randomly in the feasible space If119905119906 = 0 let the personal best (pbest) position of eachparticle P119896119895(119905119906) = X119896119895(119905119906)

Step 2 Inner Loop Operation (Solve the Lower-Level FlowAssignment)

For a given logistics authority decision X119896119895(119905119906) use themethod of successive averages (MSA) to solve the lower-levelflow assignment problem for each scenario119904 isin Ω and obtainoptimal solutions V119896(X119896119895(119905119906))Step 3 Calculate the mean of the personal best (pbest)positions of all particlesm119887119890119904119905119896(119905119906) by using (28)Step 4 Update the expansion-contraction coefficient 120572119896(119905119906)by using (33)

Step 5 For each particle calculate the personal fitness value119865(X119896119895(119905119906)V119896(X119896119895(119905119906))) and pbest position P119896119895(119905119906)If 119865(X119896119895(119905119906)V119896(X119896119895(119905119906))) gt 119865(P119896119895(119905119906)V119896(X119896119895(119905119906)))

update P119896119895(119905119906) = X119896119895(119905119906)Step 6 Update the global best (gbest) position P119896119892(119905119906) 119892 =argmax119895isin119872119876 119865(P119896119895(119905119906)V119896(X119896119895(119905119906)))Step 7 For each particle generate the new local attractorpoint 119901119896119895119889(119905119906) by using (32)Step 8 For each particle update the particlersquos position119883119896119895119889(119905119906 + 1) by using (34)Step 9 Check the termination criterion for the external loopoperation If (119905119906 ge 119879) then stop the calculation and go toStep 10 otherwise let 119905119906 = 119905119906 + 1 and go to Step 2


In the upper model as shown in Figure 4 each particleis represented as one string comprising |119875119896| + 1 continuousnumbers where |119875119896| is the number of entities vector X119896 =(1199091 1199092 119909|119875119896|) that is |119863| = |119875119896| +1 where119863 is a set of |119863|consecutive positive integers

The method of successive averages used in Step 2 isdescribed in the following substeps

Step 21 Inner Loop Initialization

(1) Set the termination criterion for the external loopoperation (120577119897)

(2) Set the initial link flow V119904119896119886(0) = 0 and calculate theroute flow 119891119903119904

119896119908(0) by using (19)(3) Determine effective service route set 119877119908 119908 isin 119882119896(4) Set the inner loop iteration counter (119905119897 = 1)

Step 22 Calculate the link flow V119904119896119886(119905119897) and node flow 119891119903119904119896119908(119905119897)

by using (25) and (26) respectively

Step 23 Calculate the link service time 119905119898119904119896119886(V119898119904

119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904

119896119894(119905119897)) by using (13) and (14) respectively

Step 24 Calculate the disutility 119906119898119904119908119903(119905119897) by using (15)

Step 25 Calculate the auxiliary route flow 119891119898119904

119908119903(119905119897) by using(19)

Step 26 Update route flow by using method of successiveaverage (MSA)

Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))

Step 27 Check the termination criterion for the inner loopoperation

Let

119892119886119901119904 (119905119897)= radicsum119898isin119872sum119908isin119882119896

sum119903isin119877119908(119891119898119904

119908119903 (119905119897 + 1) minus 119891119898119904119908119903 (119905119897))2sum119898isin119872sum119908isin119882119896

sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)

if 119892119886119901119904(119905119897) le 120577119897 then stop the calculation and go to Step 28otherwise let 119905119897 = 119905119897 + 1 and go to Step 22

Step 28 Return to the inner loop optimal solutionsV119896(X119896119895(119905119906))5 Numerical Examples

As shown in Figure 5 an example multimodal logisticsnetwork of urban agglomeration is used to illustrate the avail-ability of the proposed bilevel model and QPSO algorithmThe solution procedure is coded by MATLAB R2012a andruns on a desktop Lenovo G3240 with an Intel Pentium 310GHz and 4 GB RAM

51 Main Data and Parameter Values The network com-prises 19 nodes 42 arcs and six logistics demand O-D


1

12

11

2

7

34

13

14

8 9

56

15

16

10

Industry logistics demand point(original node)

Candidate Distribution center

Virtual node

Commercial logistics demand point(original node)

Candidate Logistics park

WaterwayRailway

Urban expressway

Virtual extensionIntercity expressway

17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35

Figure 5 An example multimodal logistics network of urban agglomeration

pairs The logistics demand for each O-D pair the basicdata of each logistics node and each arc in the networkare provided in Appendix C To examine the effect oflogistics demand uncertainty on logistics network designdecisions we consider three logistics demand scenarios Thetotal construction budget for urban agglomeration is 15000$week The sensitivity parameters 120579 and 120573 are 08 and 0001respectively The value of time is 8 $h The unit investmentsubsidy for each logistics node is 05 $week The averageemissions of expressway railway and waterway are 01320022 and 0016 kgton-km respectively The maximumcarbon tax on arc is 1 $kg Unless otherwise specifiedthese input data are considered unchanged in the followinganalysis

52 Numerical Results and Discussions For comparison thedo-nothing model and the decentralized and centralizeddecision models are considered in this paper In the do-nothing model and decentralized decision model the logis-tics nodes budget for each single city is set as 0 and 5000

$week respectively However in the centralized decisionmodel the budget is designed under a total budget constraint15000 $week The optimal solutions and performance com-parison for these three models are given in Tables 2 and 3respectively

Table 2 clearly shows that under the given investmentbudget five logistics parks located at (X1-X4 X6) are con-structed in the centralized decision model and the totalprocessing capacity is 3658 tonsweek While the number oflogistics parks increases to six (X1-X6) in the decentralizeddecision model the total processing capacity decreases to3552 tonsweek By comparing the centralized decisionmodel with the decentralized decision model it shows that inthe decentralized decision model the investment budget forthe city 1 is reasonable while the investment budget for thecity 2 is insufficient and the investment budget for the city 3is in surplus Similarly as shown in Table 3 among the threedesign models the centralized decision model has the bestperformance followed by the decentralized decision modelCompared with the do-nothing model the centralized


Table 2 Optimal solutions for three logistics network design models

Models City 1 City 2 City 3X1 X2 X7 Y1 X3 X4 X8 X9 Y2 X5 X6 X10 Y3

Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0

Decentralized Tax 662 498 0 022 602 585 0 0 017 205 1000 0 024Nontax 273 939 0 0 720 468 0 0 0 182 988 0 0

Centralized Tax 630 495 0 021 829 704 0 0 021 0 1000 0 021Nontax 229 994 0 0 750 742 0 0 0 0 952 0 0

Table 3 Comparison of the three logistics network design model performances

Models Total socialwelfare ($)

Consumersurplus ($)

Producersurplus ($)

Percentage ofcombined transport

Average carbonemission rate(kgton-km)

Do-nothing 2449637 2345459 104178 0 01320

Decentralized Tax 3889751 3707380 182371 4188 00739Nontax 3879730 3698102 181628 3608 00752

Centralized Tax 3950308 3765081 185227 4200 00730Nontax 3927741 3743486 184255 3636 00741

decision model and the decentralized decision model canreduce the average carbon emission rate by approximately45 after the construction of a multimode network

Given the above to achieve overall optimality in thelayout of urban agglomeration logistics networks each logis-tics authority in the urban agglomeration should make jointdecisions allocate the investment budget and plan the quan-tity and scale of the logistics nodes rationally At the sametime the carbon emissions generated during the logisticsand transportation can be greatly reduced by constructing amultimodal network and setting a reasonable carbon tax

53 Impact Analysis of Budget Allocation on Network Per-formance As seen from Table 2 the investment budget ofcity one is reasonable To analyze the impact of budgetdistribution on network performance in the decentralizeddecision model we set 1198611 = 5 000 $week and carried outnumerical experiments of nine budget allocation scenarios(with the same total investment budget 1198612 + 1198613 = 10 000$week) Numerical results are presented in Table 4 andFigure 6

From Table 4 first we can see that the construction ofthe logistics park takes priority over the general logisticsnode Second with the increase in the investment budget incity 2 the number of logistics parks and logistics nodes willincrease and processing capacity will be enhanced graduallyTo be specific when the investment budget is equal to 1000-2000$week one logistics park is constructed when theinvestment budget is equal to 3000-8000$week two logis-tics parks are constructed and when the investment budget ismore than 9000$week two logistics parks and one logisticsnode are constructed Finally the optimal carbon tax gradu-ally declines with the increase in the investment volumeThisis because before the construction of the logistics park thereis a single highway with high carbon emissions in the logisticsnetwork and after the construction of the logistics park there

(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re

City 1City 2City 3Urban agglomeration

Budget allocation scenario (City1-City2-City3) x103

x 106

Figure 6 Social welfare for each city under different budgetallocation

will be a single highway and multimodal transportation suchas highway-railway and highway-waterway in the logisticsnetwork which effectively reduces the carbon tax in thenetwork As shown in Figure 6 the social welfare increaseswith the increase in the investment budget for a single cityHowever from the perspective of total social welfare whenthe investment budget is allocated in the scenario of 5000-6000-4000 $week the total social welfare is the maximumfor the urban agglomeration


Table 4 Optimal solutions for decentralized decision model under different budget allocation

Scenario City 1 City 2 City 3($week) X1 X2 X7 Y1 X3 X4 X8 X9 Y2 X5 X6 X10 Y3

(5-1-9)lowast103 662 498 0 022 199 0 0 0 054 1000 1000 10 003(5-2-8)lowast103 662 498 0 022 450 0 0 0 048 1000 1000 0 004(5-3-7)lowast103 662 498 0 022 579 114 0 0 042 737 1000 0 008(5-4-6)lowast103 662 498 0 022 590 341 0 0 033 470 1000 0 014(5-5-5)lowast103 662 498 0 022 602 585 0 0 017 205 1000 0 024(5-6-4)lowast103 662 498 0 022 806 654 0 0 016 0 999 0 037(5-7-3)lowast103 662 498 0 022 994 738 0 0 012 0 728 0 051(5-8-2)lowast103 662 498 0 022 1000 1000 0 0 005 0 465 0 063(5-9-1)lowast103 662 498 0 022 1000 1000 0 74 004 0 216 0 084

Table 5 Network performance of different mode strategies under different budget allocation

Scenario Total social welfare ($) Average carbon emission rate (kgton-km)($week) I II III IV I II III IV(5-1-9)lowast103 2463707 3292622 3263794 3558279 01320 00880 00900 00797(5-2-8)lowast103 2463707 3420352 3372572 3615201 01320 00841 00870 00778(5-3-7)lowast103 2463707 3568935 3511567 3777362 01320 00805 00839 00745(5-4-6)lowast103 2463707 3666169 3634317 3848109 01320 00782 00824 00751(5-5-5)lowast103 2463707 3666167 3634048 3889751 01320 00782 00815 00739(5-6-4)lowast103 2463707 3666229 3633969 3914493 01320 00782 00815 00738(5-7-3)lowast103 2463707 3579201 3571180 3912885 01320 00805 00832 00740(5-8-2)lowast103 2463707 3472760 3473270 3866673 01320 00835 00858 00752(5-9-1)lowast103 2463707 3349296 3357314 3756729 01320 00870 00891 00776

54 ImpactAnalysis ofModeChoices onNetwork PerformanceTo fully explore the impact of mode choices on network per-formance four mode combination strategies are considered(I) Expressway (II) Expressway-Railway (III) Expressway-Waterway and (IV) Expressway-Railway-Waterway The firststrategy is to simulate the traditional single-road transportstructure Considering the incomplete accessibility of othertransportation modes this paper reasonably constructs thelatter three multimodal strategies based on road transporta-tion The network performance of different mode strategiesunder different budget allocation scenarios is shown inTable 5

As can be seen from Table 5 in all budget allocationscenarios the total social welfares under multimodal trans-port strategies II III and IV are significantly better than thetraditional single-road strategy I with an average increaseof 4288 4185 and 5397 respectively In this contextthe total social welfare under the strategy IV is better thanthe strategies II and III with an average increase of 781and 858 respectively Furthermore strategy III is slightlyinferior to strategy II in most scenarios To reduce theimpact on the environment the logistics authority is alsoconcerned about the average carbon emission rate of theurban agglomeration Table 5 also shows that the averagecarbon emission rate under different multimodal transportstrategies can effectively reduce CO2 emissions Comparedwith the strategy I adopting multimodal transport strategy

II III and IV results in an average decrease of 61235561 and 7441 respectively Therefore the developmentof multimodal transport network can not only improvesocial welfare but also effectively reduce CO2 emissions Inaddition other realistic conditions of each strategy shouldbe considered when selecting a multimodal strategy Forexample taking strategy I as the benchmark there is anexpected target to reduce the average carbon emission ratein the regional multimodal network design If the target is setto 50 all multimodal strategies are feasible If set to 60strategies II and IV are feasible If set to 70 only strategy IVis feasible

6 Conclusion and Future Studies

This paper studied a multimodal green logistics networkdesign problem of urban agglomeration with four markedfeatures stochastic demand congestion effects game behav-iors of multiple logistics authorities and route choice behav-iors of logistics users To describe the game behaviors oflogistics authorities in urban agglomeration two nonlinearbilevel programming models were proposed decentralizedand centralized decision models Compared with the cen-tralized decision model the decentralized decision modelis mainly used to analyze the impact of budget allocationof urban agglomeration At the upper level each logistics


authority aims to maximize the total social welfare of its owncity by planning the investment capacity of logistics nodesand determining the carbon tax on transportation servicelinks The lower-level subproblem is a logit-based stochasticuser equilibrium (SUE) problem regarding the logisticsdemand scenario and carbon tax Next to solve the nonlinearbilevel programming models a quantum-behaved particleswarm optimization (QPSO) embedded with a Method ofSuccessive Averages (MSA) for stochastic user equilibriumflow assignment was proposed

Numerical examples show that centralized decisions arethe optimal decisions for improving the entire logisticsnetwork performance followed by decentralized decisionsamong multiple logistics authorities under a budget alloca-tion constraint Meanwhile compared with the single modelogistics network the constructed multimode logistics net-work can reduce the average carbon emission rate by approx-imately 45 In addition by adopting centralized decisionsconstructing a multimode logistics network and formulatinga reasonable carbon tax the logistics authority can achievethe overall optimization layout of the green logistics networkin urban agglomeration In short the proposed models andalgorithms can help the logistics authorities make scientificdecisions on the multimodal green logistics network designproblem of urban agglomeration

On the basis of this study some main extensions can bemade in the future such as applying our proposed modelsand algorithms to a large and realistic logistics networkand establishing multiobjective optimization model or robustoptimization model

Appendix

A Notations

Sets119870 set of all cities in the urban agglomeration119870 set of all cities including the urban agglomeration|119870| + 1119868119896 set of logistics transfer nodes in city 119896 where119868|119870|+1 = ⋃119896isin119870 119868119896119875119896 set of candidate logistics node in city 119896 where119875119896 isin119868119896 ⋃119896isin119870 119875119896 = 119875|119870|+1 isin 119868|119870|+1119860119892

119896 set of arcs of transport service in city 119896 where119860119892

|119870|+1= ⋃119896isin119870119860119892

119896119860119905119896 set of all logistics transferring service in city 119896

where 119860119905|119870|+1 = ⋃119896isin119870119860119905

119896119860119896 set of arcs of logistics service in city 119896 where119860119896 = 119860119892

119896cup 119860119905

1198961198720 1198720 = 1 2 3 set of all link transport modesin urban logistics service market where ldquo1rdquo ldquo2rdquo andldquo3rdquo represent the expressway railway and waterwayrespectively119872 119872 = 1 2 3 4 set of all route transport modesin urban logistics service market where the first

three items represent single mode and the last itemrepresents combined mode119882119896 set of all O-D pairs in the logistics network in city119896 where119882|119870|+1 = ⋃119896isin119870119882119896119877119908 set of all service paths between O-D pair 119908 isin 119882119896

in city 119896Ω set of all logistics demand scenarios

Indices

119896 single city or the urban agglomeration index 119896 isin 119870or 119896 isin 119870119894 logistics node or candidate logistics node index 119894 isin119868119896 or 119894 isin 119875119896119886 logistics transport or transferring service index 119886 isin119860119892

119896 119886 isin 119860119905

119896 or 119886 isin 119860119896119898 link or route transport mode index 119898 isin 1198720 or119898 isin 119872119908 O-D pair index 119908 isin 119882119896119903 service route index 119903 isin 119877119908119904 logistics demand scenarios index 119904 isin Ω

General Variables

119902119904119896119908 logistics demand function of city 119896 isin 119870 betweenO-D pair 119908 isin 119882119896 in scenario 119904 isin Ω (tonsweek)119902119904119896119908 potential logistics demand between O-D pair119908 isin 119882119896 in city 119896 isin 119870 and scenario 119904 isin Ω (tonsweek)

119905119898119904119896119886 transport time function of city 119896 isin 119870 on arc 119886 isin119860119892

119896by link transport mode119898 isin 1198720 in scenario 119904 isin Ω

(h)119906119903119904119896119908

disutility function on route 119903 isin 119877119908 between O-Dpair 119908 isin 119882119896 in city 119896 isin 119870 and scenario 119904 isin Ω ($)120575119898119908119903 indicator variable equals 1 if service route 119903 isin 119877119908

uses transport mode119898 isin 119872120575119898119886119903 indicator variable equals 1 if link 119886 isin 119860119896 is onroute 119903 isin 119877119908 by link transport mode 119898 isin 1198720 and 0otherwise120575119894119903 indicator variable equals 1 if a logistics transferservice is made in node 119894 isin 119868119896 along the route 119903 isin 119877119908

and 0 otherwise120582119904119896119908 expected minimal disutility between O-D pair119908 isin 119882119896 in city 119896 isin 119870 and scenario 119904 isin Ω ($)119891119903119904119896119908 freight flow on route 119903 isin 119877119908 between O-D pair119908 isin 119882119896 in city 119896 isin 119870 and scenario 119904 isin Ω (tonsweek)

119891119904119896119894 freight flow on logistics nodes 119894 isin 119868119896 in city 119896 isin 119870

and scenario 119904 isin Ω (tonsweek)V119904119896119886 freight flow on logistics service arc 119886 isin 119860119896 in city119896 isin 119870 and scenario 119904 isin Ω (tonsweek)


Continuous Decision Variables (Logistics Authority)

X119896 a vector defined as X119896 = (119909119896119894 119896 isin 119870 119894 isin119875119896) X|119870|+1 = ⋃119896isin119870X119896 which means a set ofinvestment capacities for logistics node 119894 in city 119896 isin 119870119910119896 a decision variable which means the carbon taxon logistics service arc in city 119896 isin 119870Constants119861119896 investment budget for city 119896 isin 119870 where 119861|119870|+1 =⋃119896isin119870 119861119896($)119888119898119896119886 fare of unit turnover on arc 119886 isin 119860119892

119896served by link

transport mode119898 isin 1198720 in city 119896 isin 119870 ($ton km)119888119894119896119886 transfer cost on arc 119886 isin 119860119905

119896 at logistics node 119894 isin 119868119896in city 119896 isin 119870 ($ton km)1198620119896119886 service capacity on arc 119886 isin 119860119896 in city 119896 isin 119870

(tonskm)119862119896119894 unit fare charged at logistics node 119894 isin 119868119896 in city119896 isin 119870 ($ton)1198620119896119894 unit construction cost (fixed cost) at logistics

node 119894 isin 119875119896 in city 119896 isin 119870 ($m2)120591119898119896119886 operator cost of unit turnover on arc 119886 isin 119860119892

119896

served by link transport mode119898 isin 1198720 in city 119896 isin 119870($ton km)120578119896119894 unit transfer operating cost at logistics node 119894 isin 119868119896in city 119896 isin 119870 ($ton)120587 penalty cost for shortage of a unit of flow at eachlogistics node119890119898119886 average CO2 emission per unit turnover by linktransport mode119898 isin 1198720 (kgton km)119890119896 expected CO2 emission for shipping per unitturnover in city 119896 isin 119870 (kgton km)

119897119896119886 length of arc 119886 isin 119860119892

119896 in city 119896 isin 119870 (km)

1199051198980119896119886

free-flow transport service time on arc 119886 isin 119860119892

119896by

link transport mode119898 isin 1198720 in city 119896 isin 119870 (h)1199051198940119896119886 free-flow transfer service time on arc 119886 isin 119860119905

119896 atlogistics node 119894 isin 119868119896 in city 119896 isin 119870 (h)

119905119889119896119898 average transport time interval for link transportmode119898 isin 1198720 (h)119892 processing capacity of unit construction area(kgm2)120573 demand dispersion parameter in the elasticdemand function120579 parameter for representing the perception variationof logistics users on logistics service disutility120588 parameter for capturing the effects of economies ofscale for logistics nodes119862119886119901119898

119896119886 service capacity on arc 119886 isin 119860119892

119896 served by linktransport mode119898 isin 1198720 in city 119896 isin 119870 (tonskm)

119878max119896119894 maximum establish or expansion capacity oflogistics node 119894 isin 119875119896 in city 119896 isin 119870119862ℎmax

119896 maximum carbon tax on arc in city 119896 isin 119870119911119896119894 minimum subsidy scale of logistics node 119894 isin 119875119896 incity 119896 isin 119870119878119906119887119896119894 unit investment subsidy of logistics node 119894 isin 119875119896in city 119896 isin 119870119901119904119896 probability of scenario 119904 isin Ω in city 119896 isin 119870

B Proof of Proposition 1

See Proposition 1 and (22)-(26)

Proof Substituting the constraints (25) and (26) directlyinto the objective function (22) the Lagrangian function forproblem (22) can be formulated

min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1) minus 1120579sdot sum119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]

sdot sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)

The Kuhn-Tucker (KT) conditions of problem (B1) can begiven as follows

120597119871 (F120583)120597119891119903119904119896119908

= 1120579 ln119891119903119904119896119908 + 119906119903119904119896119908 minus 120583119903 = 0forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω

(B2)

120597119871 (F120583)120597119902119904119896119908

= minus1120579 ln 119902119904119896119908 minus 119863minus1119908 (119902119904119896119908) + 120583119903 = 0forall119896 isin 119870 119908 isin 119882119896 119904 isin Ω

(B3)

119902119904119896119908 = sum119903isin119877119908

119891119903119904119896119908 forall119896 isin 119870 119908 isin 119882119896 119904 isin Ω (B4)

sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)

119891119903119904119896119908 gt 0 forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω (B6)


Table 6 OndashD demands in the network

OndashD pair (tonweek) 17997888rarr11 17997888rarr12 17997888rarr13 17997888rarr14 17997888rarr15 17997888rarr16Scenario Probability1 03 900 850 1000 950 850 7402 05 1000 900 1200 1100 900 8003 02 1100 100 1300 1200 950 850

Table 7 Basic data of each logistics node in the network

Logistics park General nodeNode number 136 245 7-10Economy of scale factor 09 09 10Candidate node scale (tonsweek) [0 1000] [0 1000] [0 400]Minimum subsidy scale (tonsweek) 500 400 -Unit fixed construction cost ($m2) 1 1 12Unit variable cost ($ton) 5 5 6Unit fare ($ton) 8 8 7Free-flow transfer time (h) 2 3 1

where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904

119896119894) + 119888119894119896119886)120575119894119903] and 120583119903 is the corre-sponding Lagrangian multiplier

The KT condition (B4) and condition (B6) ensures that119891119903119904119896119908

gt 0 and 119902119904119896119908 gt 0 then condition (B2) can be rewrittenas

119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)

forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω (B7)

As KT condition (B4) equation (B7) can easily be trans-formed to the following logit model for route choice prob-ability

119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904119896119908)sum119897isin119877119908

exp (minus120579119906119897119904119896119908)

forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω(B8)

Similarly combining KT condition (B4) with (B7) we canobtain

119902119904119896119908 = sum119903isin119877119908

exp (120579120583119903 minus 120579119906119903119904119896119908) forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω

(B9)

KT condition (B3) can be rewritten as

exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]

= 119902119904119896119908 exp [120579119863minus1119908 (119902119904119896119908)] forall119896 isin 119870 119908 isin 119882119896 119904 isin Ω

(B10)

Then combining (B9) and (B10) we can obtain

119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908

exp (minus120579119906119903119904119896119908)] 119902119904119896119908) forall119896 isin 119870 119908 isin 119882119896 119903 isin 119877119908 119904 isin Ω

(B11)

C Supplementary Data

See Tables 6 7 and 8

Data Availability

The data used to support the findings of this study areincluded within the article

Disclosure

A short version of this manuscript won the first prize in the2018 Graduate Academic Annual Conference of the School ofTransportation Engineering

Conflicts of Interest

The authors declare no conflicts of interest


Table 8 Basic data of each arc in the network

Arc From To Mode Length Free-flow Capacity Unit cost ($ton-km) Unit fare(km) time (h) (tonsweek) ($ton-km)

1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments

The work that is described in this paper was supported byFundamental Research Funds for the Central Universities ofCentral South University (No 2018zzts162) National NaturalScience Foundation of China (Nos 71371181 and 71672193)and Degree Innovation Foundation of Central South Univer-sity (No 2018-31)

References

[1] R Babazadeh J Razmi M Rabbani and M S Pishvaee ldquoAnintegrated data envelopment analysisndashmathematical program-ming approach to strategic biodiesel supply chain networkdesign problemrdquo Journal of Cleaner Production vol 147 pp694ndash707 2017

[2] A Rezaee F Dehghanian B Fahimnia and B Beamon ldquoGreensupply chain network design with stochastic demand andcarbon pricerdquo Annals of Operations Research pp 1ndash23 2015

[3] Y Zhao Q Xue Z Cao and X Zhang ldquoA two-stage chanceconstrained approach with application to stochastic intermodalservice network design problemsrdquo Journal of Advanced Trans-portation vol 2018 Article ID 6051029 18 pages 2018

[4] M Grote I Williams J Preston and S Kemp ldquoIncluding con-gestion effects in urban road traffic CO2 emissions modellingDo Local Government Authorities have the right optionsrdquoTransportation Research Part D Transport and Environmentvol 43 pp 95ndash106 2016

[5] KWu Y Chen JMa S Bai andX Tang ldquoTraffic and emissionsimpact of congestion charging in the central Beijing urbanarea A simulation analysisrdquo Transportation Research Part DTransport and Environment vol 51 pp 203ndash215 2017

[6] W Wang L Huang and X Liang ldquoOn the simulation-based reliability of complex emergency logistics networks inpost-accident rescuesrdquo International Journal of EnvironmentalResearch and Public Health vol 15 no 1 p 79 2018

[7] M A Efroymson and T L Ray ldquoA branch-bound algorithm forplant locationrdquo Operations Research vol 14 no 3 pp 361ndash3681966

[8] Q Sun F Tang and Y Tang ldquoAn economic tie network-structure analysis of urban agglomeration in themiddle reachesof Changjiang River based on SNArdquo Journal of GeographicalSciences vol 25 no 6 pp 739ndash755 2015

[9] M Beuthe B Jourquin J Geerts and C Koul A NdjangrsquoHaldquoFreight transportation demand elasticities a geographicmultimodal transportation network analysisrdquo TransportationResearch Part E Logistics and Transportation Review vol 37 no4 pp 253ndash266 2001

[10] MMarufuzzaman and S D Eksioglu ldquoDesigning a reliable anddynamic multimodal transportation network for biofuel supplychainsrdquo Transportation Science vol 51 no 2 pp 494ndash517 2017

[11] D Zhang X Li Y Huang S Li and Q Qian ldquoA robustoptimization model for green regional logistics network designwith uncertainty in future logistics demandrdquo Advances inMechanical Engineering vol 7 no 12 2015

[12] G W Xiong and Y Wang ldquoBest routes selection in multimodalnetworks using multi-objective genetic algorithmrdquo Journal ofCombinatorial Optimization vol 28 no 3 pp 655ndash673 2014

[13] Y Xiao andAKonak ldquoTheheterogeneous green vehicle routingand scheduling problem with time-varying traffic congestionrdquoTransportation Research Part E Logistics and TransportationReview vol 88 pp 146ndash166 2016

[14] D Zhang X Wang S Li N Ni Z Zhang and X Ma ldquoJointoptimization of green vehicle scheduling and routing problemwith time-varying speedsrdquo PLoS ONE vol 13 no 2 articlee0192000 2018

[15] C Mullen and G Marsden ldquoTransport economic competitive-ness and competition A city perspectiverdquo Journal of TransportGeography vol 49 pp 1ndash8 2015

[16] J Li G Rong and Y Feng ldquoRequest selection and exchangeapproach for carrier collaboration based on auction of asingle requestrdquo Transportation Research Part E Logistics andTransportation Review vol 84 pp 23ndash39 2015

[17] X Jiang X He L Zhang H Qin and F Shao ldquoMultimodaltransportation infrastructure investment and regional eco-nomic development A structural equation modeling empiricalanalysis in China from 1986 to 2011rdquo Transport Policy vol 54pp 43ndash52 2017

[18] H Min C S Ko and H J Ko ldquoThe spatial and temporalconsolidation of returned products in a closed-loop supplychain networkrdquoComputers amp Industrial Engineering vol 51 no2 pp 309ndash320 2006

[19] M K Delivand A R Cammerino P Garofalo and MMonteleone ldquoOptimal locations of bioenergy facilities biomassspatial availability logistics costs and GHG (greenhouse gas)emissions a case study on electricity productions in South ItalyrdquoJournal of Cleaner Production vol 99 pp 129ndash139 2015

[20] C Lindsey H S Mahmassani M Mullarkey T Nash and SRothberg ldquoIndustrial space demand and freight transportationactivity exploring the connectionrdquo Journal of Transport Geog-raphy vol 37 pp 93ndash101 2014

[21] I Kumar A Zhalnin A Kim and L J Beaulieu ldquoTrans-portation and logistics cluster competitive advantages in theUS regions A cross-sectional and spatio-temporal analysisrdquoResearch in Transportation Economics vol 61 pp 25ndash36 2017

[22] R Dekker J Bloemhof and I Mallidis ldquoOperations Researchfor green logistics - An overview of aspects issues contribu-tions and challengesrdquoEuropean Journal of Operational Researchvol 219 no 3 pp 671ndash679 2012

[23] M Ghane-Ezabadi and H A Vergara ldquoDecompositionapproach for integrated intermodal logistics network designrdquoTransportation Research Part E Logistics and TransportationReview vol 89 pp 53ndash69 2016

[24] N Turken J Carrillo and V Verter ldquoFacility location andcapacity acquisition under carbon tax and emissions limitsTo centralize or to decentralizerdquo International Journal ofProduction Economics vol 187 pp 126ndash141 2017

[25] I Harris C L Mumford and M M Naim ldquoA hybrid multi-objective approach to capacitated facility location with flexiblestore allocation for green logistics modelingrdquo TransportationResearch Part E Logistics and Transportation Review vol 66pp 1ndash22 2014

[26] J Yang J Guo and S Ma ldquoLow-carbon city logistics distri-bution network design with resource deploymentrdquo Journal ofCleaner Production vol 119 pp 223ndash228 2016

[27] N Zarrinpoor M S Fallahnezhad andM S Pishvaee ldquoDesignof a reliable hierarchical location-allocation model underdisruptions for health service networks A two-stage robustapproachrdquo Computers amp Industrial Engineering vol 109 pp130ndash150 2017

[28] J Gao Z Xiao B Cao and Q Chai ldquoGreen supply chain plan-ning considering consumerrsquos transportation processrdquo Trans-portation Research Part E Logistics and Transportation Reviewvol 109 pp 311ndash330 2018


[29] T Ercan N C Onat O Tatari and J Mathias ldquoPublictransportation adoption requires a paradigm shift in urbandevelopment structurerdquo Journal of Cleaner Production vol 142pp 1789ndash1799 2017

[30] B Peng H Du S Ma Y Fan and D C Broadstock ldquoUrbanpassenger transport energy saving and emission reductionpotential a case study for Tianjin Chinardquo Energy Conversionand Management vol 102 pp 4ndash16 2015

[31] C Teye M G Bell and M C Bliemer ldquoUrban intermodalterminals The entropy maximising facility location problemrdquoTransportation Research Part BMethodological vol 100 pp 64ndash81 2017

[32] H Yang X Zhang and Q Meng ldquoStackelberg games andmultiple equilibrium behaviors on networksrdquo TransportationResearch Part B Methodological vol 41 no 8 pp 841ndash861 2007

[33] D Zhang F Zou S Li and L Zhou ldquoGreen supply chainnetwork design with economies of scale and environmentalconcernsrdquo Journal of Advanced Transportation vol 2017 ArticleID 6350562 14 pages 2017

[34] C F G Loureiro and B Ralston ldquoInvestment selection modelfor multicommodity multimodal transportation networksrdquoTransportation Research Record no 1522 pp 38ndash46 1996

[35] D Zhang Q Zhan Y Chen and S Li ldquoJoint optimization oflogistics infrastructure investments and subsidies in a regionallogistics network with CO2 emission reduction targetsrdquo Trans-portation Research Part D Transport and Environment vol 60pp 174ndash190 2018

[36] X Wang Q Meng and L Miao ldquoDelimiting port hinterlandsbased on intermodal network flows Model and algorithmrdquoTransportation Research Part E Logistics and TransportationReview vol 88 pp 32ndash51 2016

[37] T Yamada B F Russ J Castro and E Taniguchi ldquoDesigningmultimodal freight transport networks A heuristic approachand applicationsrdquo Transportation Science vol 43 no 2 pp 129ndash143 2009

[38] Q Meng and X Wang ldquoIntermodal hub-and-spoke networkdesign incorporating multiple stakeholders and multi-typecontainersrdquo Transportation Research Part B Methodologicalvol 45 no 4 pp 724ndash742 2011

[39] XWang andQMeng ldquoDiscrete intermodal freight transporta-tion network design with route choice behavior of intermodaloperatorsrdquo Transportation Research Part B Methodological vol95 pp 76ndash104 2017

[40] M Patriksson ldquoRobust bi-level optimization models in trans-portation sciencerdquo Philosophical Transactions of the Royal Soci-ety A Mathematical Physical amp Engineering Sciences vol 366no 1872 pp 1989ndash2004 2008

[41] R B Dial ldquoA probabilistic multipath traffic assignment modelwhich obviates path enumerationrdquoTransportation Research vol5 no 2 pp 83ndash111 1971

[42] H Yang and M G H Bell ldquoModels and algorithms forroad network design a review and some new developmentsrdquoTransport Reviews vol 18 no 3 pp 257ndash278 1998

[43] J SunWXu andB Feng ldquoA global search strategy of quantum-behaved particle swarm optimizationrdquo in Proceedings of theIEEE Conference on Cybernetics and Intelligent Systems pp 111ndash116 Singapore December 2004

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To route the flow of goods multimodal transporta-tion is a hybrid of transportation that involves two classictransportation services the single mode of transport andcombined transport [9] Compared with the single trans-portation mode the multimodal transportation can makefull use of existing logistics networks of infrastructure andthe advantage of various modes of transport integratingtransport capacity resources meeting the transport demandand achieving the target (eg time cost and profit) [1011] In the multimodal transportation there is no effectiveconnection between each mode of transportation and thedesign of the multimodal transportation plan needs to befurther improved and optimized [12] However urban trafficcongestion and transportation-related environmental issues(eg carbon dioxide (CO2) nitrogen oxide and sulfur oxide)are the bottlenecks that restrict the sustainable developmentof cities [13 14] Consequently there is an inevitable trendtoward the future development of urban agglomeration greenlogistics systems to develop multimodal and integrativetransportation networks

11 Literature Review We classify the literature related to ourresearch into three branches (1) urban agglomeration logis-tics (2) green logistics network design for facility locationand (3) logistics network design with choice behaviors

111 Urban Agglomeration Logistics The urban agglomer-ation logistics system is an important part of the urbanagglomeration economy as it plays an important and sup-porting role in the sustainable development and evolution ofthe urban agglomeration Mullen and Marsden [15] exploredthe adaptive adjustment mechanism of regional logistics andregional economy Li et al [16] emphasized the relationshipbetween traffic investment and traffic efficiency in urbanagglomeration Jiang et al [17] analyzed the bidirectionalrelationship between multimodal transportation investmentand economic development However some scholars studiedthe spatial and temporal distribution characteristics of urbanagglomeration logistics [18 19] Lindsey et al [20] studiedthe relationships among freight transport economic marketdrivers and industrial space demand Kumar et al [21] inves-tigated spatial patterns of transportation and logistics clusterin the US regions applying spatial cluster and econometricanalyses The above studies mainly focus on the linkagemechanism between logistics and economy demand andspatial and temporal distribution and few focus on the greenlogistics system of urban agglomeration Table 1 summarizesthe main features of the proposed models in the reviewedstudies

112 Green Logistics Network Design for Facility LocationGreen logistics aims to restrain the environmental dam-age (eg greenhouse gas emissions noise and accidents)caused by logistics activity and develop a sustainable balancebetween economic social and environmental objectives [22]Facility location modeling is a strategic planning designapproach that selects the optimal set of facilities from a setof potential facilities [23] As a branch of network design

the green logistics network design problem originates fromthe classic facility location problem (FLP) [7 24] and thenextends it to the location-allocation problem (LAP) [25ndash27]

In the background of the vigorously developing greeneconomy Turken et al [24] investigated the impact of carbontax on plant capacity and location decisions of a firmYang et al [26] studied the low-carbon network designproblem of the third-party logistics distribution system Tosolve location-allocation problem with a carbon emissionsconstraint Rezaee et al [2] developed a two-stage stochasticprogrammingmodel and Gao et al [28] proposed five multi-dimensional mixed-integer nonlinear programming modelsIn practice the urban agglomeration logistics network maycomprise multiple urban logistics networks which are inde-pendently and separately managed by local governments (orlogistics authorities) with different targets Nevertheless theliterature always supposed that the network is totally designedby a single management body which may not suit the designof the logistics network in urban agglomeration

113 Green Logistics Network Design under Route ChoiceModels In general route choice models should evaluate theutility of each route and route the flow of passengers or goodsfrom origin to destination Although they have been widelyused to solve urban passenger transportation problems byresearchers and engineers [29ndash33] using these models tosolve urban cargo transportation problems has received littleattention in the literature

The logistics network design problem based on routechoice behavior can be characterized as a bilevel program-ming model or an equivalent mathematical program withequilibrium constraints (MPEC) model At the upper levelthe logistics authority determines the number location andcapacity of logistics facilities (nodes) At the lower levelshippers and carriers follow the user equilibrium (UE)principle or stochastic user equilibrium (SUE) principle [34ndash36] Yamada et al [37] presented a bilevel programmingmodel to simulate the multimodal freight transport networkdesign problem where the lower-level model is a multimodalmulticlass user equilibrium model To address the inter-modal hub-and-spoke network design problem for multiplestakeholders and multitype containers Meng and Wang [38]established anMPECmodel and used a variational inequalityto describe the operatorsrsquo route choice behavior Wang andMeng [39] extended the research work of Meng and Wang[38] by considering congestion effects and piecewise linearcost functions and solved it with a solution algorithm basedon nonlinear optimization and branch-and-bound globaloptimization

However the route choice models of these studies didnot consider the carbon emissions cost perception errorand elastic demand In addition they mainly focus on staticdetermined network design issues As strategic decision plan-ning the design of a logistics network in urban agglomerationinvolves long-term planning of a between 5- and 20-yeartimeline where the logistics demand is often uncertain withthe development of urban evolution and industrial structureoptimization Hence it is more realistic and reasonable to


Table1Ch

aracteris

ticso

fthe

review

edmod

elsp

ropo

sedforthe

greenlogistics

networkdesig

nprob

lem

Stud

yMod

elcharacteris

tics

Objectiv

efunctio

nsDecision

varia

bles

Solutio

nprocedure

Research

areas

decisio

nmakers

Transportm

odes

Dem

ands

Choice

behaviors

Num

ber

Type

Capacity

Routing

Carbo

ntax

Exact

Heuris

ticS

MS

MS

MDe

StType

Utility

SM

Xion

gandWang[12]

--

Costtim

e

MOGA

Harris

etal[25]

--

CostCO

2em

issions

SEAMO2

Yang

etal[26]

--

Cost

Cplex

Turken

etal[24]

--

Cost

FLAA

Rezaee

etal[2]

--

Cost

Cplex

Gao

etal[28]

--

Cost

Cplex

Yamadaetal[37]

UE

Costtim

e


GAGLS

MengandWang[38]

UE

Costtim

e

Cost

GA

WangandMeng[39]

UE

Costtim

e

Cost

BampB

Zhangetal[35]

UE

Costtim

e


GA+FW

ATh

isstu

dy

SU

ECosttim

eCO

2em

ission

So

cialbenefit

QPS

O+MSA

Ssin

gleMm

ultip

leD

edeterm

inisticStsto

chasticU

Euser

equilib

riumSUE

stochastic

user

equilib

riumG

AG

eneticAlgorith

mand

MOGAM

ultio

bjectiv

eGeneticAlgorith

m

SEAMO2SimpleE

volutio

nary

Multio

bjectiv

eOptim

ization2FL

AAFacilityLinear

Approxim

ationAlgorith

mG

LSG

eneticLo

calSearch

andBamp

BBranch-and

-Bou

nd

FWFrank

ndashWolfeAlgorith

mQ

PSOQ

uantum

behavedParticleSw

arm

Optim

ization

andMSA

Metho

dof

Successiv

eAverages



















(119873119894119899(119894) cup 119873119900119906119905(119894)) cup 119873119894isin1198730119873119905


DO

K1

K2

K3



a2 = (1 2 ２ＣＦＱＳ)


a4 = (2 3 ２ＣＦＱＳ)




2a1b1aO

2b1c


a2 = (1 2 ２ＣＦＱＳ)


a8 = (1 1＝)

a7 = (1 1＜)

Ain (1) = a1Aout (1) = a2 a3G1


1aO 2a 2c 3a 3c D1c

2b 2d 3b1b



a1 a7 a3

a8 a10

a9 a5 a13 a6

a4a12

a11a2

a14




a1

a1

a7 a3

a8

a9a5 a13

a6

a6a4a12a2 a14






3 Model Formulation



(1198800) minx 119864 [119865 (x y (120585) 120585)]119904119905 119864 [119866 (x y (120585) 120585)] le 0 (1)


(1198710) miny 119891 (x y (120585) 120585)119904119905 119892 (x y (120585) 120585) le 0 (2)




Logistics authority


fare and time

Carriers (supply)







user equilibrium




119901119904119865 (x y119904 (120590119904) 120590119904)119904119905 sum

119904isinΩ

119901119904119866 (x y119904 (120590119904) 120590119904) le 0 (3)


(1198711) miny119904 119891 (x y119904 (120590119904) 120590119904)119904119905 119892 (x y119904 (120590119904) 120590119904) le 0 (4)




SW119904119896 (X119896 119910119896V119896) = 119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962 (5)

where

119862119878119904119896 = sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908 minus sum119908isin119882119896


(6)

1198751198781199041198961 = sum119894isin119868119896

(119862119896119894 minus 120578119896119894) 119891119904119896119894

+ sum119894isin119875119896


119894isin119868119896


(7)

1198751198781199041198962 = sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886 (119888119898119896119886 minus 120591119898119896119886)

+ sum119898isin1198720

sum119886isin119860119892

119896




maxX119896119910119896

SW (X119896 119910119896V119896) = sum119904isinΩ

119901119904119896 (119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962) (9)


subject to


0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)






119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)



119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0


119896 119904 isin Ω(14)

where 1199051198940119896119886



119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908



119896119908 and 119866119903119904119896119908 represent



119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896


(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903


119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896


(18)




119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)


119896119908)






120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)



min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table1Ch

aracteris

ticso

fthe

review

edmod

elsp

ropo

sedforthe

greenlogistics

networkdesig

nprob

lem

Stud

yMod

elcharacteris

tics

Objectiv

efunctio

nsDecision

varia

bles

Solutio

nprocedure

Research

areas

decisio

nmakers

Transportm

odes

Dem

ands

Choice

behaviors

Num

ber

Type

Capacity

Routing

Carbo

ntax

Exact

Heuris

ticS

MS

MS

MDe

StType

Utility

SM

Xion

gandWang[12]

--

Costtim

e

MOGA

Harris

etal[25]

--

CostCO

2em

issions

SEAMO2

Yang

etal[26]

--

Cost

Cplex

Turken

etal[24]

--

Cost

FLAA

Rezaee

etal[2]

--

Cost

Cplex

Gao

etal[28]

--

Cost

Cplex

Yamadaetal[37]

UE

Costtim

e


GAGLS

MengandWang[38]

UE

Costtim

e

Cost

GA

WangandMeng[39]

UE

Costtim

e

Cost

BampB

Zhangetal[35]

UE

Costtim

e


GA+FW

ATh

isstu

dy

SU

ECosttim

eCO

2em

ission

So

cialbenefit

QPS

O+MSA

Ssin

gleMm

ultip

leD

edeterm

inisticStsto

chasticU

Euser

equilib

riumSUE

stochastic

user

equilib

riumG

AG

eneticAlgorith

mand

MOGAM

ultio

bjectiv

eGeneticAlgorith

m

SEAMO2SimpleE

volutio

nary

Multio

bjectiv

eOptim

ization2FL

AAFacilityLinear

Approxim

ationAlgorith

mG

LSG

eneticLo

calSearch

andBamp

BBranch-and

-Bou

nd

FWFrank

ndashWolfeAlgorith

mQ

PSOQ

uantum

behavedParticleSw

arm

Optim

ization

andMSA

Metho

dof

Successiv

eAverages



















(119873119894119899(119894) cup 119873119900119906119905(119894)) cup 119873119894isin1198730119873119905


DO

K1

K2

K3



a2 = (1 2 ２ＣＦＱＳ)


a4 = (2 3 ２ＣＦＱＳ)




2a1b1aO

2b1c


a2 = (1 2 ２ＣＦＱＳ)


a8 = (1 1＝)

a7 = (1 1＜)

Ain (1) = a1Aout (1) = a2 a3G1


1aO 2a 2c 3a 3c D1c

2b 2d 3b1b



a1 a7 a3

a8 a10

a9 a5 a13 a6

a4a12

a11a2

a14




a1

a1

a7 a3

a8

a9a5 a13

a6

a6a4a12a2 a14






3 Model Formulation



(1198800) minx 119864 [119865 (x y (120585) 120585)]119904119905 119864 [119866 (x y (120585) 120585)] le 0 (1)


(1198710) miny 119891 (x y (120585) 120585)119904119905 119892 (x y (120585) 120585) le 0 (2)




Logistics authority


fare and time

Carriers (supply)







user equilibrium




119901119904119865 (x y119904 (120590119904) 120590119904)119904119905 sum

119904isinΩ

119901119904119866 (x y119904 (120590119904) 120590119904) le 0 (3)


(1198711) miny119904 119891 (x y119904 (120590119904) 120590119904)119904119905 119892 (x y119904 (120590119904) 120590119904) le 0 (4)




SW119904119896 (X119896 119910119896V119896) = 119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962 (5)

where

119862119878119904119896 = sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908 minus sum119908isin119882119896


(6)

1198751198781199041198961 = sum119894isin119868119896

(119862119896119894 minus 120578119896119894) 119891119904119896119894

+ sum119894isin119875119896


119894isin119868119896


(7)

1198751198781199041198962 = sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886 (119888119898119896119886 minus 120591119898119896119886)

+ sum119898isin1198720

sum119886isin119860119892

119896




maxX119896119910119896

SW (X119896 119910119896V119896) = sum119904isinΩ

119901119904119896 (119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962) (9)


subject to


0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)






119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)



119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0


119896 119904 isin Ω(14)

where 1199051198940119896119886



119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908



119896119908 and 119866119903119904119896119908 represent



119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896


(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903


119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896


(18)




119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)


119896119908)






120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)



min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




















(119873119894119899(119894) cup 119873119900119906119905(119894)) cup 119873119894isin1198730119873119905


DO

K1

K2

K3



a2 = (1 2 ２ＣＦＱＳ)


a4 = (2 3 ２ＣＦＱＳ)




2a1b1aO

2b1c


a2 = (1 2 ２ＣＦＱＳ)


a8 = (1 1＝)

a7 = (1 1＜)

Ain (1) = a1Aout (1) = a2 a3G1


1aO 2a 2c 3a 3c D1c

2b 2d 3b1b



a1 a7 a3

a8 a10

a9 a5 a13 a6

a4a12

a11a2

a14




a1

a1

a7 a3

a8

a9a5 a13

a6

a6a4a12a2 a14






3 Model Formulation



(1198800) minx 119864 [119865 (x y (120585) 120585)]119904119905 119864 [119866 (x y (120585) 120585)] le 0 (1)


(1198710) miny 119891 (x y (120585) 120585)119904119905 119892 (x y (120585) 120585) le 0 (2)




Logistics authority


fare and time

Carriers (supply)







user equilibrium




119901119904119865 (x y119904 (120590119904) 120590119904)119904119905 sum

119904isinΩ

119901119904119866 (x y119904 (120590119904) 120590119904) le 0 (3)


(1198711) miny119904 119891 (x y119904 (120590119904) 120590119904)119904119905 119892 (x y119904 (120590119904) 120590119904) le 0 (4)




SW119904119896 (X119896 119910119896V119896) = 119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962 (5)

where

119862119878119904119896 = sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908 minus sum119908isin119882119896


(6)

1198751198781199041198961 = sum119894isin119868119896

(119862119896119894 minus 120578119896119894) 119891119904119896119894

+ sum119894isin119875119896


119894isin119868119896


(7)

1198751198781199041198962 = sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886 (119888119898119896119886 minus 120591119898119896119886)

+ sum119898isin1198720

sum119886isin119860119892

119896




maxX119896119910119896

SW (X119896 119910119896V119896) = sum119904isinΩ

119901119904119896 (119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962) (9)


subject to


0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)






119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)



119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0


119896 119904 isin Ω(14)

where 1199051198940119896119886



119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908



119896119908 and 119866119903119904119896119908 represent



119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896


(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903


119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896


(18)




119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)


119896119908)






120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)



min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



DO

K1

K2

K3



a2 = (1 2 ２ＣＦＱＳ)


a4 = (2 3 ２ＣＦＱＳ)




2a1b1aO

2b1c


a2 = (1 2 ２ＣＦＱＳ)


a8 = (1 1＝)

a7 = (1 1＜)

Ain (1) = a1Aout (1) = a2 a3G1


1aO 2a 2c 3a 3c D1c

2b 2d 3b1b



a1 a7 a3

a8 a10

a9 a5 a13 a6

a4a12

a11a2

a14




a1

a1

a7 a3

a8

a9a5 a13

a6

a6a4a12a2 a14






3 Model Formulation



(1198800) minx 119864 [119865 (x y (120585) 120585)]119904119905 119864 [119866 (x y (120585) 120585)] le 0 (1)


(1198710) miny 119891 (x y (120585) 120585)119904119905 119892 (x y (120585) 120585) le 0 (2)




Logistics authority


fare and time

Carriers (supply)







user equilibrium




119901119904119865 (x y119904 (120590119904) 120590119904)119904119905 sum

119904isinΩ

119901119904119866 (x y119904 (120590119904) 120590119904) le 0 (3)


(1198711) miny119904 119891 (x y119904 (120590119904) 120590119904)119904119905 119892 (x y119904 (120590119904) 120590119904) le 0 (4)




SW119904119896 (X119896 119910119896V119896) = 119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962 (5)

where

119862119878119904119896 = sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908 minus sum119908isin119882119896


(6)

1198751198781199041198961 = sum119894isin119868119896

(119862119896119894 minus 120578119896119894) 119891119904119896119894

+ sum119894isin119875119896


119894isin119868119896


(7)

1198751198781199041198962 = sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886 (119888119898119896119886 minus 120591119898119896119886)

+ sum119898isin1198720

sum119886isin119860119892

119896




maxX119896119910119896

SW (X119896 119910119896V119896) = sum119904isinΩ

119901119904119896 (119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962) (9)


subject to


0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)






119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)



119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0


119896 119904 isin Ω(14)

where 1199051198940119896119886



119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908



119896119908 and 119866119903119904119896119908 represent



119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896


(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903


119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896


(18)




119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)


119896119908)






120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)



min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Logistics authority


fare and time

Carriers (supply)







user equilibrium




119901119904119865 (x y119904 (120590119904) 120590119904)119904119905 sum

119904isinΩ

119901119904119866 (x y119904 (120590119904) 120590119904) le 0 (3)


(1198711) miny119904 119891 (x y119904 (120590119904) 120590119904)119904119905 119892 (x y119904 (120590119904) 120590119904) le 0 (4)




SW119904119896 (X119896 119910119896V119896) = 119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962 (5)

where

119862119878119904119896 = sum119908isin119882119896

int119902119904119896119908

0119863minus1

119908 (119908) 119889119908 minus sum119908isin119882119896


(6)

1198751198781199041198961 = sum119894isin119868119896

(119862119896119894 minus 120578119896119894) 119891119904119896119894

+ sum119894isin119875119896


119894isin119868119896


(7)

1198751198781199041198962 = sum119898isin1198720

sum119886isin119860119892

119896

V119898119904119896119886 119897119896119886 (119888119898119896119886 minus 120591119898119896119886)

+ sum119898isin1198720

sum119886isin119860119892

119896




maxX119896119910119896

SW (X119896 119910119896V119896) = sum119904isinΩ

119901119904119896 (119862119878119904119896 + 1198751198781199041198961 + 1198751198781199041198962) (9)


subject to


0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)






119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)



119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0


119896 119904 isin Ω(14)

where 1199051198940119896119886



119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908



119896119908 and 119866119903119904119896119908 represent



119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896


(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903


119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896


(18)




119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)


119896119908)






120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)



min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



subject to


0 le 119910119896 le 119862ℎmax119896 (11)

sum119894isin119868119896

1198620119896119894 (119892119909119896119894)120588 le 119861119896 (12)






119905119898119904119896119886 (V119898119904

119896119886 )

=

1199051198980119896119886

(1 + 015( V119898119904119896119886119862119886119901119898

119896119886

)4) 119898 = 1 21199051198980119896119886 + 119905119889119896119898max (V119898119904

119896119886minus 119862119886119901119898

119896119886 0)119862119886119901119898119896119886

119898 = 3 4forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω

(13)



119905119894119904119896119886 (119891119904119896119894) =

1199051198940119896119886(1 + 1205720 (119891119904

119896119894119909119896119894)1205730) 119909119896119894 = 0


119896 119904 isin Ω(14)

where 1199051198940119896119886



119906119903119904119896119908 = 119862119903119904119896119908 + 120591V119900119905119879119903119904

119896119908 + 119866119903119904119896119908



119896119908 and 119866119903119904119896119908 represent



119862119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119888119898119896119886119897119896119886120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896


(16)

119879119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896

119905119898119904119896119886 (V119898119904

119896119886 ) 120575119898119886119903 + sum119894isin119868119896

sum119886isin119860119905119896

119905119894119904119896119886 (119891119904119896119894) 120575119894119903


119866119903119904119896119908 = sum

119898isin1198720

sum119886isin119860119892

119896


(18)




119891119903119904119896119908 = 119902119904119896119908 exp (minus120579119906119903119904

119896119908)


119896119908)






120582119904119896119908 = minus1120579 ln sum119903isin119877119908

exp (minus120579119906119903119904119896119908) (21)



min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




min119885 (F) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904

119896119908 minus 1)minus 1120579 sum

119908isin119882119896


int119902119904119896119908

0119863minus1

119908 (119908) 119889119908+ sum

119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119896] V119904119896119886

+ sum119894isin119868119896

sum119886isin119860119905119896

(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886)119891119904

119896119894

(22)

subject to

sum119903isin119877119908



where

V119904119896119886 = sum119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119898119886119903 forall119896 isin 119870 119886 isin 119860119892

119896 119904 isin Ω (25)

119891119904119896119894 = sum

119908isin119882

sum119903isin119877119908






maxX|119870|+1 119910|119870|+1

SW (X|119870|+1 119910|119870|+1V|119870|+1)= sum

119904isinΩ

119901119904 ((119862119878119904|119870|+1 + 119875119878119904|119870|+11 + 119875119878119904|119870|+12)) (27)


119894 forall119894 isin 119875|119870|+1 (28)

0 le 119910|119870|+1 le 119862ℎmax|119870|+1 (29)

sum119894isin119868|119870|+1

1198620119894 (119892119909119894)120588 le 119861|119870|+1 (30)


4 Solution Methods


= 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895 (119905119906) = (

110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin1198721198761198751198951 (119905119906)

110038161003816100381610038161198721198761003816100381610038161003816

sdot sum119895isin119872119876

1198751198952 (119905119906) 110038161003816100381610038161198721198761003816100381610038161003816 sum119895isin119872119876119875119895|119863| (119905119906))

(31)


120572 (119905119906) = 1205720 minus (1205720 minus 1205721) sdot 119905119906119879 (33)





Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Begin the program









End the program


criterion

Yes

No









criterion

Yes

No




k(tu) by using (33)








fms






119894isin119868119896

1198620119896119894 (119909119896119894)120588 minus 119861119896 0))

2(35)








Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Carbon tax



















119896119886(119905119897)) and node

service time 119905119894119904119896119886(119891119904




119908119903(119905119897) by using(19)


Let 119891119898119904119908119903 (119905119897 + 1) = 119891119898119904

119908119903 (119905119897) + (1119905119897)(119891119898119904

119908119903(119905119897) minus 119891119898119904119908119903 (119905119897))


Let


sum119903isin119877119908(119891119898119904


sum119903isin119877119908119891119898119904119908119903 (119905119897) (36)






1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1

12

11

2

7

34

13

14

8 9

56

15

16

10



Virtual node



WaterwayRailway

Urban expressway


17

1 2 3 4 15 16 17 18 31 32 33 345

6

78

109 11

12

21

22

23

20

24

2526

2728

29

37

38 3940

41

42

4443

1419

City 1

City 2

City 3

1819

3036

13

35









Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Do-nothing 0 0 0 0 0 0 0 0 0 0 0 0 0





Consumersurplus ($)

Producersurplus ($)



Do-nothing 2449637 2345459 104178 0 01320







(5-1-9) (5-2-8) (5-3-7) (5-4-6) (5-5-5) (5-6-4) (5-7-3) (5-8-2) (5-9-1)0

05

1

15

2

25

3

35

4

Soci

al w

elfa

re



x 106


















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

















Appendix

A Notations



|119870|+1= ⋃119896isin119870119860119892


where 119860119905|119870|+1 = ⋃119896isin119870119860119905


119896cup 119860119905




Indices


119896 119886 isin 119860119905


General Variables




(h)119906119903119904119896119908














119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










119896



119896 in city 119896 isin 119870 (km)

1199051198980119896119886


119896by











min119871 (F120583) = 1120579 sum119908isin119882119896

sum119903isin119877119908

119891119903119904119896119908 (ln119891119903119904



int119902119904119896119908

0119863minus1

119908 (119908) 119889119908

+ sum119898isin1198720

sum119886isin119860119892

119896

[120591V119900119905119905119898119904119896119886 (V119904119896119886) + 119888119898119896119886119897119896119886 + 119890119898119897119896119886119910119898

119896119886]


sum119903isin119877119908

119891119903119904119896119908120575119898119886119903

+ sum119894isin119868119896

sum119886isin119860119905119896

[(120591V119900119905119905119894119896119886 (119891119904119896119894) + 119888119894119896119886) sum

119908isin119882

sum119903isin119877119908

119891119903119904119896119908120575119894119903]

minus sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908)

(B1)


120597119871 (F120583)120597119891119903119904119896119908


(B2)

120597119871 (F120583)120597119902119904119896119908


(B3)

119902119904119896119908 = sum119903isin119877119908


sum119903isin119877119908

120583119903( sum119903isin119877119908

119891119903119904119896119908 minus 119902119904119896119908) = 0 (B5)







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







where119906119903119904119896119908

= sum119898isin1198720sum119886isin119860

119892

119896[120591V119900119905119905119898119904

119896119886(V119904119896119886)+119888119898119896119886119897119896119886+119890119898119897119896119886119910119898

119896119886]120575119898119886119903+ sum119894isin119868119896

sum119886isin119860119905119896[(120591V119900119905119905119894119896119886(119891119904




119891119903119904119896119908 = exp (120579120583119903) exp (minus120579119906119903119904119896119908)




exp (minus120579119906119897119904119896119908)



119902119904119896119908 = sum119903isin119877119908


(B9)


exp (120579120583119903) = exp [ln 119902119904119896119908 + 120579119863minus1119908 (119902119904119896119908)]


(B10)


119902119904119896119908 = 119863119908(minus1120579 ln[ sum119903isin119877119908


(B11)



Data Availability


Disclosure







1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1 17 12 1 270 450 100 04 062 17 1 3 210 700 400 03 0453 17 2 2 240 480 800 025 044 17 2 1 260 433 50 04 0455 17 11 1 230 383 100 04 066 2 1 1 20 033 300 032 0557 1 7 1 22 037 400 034 0558 1 12 1 27 045 300 036 0559 1 11 1 25 042 300 036 05510 2 12 1 30 050 300 036 05511 2 11 1 23 038 300 036 05512 7 12 1 10 022 300 036 05513 11 12 1 11 024 300 036 05514 2 18 1 18 030 300 036 05515 17 14 1 260 433 100 04 0616 17 3 3 235 783 500 03 04517 17 13 1 235 392 100 04 0618 17 4 2 205 410 900 025 0419 18 3 1 22 037 300 036 05520 3 4 1 18 030 300 032 05521 3 8 1 23 038 400 034 05522 3 14 1 32 053 300 036 05523 3 13 1 21 035 300 036 05524 4 13 1 19 032 300 036 05525 4 14 1 33 055 300 036 05526 4 9 1 22 037 400 034 05527 8 14 1 13 029 300 036 05528 13 14 1 9 020 100 036 05529 9 14 1 14 031 300 036 05530 4 19 1 20 033 300 036 05531 17 15 1 230 383 100 04 0632 17 5 2 210 420 400 025 0433 17 16 1 260 450 100 04 0634 17 6 1 245 408 50 04 04535 17 6 3 220 800 800 03 04536 19 5 1 14 023 300 036 05537 5 6 1 18 030 300 032 05538 5 15 1 26 043 300 036 05539 6 5 1 30 050 300 036 05540 6 15 1 24 040 300 036 05541 6 16 1 28 047 300 036 05542 6 10 1 22 037 400 034 05543 15 16 1 13 029 300 036 05544 10 16 1 11 024 300 036 055


Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


multimodal green logistics network design of urban...

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