research article simulation-based optimization for...

Research ArticleSimulation-Based Optimization for Yard Design at MegaContainer Terminal under Uncertainty

Yong Zhou Wenyuan Wang Xiangqun Song and Zijian Guo

State Key Laboratory of Coastal and Offshore Engineering Dalian University of Technology Dalian China

Correspondence should be addressed to Wenyuan Wang wangwenyuandluteducn

Received 19 May 2016 Accepted 30 August 2016

Academic Editor Ricardo Aguilar-Lopez

Copyright copy 2016 Yong Zhou 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

The conventional approach of designing a container yard should be reexamined in the context of sustainable port developmentConsidering the uncertain future throughput a simulation-based optimization framework is proposed to obtain a cost-effectiveand reliable design solution to the physical layout and equipment deployment strategy of the yard at a mega container terminal Inthis framework a two-stage stochastic programming model is presented aided with a simulation procedure of terminal operationsFinally an application is given and the results show that the proposed integrated decision framework is effective and helpful foroptimizing container yard design in the context of sustainable development of container terminals

1 Introduction

Worldwide container throughput has been steadily growingover the past decades Between 1990 and 2014 the worldrsquoscontainer trade expanded at an average annual rate of 84[1] Many ports especially those in the countries with fast-growing economy such as China have gone through orare currently undergoing expansion of existing facilities orbuild-out of new terminals to cope with the increasingcontainer traffic and ship size However the global maritimelogistics market contains various uncertainties such as worldeconomy trade policies and freight rates which results in afluctuation of the demand for freight transportation [2 3]For example container trade volume fell sharply by 90 in2009 due to the global economy crisis [4] and the volumeof containers exported from China to US dropped by about20 following 911 terrorist attacks [5] Port infrastructureespecially the mega container terminal is capital intense andserves long-term societal needs and thus should be reliableand adaptive to future uncertainties

With the advancements of quay side technologies thebottleneck of terminal operations has moved from quay sideto yard side [6 7]The design of container yard is a factor thataffects terminal productivity and competitiveness Howeveryard design is determined during the initial planning stagewhen the available information and details are lacking [8]

which may not be reliable during the future operation stageIn China yard design in engineering practice addressesuncertainties through the introduction of an unbalance fac-tor the value of which is driven by experience Yard block sizeand equipment deployment are also empirically determined[9 10]This design approach easily gives rise to either an over-allocation of yard resources or a low efficiency of terminaloperation which is usually hard to be adjusted in the futureFor example the second phase of Yantian InternationalContainer Terminals (YICT) borrows part of the adjacentyard and rents off-dock yard in the peak period which raisesthe difficulty in port traffic management and increases theoperating cost The cost resulting from the increment oftrucks going back and forth between the terminal and off-dock yard and venue rental for YICT reaches 25sim35 millionChina Yuan (CNY) per year [11] Therefore a question arisesnaturally in an uncertain decision environment how can wetake into account future uncertainties in early stage of yarddesign so that it is easier to adjust to random events inoperation stage later on This question is especially relevantto developing countries where most terminals are not inplace yet thus presenting an opportunity to incorporate risksdirectly into the strategic planning of future infrastructure

For designing a container yard some researches focusedon yard storage capacity estimation by advanced simulationmodels or analytical formula [12ndash15] Other studies have

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 7467498 13 pageshttpdxdoiorg10115520167467498

2 Mathematical Problems in Engineering

sought to calculate the space requirement for planning [16ndash18] Once the main decisions about storage capacity andequipment choice have been made the next step for plan-ners involves the yard and block layout Several studies oncontainer terminal design have been conducted to compareparallel and perpendicular yard layouts using simulations[19 20] Simulation and analytical techniques have also beenused on yard design problem For example Petering [21]and Petering and Murty [22] developed a fully integratedsimulation model to analyze the influence of the width andlength of yard block on terminal performance Kim et al[23] proposed an analytical method to get the optimal yardlayout Kemme [24] examined the design of strategic yardcrane systems and block layouts and their effects on terminalperformance Lee and Kim [25] attempted to determinethe optimal size of a single block by taking into accountthe throughput requirements of yard cranes and the blockstorage requirements They provided detailed formulae forthe expected cycle times and variances of all yard craneoperations Lee and Kim [26] provided more detail on theexpression of expectation of the yard crane cycle time foryard with different block layouts useful for estimating yardcrane operating costs Lee and Kim [27] later determinedthe optimal layout of a whole container yard as specifiedby the dimensions of a block and the number of aislesHowever none of these studies attempted to analyticallydetermine storage space requirements by considering thestochastic properties of the storage yard In view of thisZhen [2] focused on the yard template planning problemunder uncertainty It considered the number of containersloaded onto (and unloaded from) each vessel within a cycletime as a stochastic parameter Alcalde et al [8] used ananalytical model based on a stochastic approach (randomvariables and probabilistic functions) to forecast storagespace requirements over an extended period However theoptimized yard dimensions were not considered as optimalbecause yard depth and block length were not optimized withthe number of handling equipment deployed simultaneously

Therefore this paper will propose an optimization frame-work to obtain a cost-effective and reliable yard designsolution that hedges well against uncertain future terminalthroughput This framework is composed of a simulationmodel for terminal operations and an optimization programwith yard depth yard block length the quantity of handlingequipment deployed and the number of containers handledin the design yard as decision variables The optimizationprogram evaluates the capital costs and benefits of variousyard layouts while the simulation model emulates trucktraffic and equipment moving at the terminal and calculatesterminal efficiency indicators The main contribution of thispaper is simultaneously optimizing yard physical layoutequipment deployment and storage schemes covering bothplanning and operation stages under uncertain environ-ment which would be more practical for yard design andmanagement in developing countries where the availabilityof data is often limited and the economic background isusually volatile Although the analytical techniques usedare not new (two-stage stochastic programming and systemsimulation) another contribution is essentially an integration

of the techniques in a unique model framework which ispowerful for decision-making

The remainder of the paper is organized as followsSection 2 describes the procedures and their limitationswhen optimizing yard designs as well as yard design underuncertainty Section 3 focuses on the modeling and solutionmethod including the proposed formulation and the solutionframework for yard optimization A numerical example andits computational results are given in Section 4 followed bydiscussions on advantages limitations and possible futureextensions of this research in Section 5

2 Problem Description

21 Quantitative andQualitative DesignGuidelines Themostcommonly used layout format of a parallel yard with trans-fer lanes at manually operated terminals in China will bestudied in this paper as depicted in Figure 1 It is notedthat container terminal operation generally consists of fourcomponents seaside operation horizontal transport yardoperation and landside operation At the seaside containersare discharged from and loaded into containerships by quaycranes deployed along the coastline Internal trucks aredispatched for transporting containers between quay cranesand certain storage stacks in the yard Container yard canusually be divided into large zones and each zone is furthercomposed of rectangular shaped blocks Each block containsseveral lanes of space for storing containers in stacks andone lane for trucks to pick up and deliver containers Forthe convenience of vehicular traffic blocks are laid out inthe unit of module which combines two blocks with transferlanes in back to back form [23] Yard cranes standing over astorage block space can be transferred from block to blockto stack and shuffle containers The landside operation isthe task of receiving or delivering containers undertakenby external trucks According to the MTPRC and severalpractical handbooks input variables and the procedures todetermine yard layout are as follows

(1) The yard capacity 119864119910 and the number of ground slots119873119904 are calculated as

119864119910 =

119876ℎ119905119889119888119870119861119870

119879119910119896

119873119904 =

119864119910

119873119897119860 119904

(1)

where 119876ℎ is the annual throughput of the containerterminal 119905119889119888 is the average cluration of the containersdetermined by the statistical material 119870119861119870 is theunbalance factor of containers stacked in the yarddetermined by the statistical material 119879119910119896 is theannual working days of the container yard 119873119897 is thestacking height of the containers determined by theyard equipment 119860 119904 is the capacity utilization of thecontainer yard

(2) The length of the yard 119861 generally is equivalent to thelength of the container terminal and it is determined

Mathematical Problems in Engineering 3

Outer laneGate

Module

Zone

Block

Driving laneTransfer lane

Berth

e

w

B

h

v

Seas

ide

Yard

Land

side

Horizontal transport

Figure 1 Typical layout of a parallel container terminal

mainly by the coastline the total amount of theberths and the tonnage of the containerships

(3) The depth of the yard 119860 should be determined bythe design container traffic volume and the han-dling technology of the container terminal and it isexpressed as

119860 =

1

2

119872 (2119890 + ℎ) + 2V (2)

where119872 is the number of rows of blocks in the yardlayout 119890 is the width of a block determined by theyard equipment ℎ and V are the width of a transferlane and driving lane respectively

(4) The length of yard block 119897 is selected taking intoaccount rational service radius of the handling equip-ment Based on the layout of berth and yard 119897 issuitable between 200 and 300 meters and it can beexpressed as

119897 =

119861 minus (119873 + 1) V119873

(3)

where 119873 is the number of columns of blocks in theyard layout

(5) There are no detailed procedures to determine thequantity of yard cranes deployed at the terminal Itcan be found from several engineering projects inoperation and under construction that the number ofdeployed yard cranes is generally 2sim4 times of quaycranes

Therefore selections of the number of rows of blocks thenumber of columns of blocks and the number of yard cranesdeployed are the key to determining the yard layout Thesethree decisions interact with each other and cause severaltrade-offs in the system For example a large number ofrows of blocks bring higher capital investment but result in alower number of relocations during retrieval operations dueto the reduced stacking height Similarly a larger number ofcolumns of blocks (equivalently a larger number of drivinglanes) bring a shorter travel distance for trucks but reducethe ground space for stacking containers which then increasethe stacking height In this paper systems approach is nec-essary to capture the interactions of various design variablessimultaneously

22 Yard Design under Uncertainty The global maritimelogistics market contains various uncertainties that inheritfrom the fluctuation of the demand for freight transportationInfluenced by terminal scale freight organization truck andship operation natural conditions and production man-agement terminal production shows unbalance responseevident by collected real data of a variety of ports in China[9] The monthly throughput of the container terminalgenerally has a long-term variation trend and seasonalfluctuations [28 29] Therefore the randomness containedin the container terminal logistics system has brought newchallenges formaking a cost-effective and reliable yard designso as to support sustainable development of the terminalinfrastructure


There are three basic programming methods dealingwith uncertainty that is stochastic fuzzy and intervalprogramming The main difference lies in the modelingmethod of uncertainty Uncertainty is described by dis-crete or continuous probability distribution function instochastic programming In fuzzy programming uncertaintyand constraint are treated as fuzzy number and fuzzy setrespectively A certain extent of constraint being not sat-isfied is allowed and the satisfaction degree is defined asmembership function of the constraint In interval program-ming value range of uncertainty is denoted in the formof interval numbers Interval programming is a relativelynew research field and direction and there are still a lotof issues to be resolved The research on fuzzy linear pro-gramming is mature but that on fuzzy nonlinear program-ming needs further study The theory and application ofstochastic programming are mature though it is difficultto get the precise probability distribution from the actualproblem

The monthly container throughput 120585 (TEUmonth) isconsidered as an uncertain parameter in this study Withhistorical data and the projection for future economy a long-term variation trend and seasonal fluctuation of 120585 can beobtained (see [28 29] for details) Since this is a complexprocess and not the main issue of this paper we assume suchinformation as given that is discrete 120585 is described by aset of scenarios and their associated probabilities With thisinformation and in view of the nonlinear characteristics wechoose stochastic programming the mature and convenientprogramming method to deal with uncertain throughput

Two-stage stochastic programming separates the a pri-ori planning decisions taken under uncertainty before theactivity cycle starts and the adjustments performed at eachperiod of operations once information becomes availableThe former makes up the first stage of the model whilethe recourse actions defining the admissible adjustmentsto the plan make up the second stage The lead time ofcontainer yard is not short In the process of yard designunder uncertain environment planning decisions such asyard size and the equipment deployment need to be madein the planning stage before the uncertain throughput isrevealed These decisions are usually capital intensive andcannot be easily adjusted once implemented For a designedcontainer yard with certain capacity the required space issometimes higher than the provided space during the realoperation In such a situation extra space will be required(eg stacking surplus containers in an adjacent yard or rentalspace from an off-dock yard) resulting in a recourse cost dueto overcapacity Operational decisions such as the amountof containers stacked in and out of the designed yard canbe adjusted (with a recourse cost) depending on the actualrealization of uncertain future throughput To distinguishdifferent natures of planning and operational decisions wechoose to develop a two-stage stochastic programming withrecourse model [30] which has been successfully used inlogistics planning [31]Thismodel can well describe the plan-ning and operation stages of container yard and recognizethe nonanticipativity of planning decisions while allowingrecourse for operational decisions

3 Methodologies

31 OptimizationModel The yard design optimization prob-lem is stated as follows which yard layout is chosen undergiven investment budget constraints to minimize the sumof capital cost and operation losses considering uncertainterminal throughput In this model the number of rowsof blocks 119872 the number of columns of blocks 119873 andthe number of yard cranes per row of blocks 119899 are first-stage decision variables while the throughput of containersthat will be stacked in or out of the designed yard 119910(120585)

and 120596(120585) are second-stage decision variables The proposedmodel addressing the yard design optimization problem isformulated as

min 119862119872119873119899 = 119862cap + 119864120585119862ope (4)

subject to

119872

2

119873 119899 isin 119885+(5)

119862cap le 119861cap (6)

119910 le 119881 (7)

119910 + 120596 = 120585 (8)

119910 120596 ge 0 (9)

where 119862cap is the capital cost of the proposed container yard119864120585 denotes mathematical expectation with respect to 120585 119861capis the expected investment budget and 119862ope is the operationlosses of trucks travelling and yard cranes moving during theprocess of achieving the throughput 120585 Constraint (5) simplyrestricts 1198722 119873 and 119899 to be positive integer Constraint(6) represents the investment budget constraint Constraint(7) sets the capacity restriction where 119881 is a predefinedmaximum capacity which is determined by 119872 119873 and themaximum stacking height Constraint (8) requires that allcontainers must be stored whether at the designed yard areaor its neighboring yards or off-dock yards Constraint (9)simply restricts 119910 120596 to be nonnegative

311 Capital Cost 119862cap Initial investment is used for the costof yard space and the purchasing of yard cranes The totalcapital cost is written as follows

119862cap = 119888119886119886 + 119888119891119899119872 (10)

where 119888119886 is the capital cost for unit area of yard permonth including the land fee and construction cost(CNYm2month) 119886 is the required area of the containeryard for given119872 119886 can be calculated by 119886 = (119890119872+ 05ℎ119872+

2ℎ)119861 (see Figure 1) 119888119891 is the fixed cost of a yard crane permonth (CNYmonth)

312 Operation Losses 119862ope If the space of the yard or thequantity of yard cranes deployed is not adequate the opera-tional cost of containers stacked in and out of the designed


yard area (denoted by 119888in and 119888out resp) will be increasedThe operation losses can be considered as the recourse costquantifying the effectiveness of the first-stage decisionThreecategories of containers namely the import export andtransit containers are considered Import containers flowfrom containerships to the storage yard by internal trucks fortemporary storage and then are picked up by external trucksto the customers Export process is opposite from importprocess Transit containers flow fromone containership to theyard and will be loaded into another ship later on Internaltrucks are designated for single berth instead of the wholeterminal They deliver containers in a single-cycle mode inwhich they repeat a loaded-then-empty travel alternatelybetween transfer positions under quay cranes and storagesites in the yard Therefore the losses are formulated as

119862ope = min119910120596

119888in120574119910 + 119888out120574120596

119888in = 2119888119903119905119905119889 + 2119888119903119905ℎ + 119888119903119905119903119877 + 120573 (2119888it119905it119889119887)

+ (1 minus 120573) (119888it119905it119889119887 + 119888et119905et119889119892)

(11)

where 120574 is the factor that converts TEUs into a number ofcontainers 119888119903119905119905119889 denotes the travel time cost of the yardcrane per move (119888119903 is the variable cost of a yard crane persecond (CNYs) 119905119905 is the travel time of yard crane per meter(sm) 119889 is the average travel distance of the yard cranebetween moves) 119888119903119905ℎ is the cycle time cost of the yard cranehandling a container (119905ℎ is the cycle time required for thehandling of a container (s)) 119888119903119905119903119877 means the relocation costof the yard crane (119905119903 is the time required for the relocationof a container (s) 119877 is the average number of rehandlesfor picking up an arbitrary container out of a bay) 120573 isthe proportion of transit containers among all containers2119888it119905it119889119887 represents the transport cost for a transit containerwhich is transported by internal trucks twice during its stayat the terminal (119888it is the cost of an internal truck per secondincluding the overhead cost and the operating cost (costsfor labour fuel and maintenance) (CNYs) 119905it is the traveltime of internal trucks per meter (sm) 119889119887 is the averagetravel distance between the berth and yard) similarly 119888it119905it119889119887+119888et119905et119889119892 is the transport cost for each importexport container(119888et is the cost of an external truck per second including theoverhead cost and the operating cost (costs for labour fueland maintenance) (CNYs) 119905et is the travel time of externaltrucks per meter (sm) 119889119892 is the average travel distancebetween the gate and yard)

For a bay of 6 stacking lanes of containers suppose thatthe relocation of containers is restricted to a single bay andthat pre-schedule for reducing relocations is ignored theexpected number of relocations 119877 then can be evaluated bythe following formula [32]

119877 =

2119879 minus 1

4

+

119879 + 1

48

(12)

where 119879 is the average stacking height which can be calcu-lated as follows

119879 =

119910119905119889119888

119905119910119896119866119860 119904

119866 =

119890119872119861 minus 119890119872V (119873 + 1)

119904

(13)

where 119905119910119896 is the monthly operational days of container yard(day)119866 is the number of ground slots for stacking containers119860 119904 is the capacity utilization of the container yard whichis between 0 and 1 because of some unused space for therequirement of relocations 119904 is the space required for a TEUincluding the allowance between containers (m2)

In the optimization model the average travel distanceof the yard crane between moves (119889) and the average traveldistance between berth and yard (119889119887) and between gateand yard (119889119892) are the key to calculating the values of theobjective function However since the container terminallogistics system is a stochastic dynamic service system withmultiple random factors and complex dynamic relations [33]these indicators are hard to be derived from the conventionalanalytical method and thus they will be computed by theincorporation of simulationmodels descried in the followingsection

32 Model Framework Figure 2 presents the proposedsimulation-based optimization framework to optimize con-tainer yard design concerning throughput uncertainty It canbe seen that the framework is composed of a two-stagestochastic programming (TSSP) model and a simulationmodel of terminal operations (SMTO) In the framework theTSSP generates feasible yard design schemes transfers it tothe SMTO and evaluates the total cost The SMTO emulatesthe container flow at mega terminal outputs the values of 119889119889119887 and 119889119892 and returns the simulation results to the TSSPTherefore the core of this framework is the TSSP aided withthe SMTO

321 Optimization Program As illustrated in Figure 2 thesolution procedure of the TSSP consists of the following stepsin sequence

(1) Input Data Generation Inputs include uncertain containerthroughput terminal handling technology terminal opera-tional parameters and cost coefficients

Uncertain container throughput is expressed by the ran-dom vector 120585(119904) depending on the scenario 119904 (119904 = 1 2 119878)with associated probabilities119901(119904) (119901(1)+119901(2)+sdot sdot sdot+119901(119878) = 1)Information about 120585(119904) and 119901(119904) can be drawn based on thehistorical data and the projection for future economy whichis not the main concern in this paper

Yard handling technology includes the type and spanwidth of the yard crane and the width of a transfer lane anda driving lane which can be determined by the MTPRC andpractical design handbooks

Yard operational parameters includemonthly operationaldays the average cluration of containers the maximum


Simulation model of terminal operation (SMTO)

Shipexternal truckarriving system

Data statistics system

Berth operating system

Yard operating system

Container flows

Container flows Container flows

Two-stage stochastic programming (TSSP)

Generate

No

Yes

No

Yes

Uncertainthroughput

Handlingtechnology

Costcoefficient

Operationalparameters

Initialization k = 1Cmin = +infin and p = 1

Search Xk = (MkNk nk)

Xk isin X998400 = X1 X2 XK

k = K + 1 Update k = k + 1

Set Cmin = Ctotalk p = k

Ctotalk lt Cmin

Optimize Q120585 and thenevaluate Ctotal

k

Output the optimal solution and the minimum cost Xp Cmin

(d db dg)

Figure 2 The simulation-based optimization framework for yard design at mega container terminal

stacking height the average moving speed of yard crane andthe average running speed of trucks

Cost coefficients involve the unit space cost the capitalcost for the yard crane and variable operational costs asso-ciated with the yard crane and trucks These cost coefficientsgenerally can be provided by the potential terminal operatoror through field investigation

(2) Feasible Solution Set Delimitation The possible yarddesign schemes 1198831015840 are enumerated by calculating all com-binations of possible block quantities (measured in 119872 and119873) and yard crane amount 119899 and all feasible solutions arenumbered in order for searching that is 119883119896 = (119872

119896 119873

119896 119899

119896)

belongs to1198831015840 = 1198831 1198832 119883119870

(3) Initialization Set 119896 = 1 the minimum total costs 119862min =+infin and the corresponding index of solution in the set 119901 = 1

(4) Simulation Activation and Objective Function EvaluationSearch the feasible solution119883119896 Transfer119883119896 to the SMTO runthe simulation model to get 119889 119889119887 and 119889119892 and return themto the TSSP Optimize the second-stage model of the TSSP

and obtain the optimal 119876 as well as the correspondingdecision variables 119910 and 120596 under uncertain throughput 120585Evaluate the objective function 119862total

119896 that is the sum of thefirst-stage and expected second-stage costs

(5) Optimization and Decision If 119862total119896lt 119862min set 119862min =

119862total119896 and 119901 = 119896 Update 119896 = 119896 + 1 If the termination

criterion is satisfied that is 119896 = 119870 + 1 stop and output theoptimal design scheme and its corresponding minimum cost119883

119901 119862min otherwise go to step (4)

322 Simulation Model A process interaction-based dis-crete event simulation model is developed for terminaloperations via commercial software Arena 100 and it isverified and validated before running productive simulations[34] According to the operational processes as outlined inFigure 3 the simulation model consists of five systems asfollows

(1) Shipexternal truck arriving system ships are cre-ated and initialized in accordance with the shippingschedule and the handling plan The processes of


Ship arrivals

Data initialization

Berth available Ship waits in queueNo

Ship berths at an availableberth

Unloadingand stowage plan of ship

Storage yardassignment for

import and transitcontainers

Loading plan andstorage site of

export containers


export containers

Unloading containers from ship by quay cranes

Requesting internal trucksfor yard cranes

Unloading process finished

Dispatching containers byyard cranes

Export or transit

Transporting export andtransit containers toassigned berths by

internal trucks

Loading containers toship by quay cranes

Loading processfinished

Ship unberths andleaves the terminal

Requesting internal trucksfor quay cranes

Transporting import and transit containers toassigned blocks by

internal trucks

Yes

No

Yes

Yes

Yes

Assigning quay cranes andinternal trucks to ship

Stacking containers byyard cranes

Import or transitYes

External trucks arrivals

Export

Transporting exportcontainers to assigned

blocks by external trucks

Yes

Loadingand stowage plan of ship

Internal trucks request rules

Transporting importcontainers to gate by

external trucksNo

No

Storage site ofimport containers

in the yard

No

External trucks exitfrom the terminal

No

Figure 3 The logic flowchart of container terminal operation

berth allocation and external trucks picking up anddelivering containers are triggered respectively

(2) Berth operating system ships begin to receiveunloading and loading service after berthing andpreparatory work Internal trucks are designatedequally among the quay cranes assigned to the

corresponding ship The operations of quay cranescoordinating with internal trucks are simulated

(3) Yard operating system import export and transitcontainers realize stockpiling and extracting by han-dling equipment in designate section of the yardaccording to the stacking plan Yard cranes are


JiangsuProvince

Donghai Bridge

Yangshan Port AreaHangzhou Bay

Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai

Figure 4 Sketch of location of Yangshan Port Area

assigned to each zone of the container yard prevent-ing the gantry move of yard crane in different zonesInternal and external truck streamlines converge hereand the next station of trucks will be the gate or berthcorresponding to their different tasks

(4) Assignment generating system both the loading andunloading plan of each ship and the storage yardassignment for corresponding import export andtransit containers are generated

(5) Data statistics system the above four systems workindependently and interact with each other by con-tainer flows Yard crane and truck information isrecorded and the average travel distance of yard cranebetween moves and the average travel distances ofinternal trucks and external trucks can be calculatedand transferred to the optimization program

4 Case Study

The framework is applied to the second phase terminal(hereafter referred to as Phase II Terminal) of ShanghaiYangshan Port Area in China as a case study With an aimto become an international shipping center Shanghai Cityhas selected Yangshan as the site for its deep-water terminalssee Figure 4 The construction of container terminals inthis port area is implemented in four phases Phase IITerminal possessing a total of 1400 meters coastline isequippedwith four container berthswhich can accommodatecontainerships over 8000 TEUs The land area of the yard

Months (Jan2007~Dec2015)

0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)

Phases I and IIPhase II

Figure 5 Monthly throughput of Phase I and Phase II Terminals

at the terminal is reclaimed from the sea and not easy tobe adjusted during the operational period Therefore dueto the huge investment economic and sustainable pressureshave acknowledged the need not only to minimize the initialinvestment but also to ensure the terminal efficiency andreliability when determining the yard design

41 Model Input The monthly throughput data of Phase Iand Phase II Terminal (two terminals have been merged inreal operation since Phase II Terminal went into operation)from 2007 to 2015 are provided by China Ports and HarboursAssociation as plotted in Figure 5 The monthly throughputof Phase II Terminal is estimated assuming it is proportionalto the length of the terminal 108 monthly throughputs areused to construct a set of discrete scenarios with equalprobabilities in this case study

Input data of the proposed optimization framework forthis container terminal are provided as shown in Table 1 [935]

This study evaluates 6 options for the initial monthlyinvestment budgets including 5 MCNY (Million CNY) 55MCNY 6 MCNY 65 MCNY 7 MCNY and 75 MCNY to beinvestigated

Based on the geographical location of Phase II Terminaland field investigation we set a relatively high recourse costthe operation cost of storing a container out of the designedyard is 10 times the value of a container stacked in thedesigned yard area

42 Results and Discussions Table 2 shows the optimal yarddesign schemes under various investment budget constraintsby the proposed optimization framework As listed in Table 2the optimal decision with the initial monthly investmentbudget of at least 7 MCNY (in fact the investment costcalculated is 657 MCNY) is 14 rows and 6 columns ofblocks and 3 yard cranes deployed in each zone of blocksThe corresponding yard design scheme of yard depth blocklength and amount of yard cranes are 413m 210m and 42respectively


Table 1 Input data of the proposed optimization framework for this container terminal

Items Unit Data input(1) Simulation time Hour 30 times 24(2) Uncertain throughput

(i) Random vector with associated probability 120585(119904) 119901(119904) See Figure 5(3) Yard handling technology

(i) Maximum span width of yard crane Meter 2347(ii) Block width 119890 Meter 1663(iii) Width of transfer lane and driving lane ℎ V Meter 20(iv) Space required for a TEU 119904 Square meter 1763

(4) Yard operational parameters(i) Monthly operational days 119905

119910119896Day 30

(ii) Capacity utilization 119860119904

07(iii) Average cluration of containers 119905dc Day 55(iv) Maximum stacking tiers 5(v) Travel time of yard crane per meter 119905

119905Secondmeter 045

(vi) Cycle time required for handling a container 119905ℎ

Second 771(vii) Average relocation time 119905

119903Second 742

(viii) Travel time of trucks per meter 119905it 119905et Secondmeter 018(5) Cost coefficients

(i) Capital cost for yard space 119888119886

CNYsquare metermonth 833(ii) Capital cost for yard crane 119888

119891MCNYmonth 0042

(iii) Variable cost for yard crane 119888119903

CNYsecond 0053(iv) Variable cost for truck 119888it 119888et CNYsecond 0023

(6) Investment budgets(i) Options 119861cap MCNY 5 55 6 65 7 75

Moreover from an engineering perspective the followingobservations are made

(1) Optimal yard design schemes change as the invest-ment budget varies For example if the monthlybudget is less than 6 MCNY 360m yard depth withhigher block length and less yard cranes deployed ispreferred However the optimal yard design schemewill not change when the monthly budget is between6 MCNY and 65 MCNY or greater than 7 MCNY asshown in Table 2 It is noted that more budgets wouldnot always obtain extra profits therefore investorsshould pay more attention to these situations to avoidunnecessary investment

(2) The investment budget has a negative correlationwiththe losses from yard operation in a certain scopeAs shown in Figure 6 when the initial monthlyinvestment budget increases from 5 MCNY to 7MCNY the operation losses will decrease from 1101MCNY to 619 MCNY and the gained benefit isabout 44 equivalently Therefore if the investmentbudget is adequate larger depth yard with less blocklength and more yard cranes deployed is favourablefor improving operation efficiency and reducing oper-ation losses

(3) Large quantity of yard cranes deployed at the con-tainer terminal results in a higher investment cost butlower operation losses However for certain layout of

Investment budgets (MCNYmonth)

Investment costOperation losses

Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75

Figure 6 The costs of optimal yard design scheme for variousinvestment budgets

the yard (with given yard depth and block length) thevariations of yard cranes deployed may not affect thetotal costs significantly As shown inTable 2 for a yardlayout with 413m depth and 210m block length thenumber of yard cranes deployed increases from 28 to42 resulting in the investment cost increasing from598 MCNY to 657 MCNY but the operation lossesdecreasing from 682 MCNY to 619 MCNY and thetotal costs being stable at about 128 MCNY In this


Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276


Table 3 The feasible yard design schemes determined by MTPRC under various investment budgets

Number Budgets(MCNYmonth)

Decisionvariables Yard design schemes Costs (MCNYmonth)

119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost

Operationlosses Total costs

1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533

case if the investment budget is allowed more yardcranes are suggested to be deployed so as to betterserve the terminal operation but with no increase inthe total costs

Table 3 lists several feasible yard design schemes deter-mined by given investment budgets according to theMTPRCand practical handbooks which use a single containerthroughput and anunbalance factor (see Section 2) As shownin Table 3 no feasible solution can be obtained to ensure thestorage capacity of the yard under the monthly investmentbudget of 5MCNYWhen the budget is greater than 5MCNYwe have various feasible solutions of yard design schemes Forexample if the budget is 7 MCNY there are nine alternativesavailable However both the MTPRC and practical hand-books do not give the quantitativemethod of determining thebetter choice and it is difficult for the designers to choose

without a specific mathematical optimization model Herewe use the proposed SMTO to get the operation losses ofthese feasible yard schemes and the proposed optimizationmodel is also adopted to choose the good yard designschemes from the alternatives as listed in Table 3 It can befound that number 11 scheme is the better choice for thebudget of 7MCNYTherefore the proposed simulation-basedoptimization framework is effective in optimizing yard designschemes and reducing planned initial investment budgetswhich is a helpful decision-making tool for both terminalinvestors and governmental agencies

5 Summary and Conclusions

This paper is a new endeavour in yard design at mega con-tainer terminals concerning throughput uncertainty Using adeveloped integrated decision framework which is composed


of a two-stage stochastic programming model and a simu-lation model of terminal operations we are able to obtaina cost-effective and reliable design solution to the layoutand equipment deployment strategy of a container yard Thereal-world case study demonstrates the applicability of theproposed framework and the value of incorporating risks inthe early stage of infrastructure planning

We are still in an early stage of this research whereour focus is mainly on proposing effective methodologiesand finding the optimal solutions for normal operations ofmega container terminalsThe precise identification of a rep-resentative set of uncertain throughput scenarios requiresknowledge and experience of past or similar containerterminals which needs some work in the future studyMoreover port facilities are generally considered as criticalinfrastructure which plays an important role in regional andglobal economy How to plan the infrastructure to protectit against extreme risks is a worthy research topic Anotherpotential extension is to incorporate multiple performancemeasures such as emission and energy consumption in thedesign objective to address pressing issues on sustainability

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

The authors would like to greatly thank helpful commentsprovided byProfessorYueyue Fan ofCivil andEnvironmentalEngineering at University of California Davis (USA) Finan-cial support from the National Natural Science Foundationof China [Grants nos 51279026 and 51309049] is gratefullyacknowledged

References

[1] UNCTAD Review of Maritime Transport 2015 UNC-TADRMT2015 UNCTAD United Nations Publication 2015httpunctadorgenPublicationsLibraryrmt2015 enpdf

[2] L Zhen ldquoContainer yard template planning under uncertainmaritime marketrdquo Transportation Research Part E vol 69 pp199ndash217 2014

[3] A G N Novaes B Scholz-Reiter V M D Silva and H RosaldquoLong-term planning of a container terminal under demanduncertainty and economies of scalerdquo Pesquisa Operacional vol32 no 1 pp 55ndash85 2012

[4] UNCTAD Review of Maritime Transport 2010 UNCTADRMT2010 UNCTADUnitedNations Publication 2010 httpwwwunctadorgendocsrmt2010 enpdf

[5] L ChenRiskAnalysisTheory andMethod for Project InvestmentChina Machine Press Beijing China 2004

[6] D Chang Z Jiang W Yan and J He ldquoIntegrating berth alloca-tion and quay crane assignmentsrdquo Transportation Research PartE Logistics and Transportation Review vol 46 no 6 pp 975ndash990 2010

[7] J He D Chang W Mi and W Yan ldquoA hybrid parallel geneticalgorithm for yard crane schedulingrdquo Transportation ResearchPart E Logistics and Transportation Review vol 46 no 1 pp136ndash155 2010

[8] EM Alcalde K H Kim and S SMarchan ldquoOptimal space forstorage yard considering yard inventory forecasts and terminalperformancerdquo Transportation Research Part E Logistics andTransportation Review vol 82 pp 101ndash128 2015

[9] Ministry of Transport of the Peoplersquos Republic of China(MTPRC) ldquoDesign code of general layout for sea portsrdquo TechRep JTS 165-2013 China Communications Press BeijingChina 2014

[10] CCCCWater Transportation Planning andDesign Institute CoLtd Planning and Design of Modern Container Port Area ChinaCommunications Press Beijing China 2006

[11] Z Wang and X He ldquoResearch on the reasonable throughputcapacity of container terminalsrdquo Port and Waterway Engineer-ing no 3 pp 16ndash20 2004

[12] S P Sgouridis D Makris and D C Angelides ldquoSimulationanalysis for midterm yard planning in container terminalrdquoJournal of Waterway Port Coastal and Ocean Engineering vol129 no 4 pp 178ndash187 2003

[13] C-Y Chu and W-C Huang ldquoDetermining container terminalcapacity on the basis of an adopted yard handling systemrdquoTransport Reviews vol 25 no 2 pp 181ndash199 2005

[14] P Angeloudis andMGH Bell ldquoA review of container terminalsimulationmodelsrdquoMaritime PolicyampManagement vol 38 no5 pp 523ndash540 2011

[15] B K Lee L H Lee and E P Chew ldquoAnalysis on container portcapacity a Markovian modeling approachrdquo OR Spectrum vol36 no 2 pp 425ndash454 2014

[16] K H Kim and H B Kim ldquoThe optimal sizing of the storagespace and handling facilities for import containersrdquoTransporta-tion Research Part B Methodological vol 36 no 9 pp 821ndash8352002

[17] K G Murty J Liu Y-WWan and R Linn ldquoA decision supportsystem for operations in a container terminalrdquoDecision SupportSystems vol 39 no 3 pp 309ndash332 2005

[18] M E H Petering ldquoDecision support for yard capacity fleetcomposition truck substitutability and scalability issues atseaport container terminalsrdquo Transportation Research Part ELogistics and Transportation Review vol 47 no 1 pp 85ndash1032011

[19] C-I Liu H Jula K Vukadinovic and P Ioannou ldquoAutomatedguided vehicle system for two container yard layoutsrdquo Trans-portation Research Part C Emerging Technologies vol 12 no 5pp 349ndash368 2004

[20] JWieseNKliewer and L Suhl ldquoA survey of container terminalcharacteristics and equipment typesrdquo Tech Rep 0901 DSampORLab University of Paderborn Paderborn Germany 2009

[21] M E H Petering ldquoEffect of block width and storage yard layouton marine container terminal performancerdquo TransportationResearch Part E Logistics and Transportation Review vol 45 no4 pp 591ndash610 2009

[22] M E H Petering and K G Murty ldquoEffect of block lengthand yard crane deployment systems on overall performanceat a seaport container transshipment terminalrdquo Computers andOperations Research vol 36 no 5 pp 1711ndash1725 2009

[23] K H Kim Y-M Park and M-J Jin ldquoAn optimal layout ofcontainer yardsrdquoOR Spectrum vol 30 no 4 pp 675ndash695 2008

[24] N Kemme ldquoEffects of storage block layout and automatedyard crane systems on the performance of seaport containerterminalsrdquo OR Spectrum vol 34 no 3 pp 563ndash591 2012

[25] B K Lee andKHKim ldquoComparison and evaluation of variouscycle-time models for yard cranes in container terminalsrdquo


International Journal of Production Economics vol 126 no 2pp 350ndash360 2010

[26] B K Lee andKH Kim ldquoOptimizing the block size in containeryardsrdquoTransportationResearch Part E Logistics andTransporta-tion Review vol 46 no 1 pp 120ndash135 2010

[27] B K Lee and K H Kim ldquoOptimizing the yard layout in con-tainer terminalsrdquoOR Spectrum vol 35 no 2 pp 363ndash398 2013

[28] Y Xiao S Wang J J Liu J Xiao and Y Hu ldquoThroughput esti-mation based port development and management policiesanalysisrdquoMaritime Policy ampManagement vol 43 no 1 pp 84ndash97 2016

[29] Y Gao M Luo and G Zou ldquoForecasting with model selectionor model averaging a case study for monthly container portthroughputrdquo Transportmetrica A Transport Science vol 12 no4 pp 366ndash384 2016

[30] J R Birge and F Louveaux Introduction to Stochastic Program-ming Springer Series in Operations Research and FinancialEngineering Springer New York NY USA 2nd edition 2011

[31] D Alem A Clark and A Moreno ldquoStochastic network modelsfor logistics planning in disaster reliefrdquo European Journal ofOperational Research vol 255 no 1 pp 187ndash206 2016

[32] K H Kim ldquoEvaluation of the number of rehandles in containeryardsrdquo Computers and Industrial Engineering vol 32 no 4 pp701ndash711 1997

[33] CA Boer andYA Saanen ldquoImproving container terminal effi-ciency through emulationrdquo Journal of Simulation vol 6 no 4pp 267ndash278 2012

[34] G Tang W Wang Z Guo X Yu and B Wang ldquoSimulation-based optimization for generating the dimensions of a dredgedcoastal entrance channelrdquo Simulation vol 90 no 9 pp 1059ndash1070 2014

[35] J Wiese L Suhl and N Kliewer ldquoMathematical models andsolution methods for optimal container terminal yard layoutsrdquoOR Spectrum vol 32 no 3 pp 427ndash452 2010

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


sought to calculate the space requirement for planning [16ndash18] Once the main decisions about storage capacity andequipment choice have been made the next step for plan-ners involves the yard and block layout Several studies oncontainer terminal design have been conducted to compareparallel and perpendicular yard layouts using simulations[19 20] Simulation and analytical techniques have also beenused on yard design problem For example Petering [21]and Petering and Murty [22] developed a fully integratedsimulation model to analyze the influence of the width andlength of yard block on terminal performance Kim et al[23] proposed an analytical method to get the optimal yardlayout Kemme [24] examined the design of strategic yardcrane systems and block layouts and their effects on terminalperformance Lee and Kim [25] attempted to determinethe optimal size of a single block by taking into accountthe throughput requirements of yard cranes and the blockstorage requirements They provided detailed formulae forthe expected cycle times and variances of all yard craneoperations Lee and Kim [26] provided more detail on theexpression of expectation of the yard crane cycle time foryard with different block layouts useful for estimating yardcrane operating costs Lee and Kim [27] later determinedthe optimal layout of a whole container yard as specifiedby the dimensions of a block and the number of aislesHowever none of these studies attempted to analyticallydetermine storage space requirements by considering thestochastic properties of the storage yard In view of thisZhen [2] focused on the yard template planning problemunder uncertainty It considered the number of containersloaded onto (and unloaded from) each vessel within a cycletime as a stochastic parameter Alcalde et al [8] used ananalytical model based on a stochastic approach (randomvariables and probabilistic functions) to forecast storagespace requirements over an extended period However theoptimized yard dimensions were not considered as optimalbecause yard depth and block length were not optimized withthe number of handling equipment deployed simultaneously

Therefore this paper will propose an optimization frame-work to obtain a cost-effective and reliable yard designsolution that hedges well against uncertain future terminalthroughput This framework is composed of a simulationmodel for terminal operations and an optimization programwith yard depth yard block length the quantity of handlingequipment deployed and the number of containers handledin the design yard as decision variables The optimizationprogram evaluates the capital costs and benefits of variousyard layouts while the simulation model emulates trucktraffic and equipment moving at the terminal and calculatesterminal efficiency indicators The main contribution of thispaper is simultaneously optimizing yard physical layoutequipment deployment and storage schemes covering bothplanning and operation stages under uncertain environ-ment which would be more practical for yard design andmanagement in developing countries where the availabilityof data is often limited and the economic background isusually volatile Although the analytical techniques usedare not new (two-stage stochastic programming and systemsimulation) another contribution is essentially an integration

of the techniques in a unique model framework which ispowerful for decision-making

The remainder of the paper is organized as followsSection 2 describes the procedures and their limitationswhen optimizing yard designs as well as yard design underuncertainty Section 3 focuses on the modeling and solutionmethod including the proposed formulation and the solutionframework for yard optimization A numerical example andits computational results are given in Section 4 followed bydiscussions on advantages limitations and possible futureextensions of this research in Section 5

2 Problem Description

21 Quantitative andQualitative DesignGuidelines Themostcommonly used layout format of a parallel yard with trans-fer lanes at manually operated terminals in China will bestudied in this paper as depicted in Figure 1 It is notedthat container terminal operation generally consists of fourcomponents seaside operation horizontal transport yardoperation and landside operation At the seaside containersare discharged from and loaded into containerships by quaycranes deployed along the coastline Internal trucks aredispatched for transporting containers between quay cranesand certain storage stacks in the yard Container yard canusually be divided into large zones and each zone is furthercomposed of rectangular shaped blocks Each block containsseveral lanes of space for storing containers in stacks andone lane for trucks to pick up and deliver containers Forthe convenience of vehicular traffic blocks are laid out inthe unit of module which combines two blocks with transferlanes in back to back form [23] Yard cranes standing over astorage block space can be transferred from block to blockto stack and shuffle containers The landside operation isthe task of receiving or delivering containers undertakenby external trucks According to the MTPRC and severalpractical handbooks input variables and the procedures todetermine yard layout are as follows

(1) The yard capacity 119864119910 and the number of ground slots119873119904 are calculated as

119864119910 =

119876ℎ119905119889119888119870119861119870

119879119910119896

119873119904 =

119864119910

119873119897119860 119904

(1)

where 119876ℎ is the annual throughput of the containerterminal 119905119889119888 is the average cluration of the containersdetermined by the statistical material 119870119861119870 is theunbalance factor of containers stacked in the yarddetermined by the statistical material 119879119910119896 is theannual working days of the container yard 119873119897 is thestacking height of the containers determined by theyard equipment 119860 119904 is the capacity utilization of thecontainer yard

(2) The length of the yard 119861 generally is equivalent to thelength of the container terminal and it is determined


Outer laneGate

Module

Zone

Block


Berth

e

w

B

h

v

Seas

ide

Yard

Land

side





119860 =

1

2

119872 (2119890 + ℎ) + 2V (2)



119897 =

119861 minus (119873 + 1) V119873

(3)









3 Methodologies



min 119862119872119873119899 = 119862cap + 119864120585119862ope (4)

subject to

119872

2

119873 119899 isin 119885+(5)

119862cap le 119861cap (6)

119910 le 119881 (7)

119910 + 120596 = 120585 (8)

119910 120596 ge 0 (9)



119862cap = 119888119886119886 + 119888119891119899119872 (10)






119862ope = min119910120596

119888in120574119910 + 119888out120574120596

119888in = 2119888119903119905119905119889 + 2119888119903119905ℎ + 119888119903119905119903119877 + 120573 (2119888it119905it119889119887)

+ (1 minus 120573) (119888it119905it119889119887 + 119888et119905et119889119892)

(11)



119877 =

2119879 minus 1

4

+

119879 + 1

48

(12)


119879 =

119910119905119889119888

119905119910119896119866119860 119904

119866 =

119890119872119861 minus 119890119872V (119873 + 1)

119904

(13)















Container flows



Generate

No

Yes

No

Yes

Uncertainthroughput

Handlingtechnology

Costcoefficient





k = K + 1 Update k = k + 1


Ctotalk lt Cmin


k


(d db dg)





119896 119873

119896 119899

119896)

belongs to1198831015840 = 1198831 1198832 119883119870












Ship arrivals

Data initialization







export containers


export containers





Export or transit


internal trucks






internal trucks

Yes

No

Yes

Yes

Yes





Export



Yes




external trucksNo

No


in the yard

No


No







JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Outer laneGate

Module

Zone

Block


Berth

e

w

B

h

v

Seas

ide

Yard

Land

side





119860 =

1

2

119872 (2119890 + ℎ) + 2V (2)



119897 =

119861 minus (119873 + 1) V119873

(3)









3 Methodologies



min 119862119872119873119899 = 119862cap + 119864120585119862ope (4)

subject to

119872

2

119873 119899 isin 119885+(5)

119862cap le 119861cap (6)

119910 le 119881 (7)

119910 + 120596 = 120585 (8)

119910 120596 ge 0 (9)



119862cap = 119888119886119886 + 119888119891119899119872 (10)






119862ope = min119910120596

119888in120574119910 + 119888out120574120596

119888in = 2119888119903119905119905119889 + 2119888119903119905ℎ + 119888119903119905119903119877 + 120573 (2119888it119905it119889119887)

+ (1 minus 120573) (119888it119905it119889119887 + 119888et119905et119889119892)

(11)



119877 =

2119879 minus 1

4

+

119879 + 1

48

(12)


119879 =

119910119905119889119888

119905119910119896119866119860 119904

119866 =

119890119872119861 minus 119890119872V (119873 + 1)

119904

(13)















Container flows



Generate

No

Yes

No

Yes

Uncertainthroughput

Handlingtechnology

Costcoefficient





k = K + 1 Update k = k + 1


Ctotalk lt Cmin


k


(d db dg)





119896 119873

119896 119899

119896)

belongs to1198831015840 = 1198831 1198832 119883119870












Ship arrivals

Data initialization







export containers


export containers





Export or transit


internal trucks






internal trucks

Yes

No

Yes

Yes

Yes





Export



Yes




external trucksNo

No


in the yard

No


No







JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













3 Methodologies



min 119862119872119873119899 = 119862cap + 119864120585119862ope (4)

subject to

119872

2

119873 119899 isin 119885+(5)

119862cap le 119861cap (6)

119910 le 119881 (7)

119910 + 120596 = 120585 (8)

119910 120596 ge 0 (9)



119862cap = 119888119886119886 + 119888119891119899119872 (10)






119862ope = min119910120596

119888in120574119910 + 119888out120574120596

119888in = 2119888119903119905119905119889 + 2119888119903119905ℎ + 119888119903119905119903119877 + 120573 (2119888it119905it119889119887)

+ (1 minus 120573) (119888it119905it119889119887 + 119888et119905et119889119892)

(11)



119877 =

2119879 minus 1

4

+

119879 + 1

48

(12)


119879 =

119910119905119889119888

119905119910119896119866119860 119904

119866 =

119890119872119861 minus 119890119872V (119873 + 1)

119904

(13)















Container flows



Generate

No

Yes

No

Yes

Uncertainthroughput

Handlingtechnology

Costcoefficient





k = K + 1 Update k = k + 1


Ctotalk lt Cmin


k


(d db dg)





119896 119873

119896 119899

119896)

belongs to1198831015840 = 1198831 1198832 119883119870












Ship arrivals

Data initialization







export containers


export containers





Export or transit


internal trucks






internal trucks

Yes

No

Yes

Yes

Yes





Export



Yes




external trucksNo

No


in the yard

No


No







JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119862ope = min119910120596

119888in120574119910 + 119888out120574120596

119888in = 2119888119903119905119905119889 + 2119888119903119905ℎ + 119888119903119905119903119877 + 120573 (2119888it119905it119889119887)

+ (1 minus 120573) (119888it119905it119889119887 + 119888et119905et119889119892)

(11)



119877 =

2119879 minus 1

4

+

119879 + 1

48

(12)


119879 =

119910119905119889119888

119905119910119896119866119860 119904

119866 =

119890119872119861 minus 119890119872V (119873 + 1)

119904

(13)















Container flows



Generate

No

Yes

No

Yes

Uncertainthroughput

Handlingtechnology

Costcoefficient





k = K + 1 Update k = k + 1


Ctotalk lt Cmin


k


(d db dg)





119896 119873

119896 119899

119896)

belongs to1198831015840 = 1198831 1198832 119883119870












Ship arrivals

Data initialization







export containers


export containers





Export or transit


internal trucks






internal trucks

Yes

No

Yes

Yes

Yes





Export



Yes




external trucksNo

No


in the yard

No


No







JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















Container flows



Generate

No

Yes

No

Yes

Uncertainthroughput

Handlingtechnology

Costcoefficient





k = K + 1 Update k = k + 1


Ctotalk lt Cmin


k


(d db dg)





119896 119873

119896 119899

119896)

belongs to1198831015840 = 1198831 1198832 119883119870












Ship arrivals

Data initialization







export containers


export containers





Export or transit


internal trucks






internal trucks

Yes

No

Yes

Yes

Yes





Export



Yes




external trucksNo

No


in the yard

No


No







JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Ship arrivals

Data initialization







export containers


export containers





Export or transit


internal trucks






internal trucks

Yes

No

Yes

Yes

Yes





Export



Yes




external trucksNo

No


in the yard

No


No







JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










JiangsuProvince

Donghai Bridge


Yangtze Estuary

Chongming Island

JiangsuProvince

ZhejiangProvince

City of Shanghai





4 Case Study



0

10

20

30

40

50

60

70

80

Jul1

5Ja

n15

Jul1

4Ja

n14

Jul1

3Ja

n13

Jul1

2Ja

n12

Jul1

1Ja

n11

Jul1

0Ja

n10

Jul0

9Ja

n09

Jul0

8Ja

n08

Jul0

7Ja

n07

Mon

thly

thro

ughp

ut (times

104TEU)















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















119910119896Day 30






119903Second 742














Total costs

4

6

8

10

12

14

16

18

Cos

ts (M

CNY

mon

th)

5 55 6 65 7 75




Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table2Th

edecision

varia

bles

andop

timalyard

desig

nschemes

underv

arious

investmentb

udgets

Num

ber

Budgets

(MCN

Ymon

th)

Decision

varia

bles

Yard

desig

nschemes

Costs(M

CNYmon

th)

119872119873

119899

Yard

depth

(m)

Blockleng

th(m

)of

yard

cranes

Investm

ent

cost

Operatio

nlosses

Totalcosts

15

122

1360

670

12469

1101

1570

255

123

2360

440

24519

881

1400

36

146

2413

210

28598

682

1280

465

146

2413

210

28598

682

1280

57

146

3413

210

42657

619

1276

675

146

3413

210

42657

619

1276





119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119872 119873 119899

Yard depth(m)

Block length(m)

of yardcranes

Investmentcost


1 52 55 14 5 1 413 256 14 540 876 14163 6 14 5 1 413 256 14 540 876 14164 14 5 2 413 256 28 598 687 12855 65 14 5 1 413 256 14 540 876 14166 14 5 2 413 256 28 598 687 12857 16 5 1 466 256 16 610 865 14758 16 6 1 466 210 16 610 859 14699 7 14 5 1 413 256 14 540 876 141610 14 5 2 413 256 28 598 687 128511 14 5 3 413 256 42 657 624 128112 16 5 1 466 256 16 610 865 147513 16 5 2 466 256 32 677 677 135414 16 6 1 466 210 16 610 859 146915 16 6 2 466 210 32 677 671 134816 18 5 1 519 256 18 681 859 154017 18 6 1 519 210 18 681 852 153318 75 14 5 1 413 256 14 540 876 141619 14 5 2 413 256 28 598 687 128520 14 5 3 413 256 42 657 624 128121 14 5 4 413 256 56 715 593 130822 16 5 1 466 256 16 610 865 147523 16 5 2 466 256 32 677 677 135424 16 5 3 466 256 48 744 614 135825 16 6 1 466 210 16 610 859 146926 16 6 2 466 210 32 677 671 134827 16 6 3 466 210 48 744 608 135228 18 5 1 519 256 18 681 859 154029 18 6 1 519 210 18 681 852 1533









Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Competing Interests


Acknowledgments


References













































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article simulation-based optimization for...

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