a review and critique on integrated production distribution planning models and techniques

Journal of Manufacturing Systems 32 (2013) 1 19

Contents lists available at SciVerse ScienceDirect

Journal of Manufacturing Systems

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Review

A revieand tec

Behnam a Room J1-11, Mb Room 330, Dec Room J2-09, Md Room J1-14B,

a r t i c l

Article history:Received 18 JuReceived in re14 December 2Accepted 10 JuAvailable onlin

Keywords:ProductiondiSupply chain mIntegration, OpSurvey

Contents

1. Introd2. Integr3. Comp

3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7.

4. Soluti4.1. 4.2. 4.3. 4.4.

5. Implic5.1.

5.2.

CorresponE-mail add

0278-6125/$ http://dx.doi.ouction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2ated PD planning problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2lexity-based classication of literature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Single-product models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Multiple-product, single-plant models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Multiple-product, multiple-plant, single or no warehouse models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Multiple-product, multiple-plant, multiple-warehouse, single/no end-user models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Multiple-product, multiple-plant, multiple-warehouse, multiple-end user, single-transport path models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Multiple-product, multiple-plant, multiple-warehouse, multiple-end user, multiple-transport path, no-time period models . . . . . . . . . . . 11Multiple-product, multiple-plant, multiple-warehouse, multiple-end user, multiple-transport path, no-time period models . . . . . . . . . . . 11

on-based classication. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Mathematical techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Heuristic techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Simulation modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Genetic algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14ations for the future of PD planning and optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Category-based modelling implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.1.1. Category-based observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.1.2. Identied research gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.1.3. Future research trends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15General PD modelling implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2.1. General observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

ding author. Tel.: +61 8 83023552; fax: +61 8 83023380.ress: [email protected] (B. Fahimnia).

see front matter 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.rg/10.1016/j.jmsy.2012.07.005w and critique on integrated productiondistribution planning modelshniques

Fahimniaa,, Reza Zanjirani Farahanib, Romeo Marianc, Lee Luongd

awson Lakes Campus, University of South Australia, School of Advanced Manufacturing and Mechanical Engineering, Mawson Lakes, SA 5095, Australiapartment of Informatics and Operations Management, Kingston Business School, Kingston University, Kingston Hill, Kingston Upon Thames, Surrey KT2 7LB, UKawson Lakes Campus, University of South Australia, School of Advanced Manufacturing and Mechanical Engineering, Mawson Lakes, SA 5095, Australia

Mawson Lakes Campus, University of South Australia, School of Advanced Manufacturing and Mechanical Engineering, Mawson Lakes, SA 5095, Australia

e i n f o

ne 2010vised form011ly 2012e 11 August 2012

stribution planninganagementtimisation

a b s t r a c t

Optimisation modelling of integrated productiondistribution (PD) plans has raised signicant interestamong both researchers and practitioners over the past two decades. This paper provides the readerswith a comprehensive review and critique on the current PD planning and optimisation literature. Weclassify the published PD planning models into seven categories based on their degree of complexityand hence capability in addressing real-life scenarios. Summary tables highlight the main characteristicsof the selected models at each category. Next, the paper reclassies and evaluates the proposed modelsbased on the solution techniques used. Lastly, the unaddressed areas in the current literature are high-lighted, important managerial implications are proposed and directions for future research in the areaare suggested.

2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

2 B. Fahimnia et al. / Journal of Manufacturing Systems 32 (2013) 1 19

5.2.2. Identied research gaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.2.3. Future research trends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6. Conclusions and directions for future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1. Introdu

A supplychronising aacquire rawand parts into either reamong varidistributors[1]. The twodistributionhiring and subcontractplanning honing decisiofacility(ies)

In a convand retailertheir own pprot for thduction andand need toner [3]. Devnaturally lemally. For tthe literatusmall to me

Producticontext of sinterest foryears. Therpositively aintegrationing the leadand hence able eventsthe extensition of intecomprehenplanning woptimisatiowill highligposes impofor future re

2. Integrat

A vast asation of prhave investtion planninproductionon the intetion and diA PD systeproducing ttion centrewhere the dproblem is

les oseqution

ompllowin

tity ch petity

peritity ch pek-in-of eantory

bufftity es dutity g eatity usersntoryd.tity

amo

to ted blutiohis tmplevolv]. IndC manninms [2riety

ple

not PDting

the dimis.re is be m

literexist

liteubliss, ouction

chain (SC) can be dened as an integrated system syn- series of interrelated business processes in order to: (1)

materials and parts, (2) transform these raw materialsto nished products, and (3) distribute these productstailers or customers. A SC facilitates information owous business entities such as suppliers, manufacturers,, third party logistic providers, retailers and customers

core optimisation problems in a SC are production and planning. In production planning, decisions regardingring of labour, regular time and overtime production,ing, and machine capacity levels are made for a deniterizon (i.e. usually a one year period). Distribution plan-ns, on the other hand, pertain to determining which

would cater to the demands of which market(s).entional SC, independent manufacturers, wholesalers,s are separate business entities seeking to maximiserots, although this goal is known to eventually producee system as a whole [2]. It is now demonstrated that pro-

distribution decisions are mutually related problems be dealt with simultaneously in an integrated man-

eloping integrated SC models with centralised planningads to complex models which are difcult to solve opti-his reason alternative solution techniques developed inre are only used to provide near optimal solutions fordium-size integrated SC planning models [2].ondistribution (PD) planning and optimisation in theupply chain management (SCM) has raised signicant

both researchers and practitioners over the past fewe might be two primary reasons behind this trend: (1)ffecting the protability of the SC through the global

of production and distribution activities and (2) reduc--times and offering quicker response to market changesreducing the propagation of unexpected and undesir-

through the network [4,5]. These are the drivers forve literature addressing the modelling and optimisa-grated PD plans in SCs. This paper aims to provide asive review and critique on the current literature of PDith special emphasis placed on those targeting the globaln of production and distribution activities. The paperht the unaddressed areas in the current literature, pro-rtant managerial implications and suggests directionssearch in the area.

ed PD planning problem

mount of research has addressed the issue of optimi-oduction plans in the SC context [615]. Many othersigated the problems exclusively in the area of distribu-g [1621]. However, a new approach to the analysis of

and distribution operations has been proposed basedgration of decisions of different functions in produc-stribution networks into a single optimisation model.m (depicted in Fig. 1) is often composed of factorieshe goods and a hierarchy of warehouses or distribu-

variabmised produc

A cthe fol

Quanat ea

Quaneach

Quanat ea

Worend

Investack

Quanhous

Quandurin

Quanend-

Inveperio

Quanging

Duepresenmal sowith tthe coand in[23,24ing a SPD plprobleof a va

3. Com

It isgratedsuppor

1. All maxtion

2. Thecan

3. Thenot

Fewbeen previews (DCs) stocking goods for distribution to retail storesemand for these goods originates [22]. A PD planningthe problem of simultaneously optimising the decision

no specic posed PD the solutionf different functions that have traditionally been opti-entially in the sense that the optimised outputs of the

stage have become the input to the distribution stage.ex integrated PD plan, illustrated in Fig. 1, deals withg problems within the context of SC planning:

of each product produced in regular-time in each plantriod.of each product produced in overtime in each plant atod.of each product outsourced by each manufacturing plantriod.Progress (WIP) inventory amount in each plant at thech period.

amount of nished products temporarily stored in theers in each plant at the end of each period.of each product shipped from stack buffers to ware-ring each period.of each product shipped from warehouses to end-usersch period.of each product shipped from stack buffers directly to

during each period. of nished products stored in warehouses at each

of each product backordered (i.e. shortage or backlog-unt) in each end-user location at the end of each period.

the high number of decision variables, the problemy the PD systems analysis is so complex that opti-ns are very hard to obtain. The difculties associatedype of decision-making can be further amplied byx maze of the network, geographical span of the SC,ement of varied entities with conicting objectiveseed, simplication of a real-life scenario in develop-odel has become unavoidable as most of the complexg problems are classied under the category of NP-hard5,26]. Such simplications have led to the development

of PD planning models in the literature.

xity-based classication of literature

an easy task to classify the existing literature of inte- planning and optimisation. There are three reasons

this difculty [27]:

eveloped models consider cost minimisation, protation or a combination of both as their objective func-

a wide variety of assumptions and considerations thatade when proposing PD planning models.ature in the eld is so extensive and a unied body does.

rature surveys on the proposed PD models havehed [1,25,2744]. Despite the variety of the publishedr survey on the current literature indicates that there is

review on comparing the actual capabilities of the pro-models based on their degree of complexity as well as

approaches applied. In this paper, we present a review

B. Fahimnia et al. / Journal of Manufacturing Systems 32 (2013) 1 19 3

d PD

of recent wdegree of coof simplicing the decorder to acts achievedistribution

We dividmarised in

Category 1Category 2Category 3house PDCategory warehouseCategory warehousemodels.Category warehouseperiod PDCategory warehousetime-perio

Fig. 2 illuof PD planlished workfurther discysis later alresearch is

To evalulowing dimeach publis

of opultipiplict.ipliciplicucts xisteoringFig. 1. A complex real-life integrate

ork on integrated analysis of PD systems based on themplexity of the models proposed indicating the levelation used. We target the published models integrat-isions in production and distribution sub-systems inhieve the global optimisation and highlight the bene-d from the integration of decisions in production and

sub-systems.e the published models into the seven categories (sum-

Fig. 2):

Typeor m

Multplan

Mult Mult

prod The e

ily st: Single-product PD models.: Multiple-product, single-plant PD models.: Multiple-product, multiple-plant, single or no ware-

models.4: Multiple-product, multiple-plant, multiple-, single or no end-user PD models.5: Multiple-product, multiple-plant, multiple-, multiple-end user, single-transport path PD

6: Multiple-product, multiple-plant, multiple-, multiple-end user, multiple-transport path, no-time

models.7: Multiple-product, multiple-plant, multiple-, multiple-end user, multiple-transport path, multipled PD models.

strates the classication of previous works in the areaning. Each level of this gure contains the related pub-s (for that certain level of complexity) which will beussed and analysed in the following sections. This anal-lows us to identify the important areas where furtherneeded.ate the degree of complexity for each model, the fol-ensions are used in the following sections to examinehed model:

Multiplic(direct/in

Multiplic Regular-t

at manufa Detailed

plant. Inventory

and invenhouses).

Shortage/of each pe

Methods

3.1. Single-

Haq et productiontiliser indurealistic conduring prolosses as wof the itemstion sites aand detaile model.

timisation (i.e. cost minimisation, prot maximisation,le objective functions).ity of products to be produced at each manufacturing

ity of geographically dispersed manufacturing plants.ity of machine centres for the production of multipleat each manufacturing plant.nce of stack buffers at manufacturing plants temporar-

products prior to their shipment to the warehouses.

ity of transport paths from plants to end-usersdirect shipment).ity of time-periods.ime/overtime production and outsourcing alternativescturing plants.production cost elements in aggregate level for each

costs (i.e. WIP inventory costs in manufacturing plantstory of nished products at stack buffers and ware-

penalty costs of not meeting demand forecast at the endriod (also known as backordering or backlogging costs).applied for modelling and optimisation.

product models

al. [22] presented the application of an integratedinventorydistribution planning model in a large fer-stry operating in North India incorporating manyditions such as set-up time and cost, lead times, losses

duction and distribution and recycling of productionell as backlogging. The study limits the manufacturing

to the production of a single product in a set of produc-nd disregards production and distribution alternativesd cost components.


grate

Chan et aand analytisimplied Pwas used foing and wedesigned anplant. A mustudy from

Demirli to-order SCwas construstudy consiin literatureand shortagtal productproducts infrom plants

A compland C atay [ity expansiois formulatthree LP reproblem. Coufacturing ptransportatcharacteristfunctioning

A singleproblem watackle prodin the propinventory aproductionA basic greeused as theanism and a

Coronaduncertaintydene the

h supodele p

aracntorprod

in thedi

six-lblemor thing

ediumo-p

was ed PFig. 2. The classication of literature on inte

l. [45] used a combined hybrid genetic algorithm (HGA)c hierarchy process (AHP) approach for optimising aD problem in multi-factory SCs. Linear programmingr the modelling of the problem and AHP for organis-ighting the decision-making criteria. A HGA was thend implemented to determine job allocation for eachlti-factory production network is investigated in thiswhere products are transported directly to the markets.and Yimer [46] proposed a planning model for a build-

with uncertain cost parameters. The proposed modelcted as a mixed integer fuzzy programming (MIFP). Thisders some key features of a PD model rarely attended, such as assembly cost components, inventory costs,e costs. However, it disregards a number of fundamen-ion characteristics such as the production of multiple

multiple time-periods and the distribution of products

to eacThis movertimtant chof invemulti-garded

Hamsolve aSC proinput fgrammand m

A twrithm simpli to customers through multiple transport paths.ex single-product PD model was studied by Yilmaz47]. The major contribution of this study is the capac-n characteristic of the developed model. The problem

ed as a mixed integer programming (MIP) model andlaxation-based heuristics are developed to solve thensidering unlimited inventory holding capacity at man-lants and ignoring the backlogging possibilities and theion of products from DCs to end-users are among theics which may considerably preclude the model from

effectively in real-life scenarios.-product, single-plant, no-warehouse PD plannings investigated using meta-heuristics to simultaneously

uction and routing decisions [48]. The objective functionosed linear integer model minimises the sum of setup,nd transportation costs for determining the optimal

amount and quantities to be shipped to each customer.dy randomised adaptive search procedure (GRASP) was

solution approach improved through a reactive mech- path-relinking process.o [49] studied a SC optimisation model considering

at suppliers nominal capacity. This model tries tobest diversication and safety stock level allocated

tion plant pproducts dimises the costs at the

Table 1 proposed mmodel indicthe concern

3.2. Multip

Models narios withthe applicaband merginpanies to defciency [characterisa single wostockpile ois able to copolicies forprecluded td PD planning.

plier when minimising the overall expected SC cost. incorporates the cost components for regular-time androduction of goods and proposes some other impor-teristics rarely attended in the literature (e.g. all typesy costs). Backlogging issues and the transportation ofucts from multi-plants to multi-end-users are disre-is model.

et al. [50] proposed a hierarchical solution algorithm toevel, single-objective, multi-period, and single-product

in the sense that the solutions of one section are used ase next section. The proposed mixed integer linear pro-(MILP) mathematical model was tested for a few small

size samples in real world gas industries.hase approach centring on reactive tabu search algo-developed by Bard and Nananukul [51] to solve aD planning problem incorporating a single produc-

roducing a single product and distributing the nishedirectly to end customers. The objective function min-sum of production setup costs, routing costs, holding

plant, and holding costs at the customer sites.summarises and compares the characteristics of theodels in Category 1. The number of ticks in front of aates the dimensions/characteristics accommodated ined PD model.

le-product, single-plant models

classied in this category can only work in the PD sce- a single manufacturing plant. This signicantly limitsility of the developed models because the globalisationg processes have encouraged the manufacturing com-evelop multi-plant policies in order to improve their52]. Pyke and Cohen [53] examined the performancetics of a simple integrated PD system comprised ofrk centre at a factory producing multiple products, af nished goods, and a single retailer. The algorithmmpute expedite and replenishment inventory control

the entire chain. The large number of decision variableshe extensive accuracy testing of the algorithm.

B. Fahim

nia et

al. /

Journal of

Manufacturing

Systems

32 (2013) 1 195

Table 1Classication of literatureCategory 1.

Author(s), year Dimensions of the proposed model Methods applied

TCM: total costminimisationPM: protmaximisationMO: multipleobjectives

Multipleproducttypes

Multiplemanuf.plants

Multiplemachinecentres

Stackbuffersinplants

MultipleDCs

Multipleend-users

Multipletransportpaths

Multipletime-periods

Productionalternatives

Productioncostelements

Inventorycosts

Shortage/penaltycosts

Haq et al., 1991 TCM . . .ab . . . . . . . . . . . . . . . A mixed 01 integer

programmingChan et al., 2005 TCM . . .

. . . . . . . . .

. . . . . . . . . . . . . . . . . . Linear programming

and a combined hybridgenetic algorithm andanalytic hierarchyprocess

Demirli andYimer, 2006

TCM . . .

. . . . . .

. . . . . . . . .

MIFP model

Yilmaz andC atay, 2006

TCM . . .

. . . . . .

. . . . . .

. . . . . . . . . . . . MIP model solved withthree LPrelaxation-basedheuristics

Boudia et al.,2007

TCM . . . . . . . . . . . . . . .

. . .

. . . . . . Xc . . . A GRASP and twoimproved versionsusing a reactivemechanism or apath-relinking process

Coronado, 2008 TCM . . .

. . . . . . . . . . . . . . .

X . . . X X A nonlinearprogrammingformulation and aheuristic to decomposethe originalformulation into twoeasy-to-solve LPproblems

Hamedi et al.,2009

TCM . . .

. . . . . .

. . . . . . . . .

A hierarchical solutionalgorithm and a MILPcoded using LINGO8.00

Bard andNananukul,2009

TCM . . . . . . . . . . . . . . .

. . .

. . . . . . X

A two-phase approachcentring on reactivetabu search algorithm

a The characteristic is NOT considered in the developed model.b The characteristic is considered in the developed model.c The characteristic is PARTIALLY considered in the developed model.


A MIP-based PD model was presented in [2] for which theLagrangian relaxation was used to accommodate the productionand distribution sub-problems, and sub-gradient optimisation wasimplemented to coordinate the information ow in a hierarchi-cal mannerwhich modat the produ

A hierargle multinamultiple wto solve theproduct fammodel is disto reduce th

Lee andin the literadure using methods [5a number oproducts atwith two shtribution caconsidered eral PD chprogrammiing the procosts. An LPwas emplotigate a muplan.

A PD pla DC was emachine ceon transortatribution ceproductionthe generaldevelop thrresearch invical formula

Nishi et athe integrattion planniusing MILP.duction schan augmensystem waserating the obtained atmodicatiothe producwarehouse end-users ialternatives

Farahanfor a just-iSC using mwere consiminimisatioin all periodJIT deliveryuct delivericonsidered network. Sitems from variable pro

disregards the production issues and the multiplicity of manufac-turing plants.

A new solution approach was proposed by Safaei based on theintegration of mathematical and simulation techniques to solve

egratrobleobleid m

of ined maching prn altevento

chad in

ultip

hameationnatioge rduct

and tts.ew ang ttimehe p

networy mo imller (ning

PD s anductsinteCanaang re shnishthe tyts arher

are nnvolvyalk

to geulti-8, audemsite p

propnts

ippedered. In fe thetionsns.le 3 smod. This study extends the scheme by a heuristic methodies distribution decisions if capacity shortages occurction stage [54].

chical PD planning approach was developed for a sin-tional factory transporting multiple product families toarehouses or chain stores [55]. The approach attempts

problem optimally by aggregating the time periods andilies. The obtained aggregate optimal solution for theaggregated for a single period on a rolling horizon basise problem size.

Kim developed one of the most generic PD modelsture and proposed a specic problem-solving proce-a hybrid approach combining analytic and simulation6,57]. In the proposed model, the rst shop producesf parts which are used in the production of multiple

the second shop. There is only a single plant modelledops and a single stack point. The production and dis-pacity constraints in the proposed analytic model areas stochastic variables adjusted in accordance with gen-aracteristics obtained from a simulation model. Linearng was used for the problem formulation minimis-duction, distribution, inventory holding, and shortage

solver was used to implement the model and ARENAyed as the simulation tool. This study does not inves-lti-plant scenario and disregards a detailed production

anning problem between a manufacturing location andxamined by Rizk et al. [58], in which multiple parallelnters at the manufacturing location, economies of scaletion costs, as well as dynamic demand at plants and dis-ntres were taken into consideration. A MIP model of the

process and three different formulations representing piecewise linear transportation functions were used toee equivalent mathematical programming models. Theestigates the impact of choosing a suitable mathemat-tion on the problem-solving time.l. [59] studied a distributed decision-making system fored optimisation of production scheduling and distribu-ng. An integrated optimisation model was formulated

The developed model was then decomposed into pro-eduling and warehouse planning sub-problems usingted Lagrangian approach. A distributed optimisation

developed to solve the sub-problems by gradually gen-feasible solutions through repeatedly exchanging data

each sub-system (data update) to accommodate thens caused by unforeseen changes. The study formulatestion processes at a single plant and considers a singlecomprising a number of storage areas. There are nonvolved in this model and production/transportation

are simplied.i and Elahipanah [60] solved a MILP bi-objective modeln-time (JIT) distribution planning of a three-echelonulti-objective Genetic Algorithms (GAs). Two functionsdered for optimisation: cost minimisation as well asn of the sum of backorders and surpluses of productss. In fact, the second objective function represents the

and minimises the earliness and tardiness of prod-es. Delivery lead-times and capacity constraints werefor a multi-period, multi-product and multi-channel

ince the study primarily concerns the distribution ofsuppliers to retailers, this model replaces the xed andduction costs by the purchasing costs and completely

an intning pthe pra hybrsistingpropostiple mplanniductioand in

Theoutline

3.3. Mmodels

Mocorpormulti-exchanthe protories marke

A nspannimulti-lems. Tin a SCinventorder tControauto-tuworld nativeof prod

An major and Wrials asemi-ing to producfrom wThere type) i

Kanmodelin a min 200rating multi-In thethe plaare shconsidnariosbecaustive acdecisio

Tabposed ed multi-product, multi-period, multi-site PD plan-m [61]. A MILP model was developed for formulatingm. In this study, to consider the stochastic factors,athematical-simulation approach was proposed con-dependent mathematical and simulation models. Theodel can be treated as a single-plant model with mul-ne centres and many characteristics of a real world PDoblem are disregarded in this model (e.g. detailed pro-rnatives, production cost elements, backlogging costs,ry management issues).racteristics of the proposed models in Category 2 are

Table 2.

le-product, multiple-plant, single or no warehouse

d [62] studied the PD planning for multinationals. Production planning and logistics decisions fornal companies operating under varying ination andates was analysed in this research. The study modelsion of multiple products in multiple multinational fac-he distribution of produced items directly to the target

pproach was proposed by Gen and Syarif [63] calledree-based hybrid genetic algorithm (hst-GA) to solve

period production, distribution and inventory prob-roposed model integrates design and planning decisionsork. Facility location decisions, distribution costs, andanagement issues were taken into consideration. In

prove the efciency of the proposed GA, a Fuzzy LogicFLC) was hybridised to the evolutionary process for the

of the GA parameters. In this study, however, a realnetwork is simplied by disregarding production alter-

cost components as well as the indirect transportation from plants to customers.grated approach for planning steel production in adian steel making company was discussed by Chen[64]. In the proposed linear programming raw mate-ipped to the central steel plant and transformed intoed products with different specications correspond-pes of the end products to be produced. Semi-nishede transported from central plant to the other factories,e the nished products are transported to customers.o distribution centres and inventory costs (from anyed in this model.

ar and Adil [65] developed a single linear programmingnerate an integrated aggregate and detailed PD plansite production environment. Also in 2007 and laterthors proposed a robust optimisation model incorpo-and uncertainty for integrated aggregate planning ofrocurementproductiondistribution system [66,67].osed complex model, there is a supplier providing

with the required raw material, from where products to the manufacturing plants accordingly. Demand is

to be stochastic and can be described in different sce-act, the developed model may not be fully integrated,

distribution decisions are only responsible for correc- and do not have direct consequences on the production

ummarises and compares the characteristics of the pro-els in this category.

B. Fahim

nia et

al. /

Journal of

Manufacturing

Systems

32 (2013) 1 197







Stackbuffersinplants

MultipleDCs

Multipleend-users





Inventorycosts


Pyke and Cohen,1993, 1994

TCM

. . . . . .

. . . . . . . . .

. . . . . .

Using theapproximation ofsteady statedistributions of keyrandom variables

Barbarosoglu andOzgur, 1999

TCM

. . . . . . . . .

. . .

. . . X

. . . A MIP model solvedusing Lagrangianheuristic and subgradient optimisation

Ozdamar andYazgac, 1999

TCM

. . . . . . . . .

. . . . . .

. . . . . . X

A hierarchical PDplanning approach

Lee and Kim,2000, 2002

TCM

. . .

. . .

. . . . . .

A hybridanalytic-simulationapproach using linearprogram, GeneralAlgebraic ModellingSystem and ARENAsimulation package

Rizk et al., 2006 TCM

. . . . . . . . . . . . . . .

. . . . . . X . . . A MIP model solvedwith CPLEX

Nishi et al., 2007 TCM

. . .

. . . . . . . . . . . .

. . . X

A MILP and using aLagrangian approach todecompose theproblem intosub-problems

Elahipanah andFarahani, 2008

TCM

. . . . . . . . .

. . . . . . X

A MILP model solvedusing a multi-objectiveGA

Safaei et al., 2009 TCM

. . . . . . . . .

. . . . . . X . . . A hybridmathematical-simulationapproach


Table

3Cla

ssi

cation

of

lite

ratu

re

Cat

egor

y

3.

Auth

or(s

),

year

Dim

ension

s

of

the

pro

pos

ed

mod

el

Met

hod

s

applied

TCM

:

tota

l cos

tm

inim

isat

ion

PM:

pro

t

max

imisat

ion

MO:

multip

leob

ject

ives

Multip

lepro

duct

types

Multip

lem

anuf.

pla

nts

Multip

lem

achin

ece

ntr

es

Stac

kbu

ffer

sin pla

nts

Multip

leDCs

Multip

leen

d-u

sers

Multip

letr

ansp

ort

pat

hs

Multip

letim

e-per

iods

Prod

uct

ion

alte

rnat

ives

Prod

uct

ion

cost

elem

ents

Inve

nto

ryco

sts

Shor

tage

/pen

alty

cost

s

Chen

and

Wan

g,19

97PM

. .

.

. .

.

. .

.

. .

.

. .

.

X

. .

.

. .

.

A

linea

r

pro

gram

min

gap

pro

ach

Moh

amed

, 199

9

MO

. .

.

. .

.

. .

.

. .

.

X

X

Anal

ysin

g

diffe

rent

mat

hem

atic

al

mod

els

for

diffe

rent

scen

ario

sGen

and

Syar

if,

2005

TCM

. .

.. .

.. .

.

. .

.

. .

.

. .

.

X

. .

.

Solv

ing

a

PD

LPM

using

span

nin

gtr

ee-b

ased

hyb

rid

genet

ic

algo

rith

ms

and

fuzz

y

logi

c

contr

olle

r(F

LC)

Kan

yalk

ar

and

Adil, 2

008

TCM

. .

.

. .

.

. .

.

. .

.

. .

.

. .

.

A

linea

r

mat

hem

atic

alfo

rmula

tion

solv

edusing

GLP

K

solv

er

3.4. Multiple-product, multiple-plant, multiple-warehouse,single/no end-user models

Cohen and Lee [68] presented a strategic modelling frame-work and ainteractionapproximatSC: materiatribution nsub-model model soluhowever, reand solve tmost locati

An integ[69] in whiand lot siziof transpordecompositmodel comThe proposthe contribapproach bare solved.

Tasan [7a PD plan.tion quantiauthor thenand decidesthe DCs witvehicle rouing Applicasingle-echetion plans centres to t

Kanyalkprogrammiand distributiple paralland servingmodel usesand short-ttion and disis solved heimplementsolver. Thisalternativesemploying

A GA wning problmulti-prodning probleactivities isagement isThe develoDCs to custfaced in rea

A fuzzy oped by Lmulti-timedesigned toery time. Arepresent tposed PD interactive ple machin hierarchical decomposition approach to analyse thes between functions in a SC. They consider four linkede sub-modules each representing a part of the overalll control, production control, product stockpile, and dis-etwork control. In a hierarchical decomposition, eachwas heuristically optimised and the output of a sub-tion is used as the input data to others. The model,lies on the non-tested approximations to characterisehe random variables describing the linkages betweenons [53].rated two-layer model was developed by Tang and Yungch the rst layer integrates the production assignmentng problems and the second layer integrates decisionstation and order quantity determination. A two-layerion method is developed for solving the proposedbining two heuristics: assignment and transportation.ed model is a typical supplier-warehouse model andution of the paper is built around the proposed solutiony which several medium and large-scale test problems

0] proposed a two-step approach for the developing of A MIP model is developed for determining the produc-ties and allocation of this production to demands. The

uses the outputs of the rst step as inputs to the next how the allocated product quantities are transported toh vehicle routing consideration. GA is employed as theting tool and the model is executed in GA Based Rout-tion (GABRA). The proposed model is, however, a basiclon PD plan disregarding many key aspects of produc-as well as the distribution of items from distributionhe customers.ar and Adil [71] proposed a mixed integer linear goalng model for an integrated procurement, productiontion planning problem comprising a system with mul-

el production plants supplied from multiple suppliers multiple DCs. To reduce the computational burden, the

different time-grids and planning horizons (long-termerm) for aggregate and detailed procurement, produc-tribution planning. The goal programming formulationuristically using weighted and pre-emptive methods,

ed in Linux based Gnu Linear Programming Kit (GLPK) model simplies the detailed production/outsourcing

and cost components and disregards the complexity ofmultiple transport options.as developed for solving an integrated PD plan-

em by Park et al. [3]. The problem studied was auct, multi-supplier, multi-plant, and multi-DC plan-m. Although integration of production and distribution

the main target, the procurement and inventory man-sues were also properly accommodated in this model.ped model disregards the transportation of items fromomers and simplies many production planning issuesl world scenarios.multi-objective linear programming model was devel-iang [72] to solve integrated multi-product and

period PD planning problems. Two objectives were minimise the total system-wide costs and total deliv-

piecewise linear membership function was adopted tohe fuzzy objectives of the decision-maker for the pro-problem, and to achieve more exible doctrines via andecision-making process. However, considering multi-e centres and stack buffers at plants, multiple end-users,


the direct/indirect transportation of products from plants to end-users, and also taking into consideration the detailed productioncost elements for every single product could considerably increasethe complexity of the developed model by Liang.

A fuzzy posed by Biincorporatitiple DCs. TFMIP modewere furthfactors andAlthough threalistic faccharacterist(refer to sum

A fuzzy and distribuincorporatitotal cost o(3) minimisdeliveries. TMILP. To cathe impreciactive fuzzywas then coa compromprevious wotic programproduction incorporatening) and dstage as apusers were the transpo

Table 4 c4.

3.5. Multipmultiple-en

An indusFlipo and Fmodel and the solver. in each procertain production linebackloggingtion/distribsystem, we

Chen anof multiple under markelled as disexpected ouThe model iming (MINLof satisfactimethod is paggregationthe best comdegree of samodel is deonly one siaspects at eand stack b

distribution of products from plants to end-users are ignored inthe proposed model.

Lim et al. [77] presented a simulation approach for the PDplanning based on the work of Jang et al. [78] to determine the

ties ooliciacity

e devalysd loula

udy, g difnentv etperiohe mmmise pn watives.esearg wast mve ln. Decorpch. I

studoblee. co

weigportueighs seeterisentmbiith tagenhe methosatioposeds w

wor of sagenutiongiano-le

[81] sing cou

s inced cos, asAt thhrou

be pd nrketory c

The ectiomathematical programming based approach was pro-lgen [73] to solve an integrated PD planning problemng multiple production lines, multiple plants and mul-he model was rst formulated using MILP and threels (corresponding to different aggregation operators)er developed to facilitate the embodied uncertainty

fuzziness of constraints, objectives and parameters.e proposed model introduces the inclusion of such

tors as production lines in manufacturing plants, manyics of a real world model are disregarded in this studymary Table 4).

production planning model integrating procurementtion plans was developed by Torabi and Hassini [74]

ng four objectives simultaneously: (1) minimisation off logistics, (2) maximisation of total purchasing value,ation of defective items, and (4) minimisation of latehe initial model was formulated using a multi-objectivepture the inherent fuzziness of the critical data andse nature of the objectives aspiration levels, an inter-

goal programming formulation was proposed whichnverted into an auxiliary crisp formulation for ndingise solution. This study is the extension of the authorsrk, in which a fuzzy single-plant bi-objective possibilis-ming model was proposed to formulate a SC masterschedule [75]. The proposed models, however, aim to

the decisions at a tactical level (i.e. mid-term SC plan-o not include the operational decisions at productionpears in an aggregate production plan. Further, end-not considered in these models as a SC node and hencertation issues were only considered up to the DC level.ompares the characteristics of the models in Category

le-product, multiple-plant, multiple-warehouse,d user, single-transport path models

trial PD planning problem was studied by Dhaenens-inke [52] proposing a MILP for the formulation of theusing CPLEX commercial linear programming codes asIn this study multiple states and lines are consideredduction facility each dedicated to the production of aduct. However, multiple machine centres in the pro-

of each product, stack buffers at manufacturing plants, costs, detailed production cost elements and produc-ution alternatives, all the characteristics of a complex SCre not taken into consideration in the proposed model.d Lee [76] investigated the simultaneous optimisationobjectives in a typical SC with uncertain product priceset demand uncertainties. Demand uncertainty is mod-crete scenarios with given probabilities for differenttcomes. Uncertainties are described as fuzzy variables.s constructed using Mixed Integer Nonlinear Program-P) to achieve conicting objectives. To nd the degreeon of the multiple objectives, a fuzzy decision-makingroposed, where the nal decision is acquired by fuzzy

of the fuzzy goals and the fuzzy product prices, andpromised solution is derived by maximising the overalltisfaction for the decision. Although a multiple-productveloped in this study, every plant batch-manufacturesngle product at one period. Also, detailed productionach plant (e.g. considering capacity of machine centresuffers, and outsourcing opportunities) and the direct

capaciment pthe captest tha SC antion anand simthis stsiderincompo

Aliemulti-[79]. Tto accoimprecsolutioalternamodel

In rmakinand coobjecticoncerwere inapproaios arecase prtive (i.uses athe opnant wentitiecharacimplem

A coet al. wmulti-[80]. Ttion moptimithe promethoagentsqualityother ter solLagran

A twgupta addresmay entaintieexpectpolicietimes. costs tucts toDCs anisfy mainventtainty.the self facilities in a PD network considering three replenish-es. The study presents a mathematical model to decide

of facilities and uses Microsoft Excel premium solver toeloped model. It also develops a simulation model usinger to execute a PD plan for higher customer satisfac-wer total relevant costs. The developed mathematicaltion model were applied to a simple test problem. Inthe focus is given to replenishment policies and con-ferent production/transportation alternatives and costs are ignored.

al. proposed a fuzzy integrated formulation for ad and multi-product aggregate PD planning problemodel was formulated in terms of fuzzy programmingodate the inherent uncertainties in market demands,rocess times and other related factors. The optimals then sought using GA. Production and distribution

and production cost elements are disregarded in this

ch by Selim and Ozkarahan [54], collaborative decision-s studied with the objectives of prot maximisationinimisation in a PD planning problem. A multi-

inear programming model was developed for thiscision-makers imprecise aspiration levels for the goalsorated into the model using a fuzzy goal programmingn this article, centralised and decentralised SC scenar-ied and computational experiments are provided on am. This model does not take into account a single objec-st minimisation or prot maximisation), but insteadhted additive approach and gives the decision-makernity to decide which partner will possess the domi-t. Different SC participants are considered as differentking separate objectives. Considering other operationaltics in this model could make it far more applicable foration in different SC environments.national PD planning problem was studied by Kazemihe objective to evaluate the performance of a GA-basedt system compared to a Lagrangian relaxation approachulti-agent system approach was adopted as a solu-

dology because of the difculties associated with then of a complex integrated PD planning problem. Ind approach, three GA models with different crossover

ere developed playing the role of three agents. The threek independently with the objective of enhancing theolutions achieved in the preceding generation by thets. The approach was demonstrated to generate bet-s in large-scale PD planning problems compared to

relaxation.vel mathematical model was proposed by Das and Sen-for simulating SC strategic and operational planningvarious uncertainties that a multinational corporationnter due to changes in government regulations. Uncer-orporated in this model include the changes in thest of input material, border crossing costs, tariffs, tax

well as the variations in demand and transportatione strategic level, the model maximises the overall SCgh the selection of plants, quantity and type of prod-roduced at each plant, the allocation of the plants toally the allocation of DCs to customer locations to sat-

demands. At the operational level, the model minimisesosts at DCs addressing the transportation time uncer-sensitivity analyses results indicate that the changes inn of plant set and supply quantity occur when the input

10B.

Fahimnia

et al.

/ Journal

of M

anufacturing System

s 32 (2013) 1 19







Stackbuffersin plants

MultipleDCs

Multipleend-users





Inventorycosts


Cohen and Lee,1988

TCM

. . . . . . . . . . . . X

Four linked,approximatesub-modelsheuristically optimisedusing hierarchicaldecompositionapproach

Tang and Yung,2004

TCM

. . . . . .

. . . . . . . . . . . . X . . . . . . A non-linearmathematical modelsolved using atwo-layerdecompositionsolution approach.

Tasan, 2006 TCM

. . . . . .

. . . . . .

. . . . . .

. . . A MIP model solvedusing GAs

Kanyalkar andAdil, 2005,2007, 2008

TCM

. . .

. . . . . .

. . . . . .

. . . A mixed integer lineargoal programmingmodel solvedheuristically usingweighted andpre-emptive methods

Park et al., 2007 TCM

. . . . . .

. . . . . .

. . . . . .

. . . A linear mathematicalmodel solved usingGAs

Liang, 2008 TCM

. . . . . .

. . . . . .

. . .

A fuzzy two-objectivemathematicalprogramming modelwith piecewise linearmembership function

Bilgen, 2009 TCM

. . .

. . . . . .

. . . . . . X

A MILP modelequipped with threeFMIP modelsaccommodating theembodied uncertaintyfactors

Torabi andHassini, 2009

MO

. . . . . .

. . . . . .

. . . . . . X . . . A multi-objective fuzzygoal programmingformulation solvedthrough an auxiliarycrisp formulation


resource costs change, triggered by the changes in governmentregulations.

A two-phase MILP model and a GA-based solution procedurewas proposed for the scheduling of a build-to-order SC [82].The originamodels: theplanning ofond model procuremenmentation test problemical programthat the sofor small-scmal solutiosolution to provide a siactivities, bsystems and

The charhighlighted


There arthis categormore compareas, partistudied by a major Eurproposed foCPLEX as somajor advamodels areply sides anwas designconsideratimodel.

Ferrio aning and repup of produbution centimplementenetwork wainventory mtres, and delogistics coformerly re

An integfuel renerlocations [8to multiplemarkets. A Mmaximisingstudies presresulting frbution of futhrough the

Table 6 c


In termsplex model

our knowledge, the sole paper that could t in this category is thestudy conducted by Fahimnia et al. [86]. Based on the integration ofAggregate Production Plan and Distribution Plan, the authors devel-oped a MILP for a two echelon SC considering several real world

es anped meded aarise

ution

a co spacds oacturers vfor e plasatiomodh [2

surv havan. E

and ms. Tus mn tecl tec

athem

themprogrion adopmmin,46,5tion mthemful ans thoLP) isproces ineger

consis muion maintsjectivach wes ny ma

nearre ardellin

hemassoclgor

100] a hiticall complex problem was decomposed into two sub- rst model concerns the assembling and distribution

nal products as per customer order, while the sec-involves the production scheduling and raw-materialst based on the outputs of the rst model. The imple-

of the proposed GA-based approach in solving a set ofs was compared with the performance of mathemat-ming approach (using LINGO). The results revealed

lutions achieved from both approaches are identicalale problems while LINGO could not converge to opti-n for medium-size problems and failed to provide anythe large test problems. The proposed model does notngle optimisation algorithm for planning the entire SCut instead it decomposes the problem into two sub-

evaluates them sequentially.acteristics of the models presented in Category 5 are

in Table 5.

le-product, multiple-plant, multiple-warehouse,d user, multiple-transport path, no-time period models

e only few models in the literature which can t iny and this indicates the need for the development oflex PD models able to accommodate the unaddressedcularly in Categories 6 and 7. A real-life case study wasGunnarsson et al. [83] for modelling the entire SC ofopean pulp mill company. A mathematical model wasr the planning of the entire SC, using the commerciallver network all the way to the nal destinations. Thentages of the proposed model compared to the former

the accurate representation of both demand and sup-d the optimisation of distribution model. This model

ed for a single time-period SC and does not take intoon the inventory management aspect of a complex PD

d Wassick [84] presented a MILP capable of redesign-lanning an existing chemical supply network madection sites, an arbitrary number of echelons of distri-res, and customer sites. The mathematical model wasd by GAMS/CPLEX solver. Although a single-period SCs modelled by the authors and such crucial factors asanagement, backlogging of products at customer cen-tailed production cost elements were disregarded, thests are considered in more detail compared to thoseported in the literature.rated model was proposed for the collaboration amongies manufacturing multiple fuel products at different5]. Fuel products are transported from the reneries

distribution centres and from there to different targetINLP was proposed to formulate the objective function

the prot for the integrated SC. Three real world caseented in this study demonstrate the potential benetsom collaborative planning for production and distri-el products (19.7%. reduction in overall delivery costs

collaborative network planning).ompares the characteristics of Category 6 models.

le-product, multiple-plant, multiple-warehouse,d user, multiple-transport path, no-time period models

of multiplicity, this category contains the most com-s in the area of integrated PD planning. To the best of

variabldeveloworld propossumm

4. Sol

Forsearchhundremanufend-usspace discretoptimisation researc

TheniquesPD plnessesproblepreviosolutiomatica

4.1. M

Malinear relaxatbeen Prograels [22Relaxa

Mabe usesuch aming (world variablare intall thewhich relaxatconstrthe ob[99]. Ethat doare fulltion or

Thecal mo

1. Matthe cal a[26,withemad constraints. GA was used for the optimisation of themodel and numerical results were presented for a realium size case problem. The authors failed to test thepproach on solving large-scale case problems. Table 7s the characteristics of the sole model in this category.

-based classication

mplex realistic PD planning problem, the size of thee could become extremely large. In a real-life scenariof types of products may be manufactured in a set ofing plants and the nal products distributed to severalia a number of warehouses. In such cases, the searchnding the optimal PD plan may contain thousands ofnning options. For this reason, selecting an effectiven technique for solving a complex real life SC optimi-el is so vital and has always been a real challenge in past6].ey on the current literature indicates that many tech-e been proposed for the optimisation of an integratedach of these techniques has its own strengths and weak-can be helpful in solving certain types of PD planningable 8 summarises the solution approaches used in

odels to solve PD planning problems. These proposedhniques can be classied into four categories: mathe-

hniques, heuristics techniques, simulation, and GAs.

atical techniques

atical techniques include linear programming, non-amming, mixed integer programming, and Lagrangian[8789]. Different mathematical techniques haveted to solve SC problems. These include Linearg models [6467,72], Mixed Integer Programming mod-0,52,54,58,62,73,76,81,8385,9093], and Lagrangianodels [2,59,94,95].

atical programming models have been demonstrated toalytical tools in optimising decision-making problems

se encountered in SC planning [96,97]. Linear program- applicable when all of the underlying models of the realesses are linear [89,98]. MIP is used when some of the

the model are real values (fractional values) and othersvalues (0, 1). MILP occurs when objective function andtraints are in linear form, otherwise it is called MINLPch harder to solve [88]. The idea behind the Lagrangianethodology is to relax the problem by removing the

that make the problem hard to solve, putting them intoe function, and assigning a weight to each constrainteight represents a penalty which is added to a solution

ot satisfy the particular constraint. All these techniquestured and thus guaranteed to produce the optimal solu-

optimal solutions for a certain type of problem [26].e two issues that restrict the application of mathemati-g in solving complex real world SC planning problems:

atical equations are not always easy to formulate, andiated complexities in the development of mathemati-ithms increase as the number of constraints increases. Since most of the realistic SCs are complex in naturegh number of variables and constraints involved, math-

optimisation methods such as LP and MIP may not be

12B.

Fahimnia

et al.

/ Journal

of M

anufacturing System

s 32 (2013) 1 19








MultipleDCs

Multipleend-users





Inventorycosts


Dhaenens-Flipoand Finke,2001

TCM

. . . . . .

. . .

. . . . . . X . . . A MILP formulationsolved with CPLEX

Chen and Lee,2004

MO

. . . . . .

. . .

X . . .

A MINLP and a fuzzydecision-makingmethod to nd thedegree of satisfactionof multiple objectives

Lim et al., 2006 TCM

. . . . . .

. . .

. . . . . .

. . . A mathematical modelsolved using a supplychain simulationoptimiser (SCA)

Aliev et al., 2007 PM

. . . . . .

. . .

. . . . . . X . . . A fuzzy programmingmodel solved usingGAs

Selim et al., 2008 MO

. . .

. . .

X . . . . . .

A multi-objectivelinear programmingmodel solved with aFuzzy mathematicalprogrammingapproach

Kazemi, et al.,2009

TCM

. . . . . .

. . .

. . . . . . X . . . Comparing theperformance of aGA-based multi-agentapproach with theLagrangian relaxationapp.

Das andSengupta, 2009

MO

. . . . . .

. . .

. . . X X . . . A two-levelmathematical modelsolved with LINGO

Yimer andDemirli, 2009

TCM

. . . . . .

. . .

X . . . X

A GA based solutionprocedure is comparedwith the performanceof mathematicaltechniques

B. Fahim

nia et

al. /

Journal of

Manufacturing

Systems

32 (2013) 1 1913








MultipleDCs ware-houses)

MultipleDCs





Inventorycosts


Gunnarssonet al., 2007

PM

. . .

. . . . . . . . . . . . . . . A mathematical modelsolved using CPLEX

Ferrio andWassick, 2008

TCM

. . . . . .

. . . . . . . . . . . . . . . A MILP modelimplemented usingGAMS/CPLEX

Kim et al., 2008 PM

. . . . . .

. . . . . . . . . . . . . . . A MINLP model solvedusing GAMS/DICOPT


Author, year Dimensions of the proposed model Methods applied






MultipleDCs ware-houses)

MultipleDCs





Inventorycosts


Fahimnia et al.,2011

TCM

A MILP model solvedusing geneticalgorithms


Table 8Techniques and tools used for the development of PD optimisation models.

Techniques/

MathematicLinear pro

Mixed inte

Lagrangian

Heuristic tec

Simulation

Genetic algo

very effeFor this solving sited varia

2. Even if itlem intointractabmodel sifather ofCPU timealgorithmtechniquunless ov

4.2. Heuristic techniques

limitations of mathematical techniques as outlined in Sec- have forced the use of heuristics in nding feasible solutions

ge-scexpeercom. A hn thaen m

otherweveeredted

risticlemtools Authors

al techniquesgramming Chen and Wang (1997)

Kanyalkar and Adil (2005, 2007, 2008)Liang (2008)

ger programming Haq et al. (1991)Mohamed (1999)Dhaenens-Flipo and Finke (2001)Yan et al. (2003)Bhutta et al. (2003)Chen and Lee (2004)Demirli and Yimer (2006)Rizk et al. (2006)Gunnarsson et al. (2007)Paksoy et al. (2007)Tsiakis and Papageorgiou (2008)Kim et al. (2008)

Thetion 4.1for larerally and ovniquessolutioalso beusing are, hoconsidintegra

1. HeuprobFerrio and Wassick (2008)Selim et al. (2008)Hamedi et al. (2009b)Das and Sengupta (2009)Bilgen (2009)

relaxation Barbarosoglu and Ozgur (1999)Jayaraman and Pirkul (2001)Syam (2002)Nishi et al. (2007)

hniques Cohen and Lee (1988)Pyke and Cohen (1993, 1994)Ozdamar and Yazgac (1999)Yeh (2005)Yilmaz and C atay (2006)Coronado (2008)Tang and Yung (2004)

Lee and Kim (2000, 2002)Ritchie-Dunham et al. (2000)Jain et al. (2001)Williams et al. (2003)Yan et al. (2003)Moyaux et al. (2004)Sarker et al. (2005)Lim et al. (2006)Safaei (2009)

rithms Syarif et al. (2002)Chan et al. (2005)Gen and Syarif (2005)Altiparmak et al. (2005, 2006, 2007)Yeh (2006)Tasan (2006)Aliev et al. (2007)Park et al. (2007)Elahipanah and Farahani (2008)Kazemi et al. (2009)Yimer and Demirli (2009)Fahimnia et al. (2011)

ctive in solving real world SC planning problems [26,87].reason, mathematical techniques are only suitable formall to medium size PD planning problems with lim-bles and constraints.

is possible to translate an immense and difcult prob- mathematical equations, the problem would becomele or NP-Hard due to the exponential growth of theze and complexity [3,26]. According to Dantzig [98], the

linear programming, high computer memory and long is required in order to process complex mathematicals. This makes it almost impossible using mathematical

es to cope with large real-life PD planning problems,ersimplied.

not guarable to glems [10

2. In compheuristiceffectiveAlthoughto make efcienccharacte[104].

4.3. Simula

Simulatia real systeof changes sible solutiobe ideal forMany previmodelling i

Becausetodays SCsoperationalWhile this detailed sitof this methproblems [3

1. It is difcniques. Lof a simuof the deoptimal

2. It is costlresults. Ssive to pu(i.e. auto

4.4. Genetic

Introducegorised insimulate thGAs combinto achieve of the seareffective anmanufacturale SC planning problems. Heuristic methods are gen-rience-based techniques that help in problem-solvinge many shortcomings of traditional optimisation tech-euristic method is normally used to rapidly nd at is hoped to be close to the optimal solution. There haveany attempts in literature for solving PD problems

heuristic techniques [47,49,53,55,68,101,102]. Therer, two reasons why heuristic techniques are not always

as an effective method for the optimisation of complexPD plans:

techniques do not promise an optimal solution to the. As opposed to mathematical techniques, heuristics doantee the optimal solutions but are usually (not always)ive a good acceptable solution in solving complex prob-3].lex SC planning problems with vast search spaces,

techniques (e.g. Simulated Annealing) are not always in locating the global optimal or near optimal solutions.

the Simulated Annealing approach can often manageits way through the traps of local optima, its ability andy in exploring the search space is highly limited by itsristic of examining only one point of the space at a time

tion modelling

on modelling in the area of SCM is used to observe howm performs, diagnose problems and predict the effectin the system, evaluate SC activities, and suggest pos-ns for improvements [105]. Simulation techniques can

reproducing the behaviours of complex systems [105].ous studies have analysed the capability of simulationn SC modelling and optimisation [5,61,105121].

of many inuential sources of stochastic variation in, simulation can be a highly effective tool in makingly and economically sound business decisions [122].technique is capable of describing various real and

uations, the following can justify the limited applicationodology for the optimisation of complex PD planning,26]:

ult to search for an optimal value using simulation tech-ike heuristic techniques, the rst and primary drawbacklation modelling is its inability to guarantee optimalityveloped solution. In many cases, even nding the nearsolution cannot be guaranteed by this method.y and takes much time and effort to analyse the obtainedimulation software packages are generally very expen-rchase and very time-consuming to analyse the outputs-generated codes or reports).

algorithms

ed by Holland [123], GAs are stochastic algorithms cat- the class of general-purpose search methods whiche processes in a natural evolution system [12,124].e directed and stochastic search methods and are ablea good balance between exploration and exploitationch space [86]. GAs have been proven to be a highlyd efcient tool in solving complex engineering anding problems and some of their successful applications


in the optimisation of SC models have been proposed in literature[3,45,60,63,70,72,79,80,82,86,125129].

The advantages of using GA techniques for solving large optimi-sation problems are their robustness, searching exibility and theirevolutionarlarge, comptates this teby the convtions increaof solutionsis sought; hfor very larg

There arcustomised[136]. The technique iaffects the the problemchromosomcedures cancomplexitytomised gechromosomis generallyimplementa

5. Implicatoptimisatio

In this observationresearch gaenable the eral observoptimisatio

5.1. Catego

The classtant managpractitionerfollowing su

5.1.1. Categ Single-pro

research cic studyin modellsector spehave wide

Developmin monopprovider telecommsolitarineelling purproposedios arise. (1) Geogr

(e.g. menterpexpre

(2) Multipare lotres, f

industry. In such cases multiple objective functions arerequired to describe the goals of the network participants.

Advancement of transportation and warehousing technologiesin one hand, and the growing interest in working with external

portse oorks

warlem.majory anult t

of tht pars are

els fr few dons aappl

Ident may

ownnsideThernal pplymodt resying ast r

imp forceideriynam

nonliges iy tim

FuturCs grufactium eogre de

actermin

the m for aisedures

mucularcts oe is aabilismic al woer tost op

nera

re arsatioy nature [104,130]. GAs are principally able to searchlicated and unpredictable search spaces which facili-chnique to locate the optimal solution demonstratedergence of the tness function as the number of evolu-ses [26,123,131133]. A GA produces a large population, for each of which the evaluation of the tness functionence, a parallel computer is required when running GAe-scale optimisation problems [134,135].e, however, a number of challenges when designing a

GA procedure to solve a certain PD planning problemrst challenge in developing a GA-based optimisations to form the chromosome structure which accordinglywhole GA procedure. Based on the size and nature of, dissimilar PD planning problems require differente representations and therefore the existing GA pro-not be used to solve different problems from various

levels. The second difculty is the construction of cus-netic operators to perform the mating process on thees. Lastly, designing a constraint handling mechanism

a complicated task in order to ensure the effectivetion of the model constraints [86].

ions for the future of PD planning andn

section, based on our ndings, we rst outline thes and modelling implications at each category, discoverps, and highlight trajectories and trends which willidentication of future research directions. The gen-ations and managerial insights for PD planning andn is next highlighted in this section.

ry-based modelling implications

ication of literature presented in this paper has impor-erial and modelling implications for SC academics ands. The category-based implications are discussed in thebsections.

ory-based observationsduct PD models are not currently drawing much

attention unless they t the purpose in a sector spe-. For instance, single-product models are broadly useding gas networks and crude oil SCs. Apart from suchcic studies, multi-product PD models may generallyr real world applications.ent of single-plant PD models is still a requirementolistic markets in which a supplying rm is the soleof a certain type of product (a typical scenario inunication and media markets). In some other cases,ss of manufacturing plants can be a privilege for mod-poses in terms of simplifying the complexity of the

solution methodology. In real-life, two possible scenar-The difference between the two is distinguished thus:aphically dispersed rms operate under solo ownershipilitary logistics systems and international monopolyrises). Here, a unied objective function is able to

ss the overall system requirement(s).le manufacturers in different geographical locations

oked at as different entities with separate power cen-or example, this is typically the case in the automotive

transtive unetwor noprob

The binadifc

Mostinpuvaluemodonlyhorizbe in

5.1.2. A SC

theiris cober. the to suPD is no

Studthe petersmayconsIn a dand chanat an

5.1.3. As S

manmedone gfor thchar

Cost-beenneedhas rmeasmorepartiaspe

Therprobdynain rehardrobu

5.2. Ge

Theoptimi providers, and on the hand have facilitated the effec-f domestic and international warehouses in distribution. For this reason, there is only a small interest in singleehouse PD models, unless developed for a specic case

rity of the developed mathematical models containd integer variables which are easy to formulate buto solve.e existing models ignore the dynamic nature of the keyameters and for simplication purposes deterministic

applied as an alternative. This precludes the developedom functioning effectively in volatile environments. Theynamic models found in the literature use discrete timend discrete approximation of key input data which may

icable in many real world situations.

ied research gaps be owned by several entities, each aiming to increase

protability. In a broad picture, every member of a SCred as a customer of the immediate upstream mem-e are, however, end-users or end customers who arerecipients of the goods and services without the need

a subsequent SC participant. In most of the developedels the signicance of addressing customer expectationpected as the ultimate SC objective.continuous time horizons has received poor attention inesearch. The volatile nature of the critical input param-osing frequent changes in managerial decision-making

SC planners to use continuous time models instead ofng equal time intervals with deterministic parameters.

ic continuous time model (probably from non-convexnear natures which are substantially harder to solver),n key parameters and managerial decisions may occure during the planning horizon.

e research trendsow larger, more participants (and in particular moreurers) join the existing SCs. Besides newly establishedand large size enterprises generally have more thanaphically dispersed production facility. This would callvelopment of more multi-plant models simulating theistics of todays SCs.imisation and service-maximisation solutions haveost widely cited attributes in the current literature. The

staying continually attuned to customer expectations the importance of developing customer satisfaction

and models. This will require the development oflti-attribute (rather than multi-objective) techniquesly using fuzzy theory concepts to accommodate variousf customer expectations.

clear growing interest in the development of dynamic,tic and stochastic PD models. Despite the fact thatmodels are more realistic and hence more practicablerld scenarios, the solution techniques are considerably

develop requiring substantial efforts and creativity (i.e.timisation techniques).

l PD modelling implications

e also some overall implications for PD planning andn. These are highlighted in the following subsections.


5.2.1. General observations A vast amount of research (above 80% of all the published works)

has focused on the development of multi-product models whichcharacterise the nature of todays SCs.

Total costrespectedmance.

The incluels has benetworks

The use olar for forhas showrealistic S

5.2.2. Ident Prot max

tive funct Despite th

real worldmodels h

For simplcomponehas not be

Stack buffbefore shrarely beecase prob

5.2.3. Futur It may no

model mFuture reformulativeried oagility angreennessimpacts, elling of require stem requvariables

There is aand multpublishedtiplicity oare sectoparticular

Allowing transporttransportpast 5 yeaalternativport whentransporttrend of gcounties/

One peremisation for tacklinnumbers straints. are still GA and ibeen reco

heuristics techniques for handing real world optimisation prob-lems [60,70,80,86,126,129]. There is still a need to further extendthe effectiveness of the existing solution approaches and to testthe new arrivals such as Ant Colony Optimization (ACO) and Bee

ny Orapiemicip aist oationintermon riencip invcipanr mo

y thempacal an

clus

r thesatiodemig pro

plars to

This lD plariablptimre in

assieldcatioquesms.pite re sed uningdingt the

t fromning s (prstic r

in fpereapplems

sma mat

baseeverning ct tot be alit

the ortheres to

larg minimisation (TCM) has been recognised as the most performance measure for the evaluation of SC perfor-

sion of multiple DCs in the proposed published mod-en highly regarded for modelling real world logistics.f traditional linear programming is no longer popu-mulating PD planning problems. Linear programmingn to be incapable of describing the actual complexity ofC planning models.

ied research gapsimisation (PM) has rarely been considered a PD objec-ion.e urgent need of bi and multi-objective PD models in

scenarios, evidence suggests that multi-objective (MO)ave not received enough attention among academics.ication purposes, considering detailed production costnts, including the costs incurred at each machine centre,en studied extensively.ers (where products are stored in manufacturing plantsipment to warehouses and/or end-users in plants) haven used for modelling purposes (except for particularlems where it may t the purpose).

e research trends longer be enough to develop a single objective SC

inimising the overall SC costs or maximising prot.search should pay special attention to quantifying andng multiple objectives which may include traditionallybjective functions (e.g. cost, service level, just-in-time,d leanness) and contemporary objective functions for

and social sustainability (e.g. social and environmentalsafety issues and voluntariness). Mathematical mod-MO models is not always straightforward and mayubstantial time and effort to formulate multiple sys-irements when dealing with thousands of independentand constraints.

clear trend towards the development of multi-producti-plant PD models. Indeed, about 65% of all the

models for the period of 20002011 address the mul-f product types and manufacturing plants. Yet therer specic studies in which the PD models may have

characteristics that do not apply to other sectors.for multiple transport paths (i.e. direct and indirectation) and shipment modes (e.g. the use of trucks, air

and sea links) has become a new research trend for thers. The key encouragement for this trend is to addresse shipment costs as well as economies of scale in trans-

developing PD models. The consideration of multiple routes and modes is primarily motivated by the recentlobalisation and the opportunity to operate in multipleregions, popularly termed as multinational SCs.nnial concern in the context of SC modelling and opti-is the development of appropriate solution approachesg large real world PD planning problems with largeof continuous, integer and binary variables and con-Simulation, heuristics and meta-heuristic techniquesthe dominant solution techniques in the literature.ts extended version, Memetic Algorithm (MA), havegnised by several researchers as the most promising

Colo The

acadershconslimiting comexpeershpartione ostudthe itacti

6. Con

Oveoptimiby acagrowiners thesupplieusers. the Psion vaart in oliteratuThis clin the classitechniproble

Desthere aremainSC planOur nsugges

Aparplannariorealirated

One tion probwithfromedgeHowplansubjemighoptimnd to funiquwithptimization (BCO) techniques.dly increasing number of SC participants requiress and practitioners to pay special attention to SC own-nd power domination issues. Modern SCs generallyf several entities with pre-existing locations, capacitys and intellectual properties. This calls for facilitat--organisational collaboration which involves sharinggoals, prots, information, expertise, resources, ande. Although generally there might not be a sole lead-olved in the modern SCs, in some cases, one or moret(s) in the chain may have the dominant power overre other participants. Overall, future research needs to

increasing complexity of SC ownership and investigatect of power domination issues on the SC strategies atd operational levels.

ions and directions for future research

last two decades, the signicance of PD planning andn at tactical and operational levels has been recognisedcs and practitioners as a competitive advantage for theduction/distribution rms. An integrated PD plan cov-

nning of activities in a vast scope from raw material manufacturers and warehouses through to the end-arge planning scope with multiple chain players makesnning problem a complex problem with several deci-es and constraints. This paper reviewed the state of theisation modelling of PD plan. We classied the currentto seven categories based on the degree of complexity.cation could be of potential value to future researchers

and is also capable of further renements. A secondn was also presented in the paper based on the solution

used for tackling the proposed integrated PD planning

the growing interest in PD planning and optimisation,till several real world planning problems which havenaddressed. We encourage academics to investigate the

problems which may now only concern practitioners.s have some important implications for SC planners and

following directions for future research in the area.

some sector specic studies, most of the former PDmodels are only the oversimplication of real world sce-incipally due to the actual complexities of SC plans). Aange of variables and constraints needs to be incorpo-uture PD models.nnial concern is the development of appropriate solu-roaches for tackling large real world PD planning. Various solution techniques have been used to dealll and medium size PD planning problems ranginghematical models, heuristics, simulation, and knowl-d system, to the latest fuzzy programming and GAs.

, nding the optimal solution in a large real world PDproblem using simplistic techniques is impossible or

heavy computing overheads. Some approaches whichable to handle large problems are not able to prove they of the solutions found or do not have the potential toptimal solution on their own. Hence, there is a need

extend the effectiveness of the existing solution tech- be capable of handling realistic PD planning problemse numbers of variables and constraints.


Considering multiple performance measures in developingPD optimisation models allows the consideration of severalattributes in systematic decision-making [26,137]. The currentliterature requires quantifying and formulating multiple PD per-formanceobjective mental im

SC ownerlooked inneeds to ing command experesearcheination isoperation

The devemodels isthese resneed to uncertain

In line wronmenta[138]. Thiand socianies are cthe enviroThe literahoped tharequires tenvironm

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ang Tjectivckettropea

aj PS, Nol for92;23nsen Dmparperatiaq ANodel fonomtty SSated hemicndey

esign 07;26omasurnalir AMon netechanrmien

roductidal CJview peratioronadpply curnalonselaanspoibutioan Doistribuent 19rimventrol 08;35eixellitique05;41

asci Aesign. enguclanninesearceamonationarzi S,

uters ileijnenationaohlich

supp520

olweghanc02;78mini pport

the 2ula J, odels

Operidro

lanninanufahimntegrattions

han FTd dis

emirlioceedrocessilmaz lannin06;51 indicators including both traditional and contemporaryfunctions (e.g. cost, service level, social impact, environ-pact, and safety measures).ship and power domination issues have been over-

the past research. Inter-organisational collaborationbe accommodated in developing PD models for shar-on goals, prots, information, expertise, resources,

rience. The areas requiring more attention by eldrs include the impact of SC ownership and power dom-sues on the SC strategies/performance at tactical andal levels.lopment of dynamic, probabilistic and stochastic PD

currently followed by relatively few researchers. Whileearchers should continue holding the course, othersbegin moving towards addressing the volatility andty of the key input

a review and critique on integrated production distribution planning models and techniques

Documents

multipleend user

multipletransport path

product models

warehouse models

published pd planning

australia mawson lakes

selected models

future of pd planning