A Multi-objective SCOR-based Decision Alignment For Supply .

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Scientia Iranica E (2018) 25(5), 2807{2823Sharif University of TechnologyScientia IranicaTransactions E: Industrial Engineeringhttp://scientiairanica.sharif.eduA multi-objective SCOR-based decision alignment forsupply chain performance managementM. Rezaei, M. Akbarpour Shirazi , and B. KarimiDepartment of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Ave., Tehran, 15875-4413, Iran.Received 10 August 2016; received in revised form 8 April 2017; accepted 17 July 2017KEYWORDSMulti-objective;NSGAII;SCOR model;Decision alignment;Supply chain;Performancemanagement.Abstract. A dynamic integrated solution to three main problems through integratingall metrics using SCOR is proposed in this research. This dynamic solution comprisesstrategic decisions in high level, operational decisions in low level, and alignment of thesetwo decision levels. In this regard, a human intelligence-based process for high-leveldecisions and machine-intelligence based Decision Support Systems (DSSs) for low-leveldecisions are proposed using a novel approach. The presented operational model considersimportant supply chain features thoroughly, such as di erent echelons, several suppliers,several manufacturers, and several products, during multiple periods. A multi-objectivemathematical programming model is then developed to yield the operational decisions withPareto e cient performance values and solved using a well-known meta-heuristic algorithm,i.e., NSGAII, the parameters of which are tuned using Taguchi method. Afterwards, anintermediate machine-intelligence module is used to determine the best operational solutionbased on the strategic idea of the decision maker. The e ciency of the proposed frameworkis shown through numerical example and then, a sensitivity analysis is conducted forthe obtained results so as to show the impact of the strategic scenario planning on theperformance of the considered supply chain. 2018 Sharif University of Technology. All rights reserved.1. IntroductionTo make agile, responsive, sustainable, robust, e ective, and competitive Supply Chain (SC), we needto employ all models and technologies that ensurepro tability and stability. In this regard, Supply ChainManagement (SCM) decisions are categorized into twolevels in this research, i.e., human-intelligence andmachine-intelligence based decisions, based upon theirnature. We develop a process-based method for high*. Corresponding author. Tel.: 98 21 64545370;Fax: 98 21 66954569E-mail address: akbarpour@aut.ac.ir (M. AkbarpourShirazi)doi: 10.24200/sci.2017.4463level decisions, a multi-objective method for low-leveldecisions, and an intermediate multi-objective methodfor aligning high- and low-level decisions using a novelapproach.Due to SCM resource constraints, only a limitednumber of objectives are able to take high priorities [1].We employ a prioritization method to deal with themulti-objective problem in the strategic level. Thispaper aims at two main objectives: (1) improvingthe Supply Chain Performance Management (SCPM)by aligning di erent decision levels in the integratedprocess of transforming strategies into operationalprograms; and (2) improving the SCPM by usingappropriate decision-making models in each level.Performance management is a necessity for organizational competitiveness [2]. It determines whatmust be maintained as the strong point and what

2808M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823needs to be overcome as the weak point [3]. Theimportant aspect that has impacts on the success ande ciency of optimization models is to design suchmodels based on reliable performance indicators. Supply Chain Operations Reference (SCOR) model is oneof the important models in performance managementthat contains major processes, metrics, and standardcharacteristics [4]. The SCOR model divides majormetrics into many partial indicators at lower levels.Although the main goals of SCPM are pursued atthe strategic level, the activities that directly createvalue-added products and services are involved inthe operational level [5]. Therefore, the alignmentof decisions is an important matter that should beinvestigated [6]. However, most of the researches inthe literature consider that the decisions at di erentlevels of SC are independent. As an attempt toll the mentioned gaps, an SCOR based frameworkfor measuring, evaluating, and improving SCPM isproposed in this research.The remainder of this paper is organized asfollows. Section 2 presents a summary of recent andmajor studies carried out on SCPM. In Section 3, themain new framework of SCPM is described. Solution approach is presented in Section 4. Section 5comprises problem description, in which a sampleSC is illustrated. Techniques and tools used in thisresearch are explained in Section 6. Experimentaldesign is explained in Section 7. Section 8 discussescomputational results, in which illustrative tables andgures are presented. Finally, Section 9 providesthe conclusions by discussing the advantages of theproposed framework and further research areas as well.2.2. Concepts2. Literature survey2.1. Review papers2.3. Mathematical modelsBecause of the importance of SCPM, signi cant studieshave been conducted on this topic and many modelshave been developed so far. In this regard, Estampeet al. (2013) classi ed and discussed the most important frameworks for performance management ina review paper [7]. They de ned ve levels for SCmaturity grid at rst and then compared 16 frameworksincluding type of usage, conditions and constraints,degree of conceptualization, and established indicators.They also presented the applications and limitations ofthe selected frameworks. Singh and Acharya (2014)investigated the e ective factors on the performanceof SC [8]. Schaltegger et al. (2014) carried out astructured review of the existing literature and researches in the eld of sustainable SC's measurementand improvement [9]. A systematic literature reviewof SCOR model applications with special attention toenvironmental issues was carried out by Ntabe et al.(2015) [10].Performance measurement provides important measures and tools for assessing the outputs and makes theoverall improvement in SC [9]. One of the key elementsin an e cient and pro table SCM is to employ an e ective performance measurement system [11]. Kocao gluet al. (2013) emphasized the structural integration ofperformance measurement and quanti cation of modelsfor selecting SC strategies [12].SCPM is an important issue in the competitivebusiness environments and plays a vital role in de ningthe objectives, evaluating the results, and determiningthe future measures. Because of the importance ofSCPM, signi cant studies have been conducted on thistopic and many models have been developed so far. Inthis regard, Estampe et al. classi ed and discussed themost important frameworks for performance management in a review paper [7].Flexibility, output, and resources are the three important aspects of SC performance [13]. However, Gunasekaran et al. classi ed the performance metrics intostrategic, tactical, and operational levels [14]. Someresearches presented administrative frameworks andstep-by-step methods for performance improvement.Cai et al. introduced a framework for performancemanagement and proposed a new approach for selectingkey performance metrics (KPIs) in strategic level [15].Elgazzar et al. suggested a performance assessmentframework based on a nancial approach using SCORmodel and Analytic Hierarchy Process (AHP) [16].Agami et al. proposed a performance improvementmodel to determine the bottleneck of KPIs using asuccessive ve-step process [11].A given SC has a multi-level, multi-criteria, andinterrelated structure in which the performance improvement of one unit does not clearly assure theoptimized performance of the whole SC [17]. Agamiet al. developed a fuzzy model so as to identify thecritical KPIs [18]. In this regard, Blanco presentedan Integer Linear Programming (ILP) model includingthree objectives and extended a solution approach forsolving the studied problem [19]. Liu and Papageorgiou presented a multi-objective Mixed Integer LinearProgramming (MILP) model to optimize a multiperiod problem dealing with production, distribution,and capacity planning in an SC in process industries[20]. Hamta et al. developed a hybrid Particle SwarmOptimization (PSO) algorithm for a multi-objectiveassembly line balancing problem with exible operationtimes, Sequence-Dependent Setup Times (SDST), andlearning e ect [21]. Kolahan and Kayvanfar developeda heuristic algorithm approach for scheduling of multicriteria unrelated parallel machines [22].Celik et al. developed a solution method using

M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823the Genetic Algorithm (GA) to solve a multi-periodreal-time model [23]. High usability and excitingphilosophy of Goal Programing (GP) for practitionersand researchers in handling decision-making problemswith multi-objective structures made it very applicable[24,25]. In [26], an interactive GP model was createdfor virtual manufacturing cells procedure, while Mahdavi et al. (2011) developed a fuzzy GP method forsolving a multi-objective model of production planningin a virtual manufacturing system [27].Wong developed a Decision Support System(DSS) using fuzzy logic based on expert judgmentsto select 3PL [28]. Xu et al. proposed a multiobjective model to optimize a multi-period SC withstochastic demand using a fuzzy method [29]. Cai et al.developed a multi-objective optimization model basedon SCOR indicators and solved the problem using PSOalgorithm [30].2.4. SCORDesigning the models based on reliable performanceindicators is one of the most important aspects a ecting the success and e ciency of optimization models.SCOR model is the performance assessment framework in the literature that provides the mentionedcomprehensiveness and reliability to respond to ourconcerns. Zhang and Reimann used ve high-levelindicators of SCOR, simultaneously, to optimize SCperformance and proposed a ve-objective multi-periodmathematical model for planning a two-echelon SCwith deterministic demand by applying customizedindicators [31]. Kocao glu et al. presented a multiobjective model to align the operational decisions withthe strategic decisions using SCOR framework [12].They determined the relative importance of di erentstrategies using AHP and the hierarchical structure ofSCOR and then selected the best scenarios in whichSC performance was optimal by applying Techniquefor Order of Preference by Similarity to Ideal Solution(TOPSIS) method.2.5. Research gapDespite devoting many e orts over the past decade,there are still gaps in this area and, owing to someshortcomings, the capabilities of SCPM frameworks arenot adequate [12,32]. Obviously, one element is notable to optimize the whole SC. The question is how wemust manage such complex system to be able to achievecontinuous and acceptable productivity [33]. Attainingappropriate optimization approach and continuous improvement as well as proper guarantee of them throughthe SC is the critical issue that should be addressedin di erent levels of SC studies [34]. Managementstrategies should be designed based on the changingconditions of the market [35]. In many studies,di erent parts of the SC are assumed independent2809and their internal relations and changing behaviors arenot considered. In addition, there are some defectsin analysis of feedback in design and implementationstages in order to adapt the behavior of SC for theenvironmental changes [36]. Many of the studies arenot comprehensive enough and cannot evaluate andimprove the performance based on the performanceindicators. Static nature of some proposed systemsfor performance evaluation is one of the critical issues.The proposed quantitative models mostly focus onindividual factors such as scal measures to assess SCperformance [37]. The problem is how we can modeland analyze the strategic and operational objectives,and connect them to each other appropriately [12].According to Wang et al. [38], despite the abilityof SCOR to provide appropriate indicators, it hasnot been used enough in the literature. Accordingto the recommendations in the literature, it is betterto employ comprehensive and reliable indicators suchas SCOR to develop the mathematical models forperformance management [39].In conclusion, with respect to the importance ofSCPM and mentioned de ciencies, more studies haveto be carried out to cover these research gaps. Finally,the main problems and defects are presented accordingto the literature. It can be claimed that most of thecurrent studies su er from one or more of the followingshortcomings: Limited number of studies on the combination ofrelated concepts (keywords of this paper) and takingadvantage of their synergies;Inability to support the continuous improvement;Local optimization;Lack of comprehensive and acceptable performanceevaluation models.As an attempt to ll the mentioned gaps, anSCOR based framework for measuring, evaluating, andimproving SCPM is proposed in this research. Thepresented framework is comprehensive, dynamic, andcontinuous. It applies sciences, techniques, and tools,namely, SCPM, strategic planning, multi-objectiveoptimization, and SCOR model, to a new SCPM.3. A SCOR-based dynamic SCPM frameworkTo design an integrated SCPM structure, SCOR modelhas been used. The SCOR model divides majormetrics into many partial indicators at lower levels.Given the hierarchical structure of SCOR, achievinghigher values for performance indicators at any levelenables better performance through the entire SC.This detailed structure enables us to design acceptableand comprehensive multi-objective functions. Figure 1shows the new SCPM proposed in this study.

2810M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823Figure 1. The logical design for integrated SCOR-based SCPM framework.Figure 2. The human-intelligence based decision-making.Given such adaptive approach, we assume thatall internal and external changes a ecting decisionsare detected and proper responses for these events arethen presented. Therefore, for adaptation to the latestchanges, related decisions will be updated. In otherwords, event-driven policy is used. Based on the natureof events and type of decisions, the new de nitionproposed in this paper categorizes decisions into twogroups. The rst category is human-intelligence baseddecisions. Such decisions are taken at the highest levelof SCPM and in uence all the lower levels. The secondgroup of decisions is machine-intelligence based deci-sions. These decisions are less complex than humanintelligence ones and more structured. Typically,problems such as inventory control, and production anddistribution planning are considered at this level.A process model is usually used for decisionson strategy planning in the literature, which onlymatches the capabilities of human intelligence [11]. Inthis paper, a speci c process is developed for humanintelligence based decisions. The main phases of theproposed process of human-intelligence based decisionmaking are illustrated in Figure 2.The rst phase (P1) de nes the strategic objec-

M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823tives. In this step, we employ a prioritization methodto deal with the multi-objective problem. In thesecond phase (P2), the current performance of eachmetric is evaluated and the gap between actual andtarget values is measured (according to Table 1). Inthe third phase (P3), the results of operations andanalysis of metrics are demonstrated in a dashboardto determine which performance metric does not meetpredetermined expectations. Such metrics are identi ed as performance bottlenecks. The performanceresults which are the \operational level's output" haveimpact on strategic design of the next level. In thenal phase (P4), according to the results, managementtakes appropriate measures to improve and achievehigher levels of performance metrics in subsequentoperations.Table 1 employs the rst level of SCOR's metricsand shows the analysis of the current condition, thestrategy setting, priority of performance objectives,and the gap between current condition and targetvalue. First, numerical column shows the currentcondition of the SCPM. The next three columns showthe benchmark values of each metric in three levels, i.e.,parity, advantage, and superior [40]. Grey cells indicatethe priority of each of the ve objectives. Finally, thelast column shows the gap between current conditionand target value. Once Table 1 is set, a new strategicplan can be designed. By determining the SC objectivepriorities, all plans and programs are designed usingthese priorities while we try to ll the gap. This is themain approach to align all SCPM decisions.To deal with operational planning problems, wecan develop DSSs using machine-intelligence. Allquantitative models including Linear Programing (LP),Non-Linear Programing (NLP), fuzzy, meta-heuristic,simulation, deterministic, stochastic, or a combinationof them can be used at machine-intelligence level.Once any change or update comes up on decisionmaking modules in the strategic and operational levels,an intermediate decision-making module is updated toalign high- and low-level decisions (Figure 3). In thiscase, the module selects a solution from the Paretooptimal solutions provided by the mathematical modelat the low level which has the highest alignment withthe strategic objectives of SCM. This module has2811Figure 3. The relationship between human- andmachine-intelligence based decisions.been developed on the basis of machine intelligence.In this case, the multi-objective function of operational plan should be adjusted according to strategicgoals and priorities. Fuzzy and TOPSIS approachescould be employed so as to develop this module aswell.4. Solution approachAny change in parameters will be detected as a newevent and, therefore, will cause change in inputs ofthe decision model. Consequently, the optimizationmodel is run again in the correspondent level and thebest decision will be updated. Then, the decisionsin all levels will be aligned with each other using theappropriate decision models.4.1. Levels of decisionStrategy setting: First, the SC's priorities are de-termined. For some objectives, worse values than thecorresponding single-objective optimum values mightbe considered. In such a condition, accessibility to solutions with higher values for higher priority objectivesTable 1. Determining the strategy and objectives of SCOR [40].

2812M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823increases. In another situation, similar to what is explained in Table 1, one can consider the least acceptablevalues for \Advantage" and \Parity" objectives andoptimize one of the objectives as \superior" at the mostpossible value. Each of these approaches is a di erentstrategic scenario, which could be taken in high levelof SC and applied to the lower levels. The multiobjective mathematical model is initially separated intothe single-objective problems. In other words, in orderto obtain the best possible value for each objective, oneshould optimize each objective separately. By doing soand setting the SC's priorities as described above, theideal solutions are obtained, which will then be usedby TOPSIS method (Machine decisions or operationaldecisions).Operational decisions: On the other hand, in thesecond step, the multi-objective problem is solved inparallel with NSGAII algorithm to achieve the feasiblesolutions to the entire problem regarding all constraints. These solutions are not optimum with respectto the obtained optimum values from the rst step.The solutions gained at this step are sorted based onnon-domination method and the best Pareto solutionscould be chosen by the decision maker (Operationaldecisions).Decisions alignment: Finally, in the third step,we need to align the strategic decisions with theoperational ones. To do so, the Pareto set solutions areused in TOPSIS method, as a multi-criteria decisionanalysis, to yield the best compromise solutions whichsatisfy the di erent objectives to the possible extent.Actually, TOPSIS compares the gained feasible solutions of Pareto set with the ideal solutions. In otherwords, TOPSIS stands on the concept that the selectedalternative should have the shortest geometric distancefrom the positive ideal solution while there should bethe longest geometric distance from the negative idealone.5. Problem formulationIn order to demonstrate how the new proposed framework performs, a sample SC is suggested and a numerical example is then solved and described to showthe e ciency of the proposed approach. Suppose atwo-echelon SC including several suppliers and manufacturer. Several products of a family are produced inthis SC and planning is accomplished during multipleperiods. A multi-objective multi-period two-echelonmathematical model for the considered SC is proposedin this section. The other assumptions are summarizedas follows: The parameters in each period are assumed to be known, deterministic, and xed throughout theplanning periods;The objective of the proposed model is to minimizethe total cost of logistics and maximize the agilityand reliability in the considered SC, simultaneously;In each period, demands are given and determined;Both xed and variable transportation costs fromsuppliers to manufacturers are considered.5.1. The mathematical modelNotationsIndicesINumber of suppliers;JNumber of plants;LNumber of products;NNumber of materials;TNumber of periods;ParametersDljtThe demand of product l from plant jin period t;UrnlThe amount of material n to produceone unit of product l;CapsnitCapacity of supplier i to supplymaterial n in period t;CappljtCapacity of plant j to produce productl in period t;V mrjThe volume of raw materials at plantwarehouse;V mpjThe volume of the nished product atplant warehouse;P cljProduction cost of one unit of productl (with the exception of raw material)by plant j ;P rniPrice of material n determined bysupplier i;HmrnjInventory holding cost of material n atplant j ;HmpljInventory holding cost of product l atplant j ;QplRequired space per unit of product l;QrnRequired space per unit of material n;F crnijFixed transportation cost for handlingmaterial l from supplier i to plant j ;V crnijTransportation cost for handling a unitof material l from supplier i to plant j ;T drnijtDelivery time of a unit batch ofmaterial n from supplier i to plant j inperiod t;T rmaxnijt Due date for delivering a unit batchesof material n from supplier i to plant jin period t;

M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823Batch size of material n at supplier i;Safety stock of material n at plantwarehouse j in period t;CblljBacklog unit cost of product l in plantj in period t;Maximum backlog amount of productljtl at plant j in period t (percent ofunsatis ed demand);Decision variablesXnijtAmount of supplied material n bysupplier i to plant j in period t;YljtAmount of produced product l byplant j in period t;IRmnjt Inventory level of material n at plant jat the end of period t;IpmljtInventory level of product l at plant jat the end of period t;T RnijtReceiving time of material n fromsupplier i by plant j in period t;Wnijt1, if plant j orders material l fromsupplier i in period t; 0, otherwise;BLgljtBacklog level of product l at plant j inperiod t;Sale amount of product l at plant j inQljtperiod t;Objective functionsTCThe cost of supply chain;T Cs (Cost)The costs of the suppliers;T Cp (Cost)The costs of the plants;Ag(Agility)Flexibility: Surplus capacity;Ags(Agility) Flexibility: Surplus capacity ofsuppliers;Agp(Agility) Flexibility: Surplus capacity of plants;Rel(Reliability)Perfect order ful lment;BsmniSSmnjtMathematical modelMinimize TC (Cost)T C T Cs T Cp ;T Cs (1)XXXXt nijXnijt :P rniXXXXtnijXXXXtniXXXtnjjWnijt :F crnijXnijt :V crnijHmrnj :IRmnjt(2)T Cp XXXt jlYljt :P cljXXXtjlXXXtjl2813Hmplj :Impljt(3)Cbllj :BLgljt :Maximize Ag(Agility)Ag Ags Agp;Ags Agp (4)XXXtniXXXtlj0@CapnitCapljtXj1Xnijt A;Yljt :(5)(6)Maximize Rel(Reliability)Rel XXXtljReltlj ;Reltlj Yljt IpmljtReltlj Dljt8l;j and 8t 2 [1; T ] ;8l;j and 8t 2 [1; T ] :(7)(8)(9)The rst main objective minimizes total costs ofsystem, including costs of suppliers and manufacturers(Eq. (1)). Supply costs (Eq. (2)) comprise raw materialcosts, xed transportation costs of raw materials andvariable transportation costs of materials to facilities,and holding cost of raw materials at plants in eachperiod. Eq. (3) signi es production costs includingmanufacturing costs, holding costs of nished productsat plants, and backlogged costs in each period. Thesecond main objective maximizes the system agility(Eqs. (4)-(6)). The most signi cant metric to measureagility of an SC is exibility, which re ects the abilityof reacting to external in uences. According to Sabriand Beamon (2000) [41], exibility could be measuredthrough surplus capacity. In this paper, in order toevaluate exibility, the maximum extra demand, whichcould be satis ed through surplus capacity of the SC,is considered. The third main objective maximizesreliability of the system. Reliability could be de ned asability of satisfying customer demands on time with theright quantity. Perfect order ful llment could be calledthe rst-level metric of reliability (Eq. (7)). The perfectorder ful llment depends on the minimum of productsavailable (Eq. (8)) and demands (Eq. (9)) in the sameperiod. The applied constraints of the considered SCare as follows:

2814M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823Subject to:Inventory levelNote: Inventory in the initial time period (period 0) iszero:IRmnjt IRmnj;t 1 XiXnijtXlUrnl :Yljt ;8t;n;j ;(10)IP mljt IP mlj;t 1 YljtIRmnjt SSmnjt ;Qljt ;8t;l;j ;8t;n;j ;(11)(12)Volume warehouseXnXlQrn :IRmnjt V mrj ;8t;j ;Qpl :Ipmljt V mpj ;(13)8t;j :(14)Product capacityXjXnijt Capnit ;Yljt Capljt ;8n;i;j;t ;(15)8l;j;t :(16)Delivery timeT drnijt (Xnijt /Bsmni ) T rmax;nijt8n;i;j;t ;(17)where:T drnijt :Xnijt /Bsmni T Rnijt ;8t;l;j :(18)Backlog demandBLgljt BLglj;t 1 DljtBLgljt 8t;l;j ;8t;l;j ;ljt :Dljt ;Qljt BLgljt ;DljtQljt ;8t;l;j :(19)(20)(21)LogicalWnijt :M1 Xnij ;Wnijt 2 f1; 0g ;M1;A very big number ;8n;i;j ;(22)(23)Xnijt ; Yljt ; IRmnjt ; Ipmljt ; T Rnijt ; Wnijt ;BLglt ; Qljt 0;8n;l;i;j :(24)Constraint sets (10) and (11) de ne the inventorybalancing equations for raw materials and nishedproducts at the warehouses of the manufacturer, respectively. Constraint (12) demonstrates the balance ofraw material safety stock at the warehouse of the manufacturer. Constraints (13) and (14) specify the limitedstorage spaces of raw materials and nished products atthe warehouses of the manufacturer, respectively. Therow material capacity of each supplier for each materialin each period is ensured through Constraint (15).The production capacity of each manufacturer for eachproduct in each period is ensured through Constraint(16). Constraints (17) and (18) deal with on timedelivery and guarantee the limited delivery time forthe manufacturers. Constraint (17) shows that thedelivery time of raw materials by suppliers is lessthan the maximum acceptable time determined bymanufacturers. Constraint (18) demonstrates deliverytime of raw materials from suppliers to manufacturersin each period. Constraints (19)-(21) are concernedwith the amount of backordered demand. In thiscontext, Eq. (19) shows the balance of backorderednumbers of products in any two consecutive periods.Constraints (20) and (21) demonstrate the boundaryof backordered amounts of each product with respectto its demand for the manufacturers. Constraint (22)ensures that the supplied raw material n will bedelivered to manufacturer j from supplier i if and onlyif the corresponding supplier is established. Finally,Constraints (23) and (24) show the binary variablesand non-negativity constraint, respectively.6. Technique and tools6.1. Non-dominated sorting geneticAlgorithm IIOptimization of con icting objectives could be investigated in terms of multi-objective optimization.Evolutionary Algorithms (EAs) are potent stochasticsearch methods which mimic the Darwinian principlesof natural selection and are adequate to solve optimization problems with large search space (Anagnostopoulos and Mamanis, 2010). Up to now, numerousMulti-Objective Evolutionary Algorithms (MOEAs)have been suggested in the literature. Non-dominatedSorting Genetic Algorithm II (Deb et al., 2002) [42]is one of the most commonly used multi-objectivealgorithms among researchers. In this research, ane ort is made to apply NSGAII to the considered multiechelon SC problem.6.2. Solution representationIt is obvious that all demand values are integer and positive. In order to represent di erent points of solutionspace, a general structure with capability of showingdi erent variables is used. This matrix-based structurehas a dimension of 2 . Since decision variables of theconsidered problem are more than one, there are di er-

M. Rezaei et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2807{2823ent matrices with di erent values of . For example,Xnijt is four-dimensional variable and represents N I J T . The contents of the rst and second columnsindicate \the value of this variable in that point" and\variable index," respectively. As an instance, 27'denotes that the number of 27 units of material n aresupplied by supplier i to manufacturer j in period t. Asimilar structure with di erent dimension is employedfor the rest of variables, such as I

the operational level [5]. Therefore, the alignment of decisions is an important matter that should be investigated [6]. However, most of the researches in the literature consider that the decisions at di erent levels of SC are independent. As an attempt to ll the mentioned gaps, an SCOR bas

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