Research ArticleSupply Chain Network Optimization Based onFuzzy Multiobjective Centralized Decision-Making Model
Xinyi Fu and Tinggui Chen
School of Management Engineering and Electronic Commerce, Zhejiang Gongshang University, Hangzhou 310018, China
Correspondence should be addressed to Tinggui Chen; [email protected]
Received 17 October 2016; Accepted 19 January 2017; Published 5 March 2017
Academic Editor: Anna M. Gil-Lafuente
Copyright ยฉ 2017 Xinyi Fu and Tinggui Chen. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.
Supply chain cooperation strategy believes that the integration of the operation process can produce value for customers, optimizethe supply chain of the connection between the vertical nodes, and constantly strengthen the performance of the advantages, so as toachieve mutual benefit and win-win results. Under fuzzy uncertain environment and centralized decision-making mode, we studymultiobjective decision-making optimization, which focuses on equilibrium and compensation of multiobjective problems; that isto say, the proper adjustment of the individual goal satisfaction levelwillmake other goalsโ satisfaction levels change greatly.Throughcoordination among the multiobjectives, supply chain system will achieve global optimum. Finally, a simulation experiment fromShaoxing textile case is used to verify its efficiency and effectiveness.
1. Introduction
If we take the supply chain network as a system to study,its involved scopes include cooperation relationship, logisticsmanagement, information flow management, enterpriseโsstrategy formulation, tactical arrangement, and operationexecution. The essence of effective supply chain networkoperation is a multiobjective optimization process under theconstraints of internal and external factors [1]. These objec-tives include speed, flexibility, quality, cost, service, and otherindicators according to actual situation. Because of differentnatures of supply chain networks, the target selection and theweight settingwill be very different, which is closely related tothe organization ways, decision structure, and decision-making model of supply chain networks [2]. Therefore, themultiobjective optimization of the supply chain network isalso the decision-making optimization process.
Inventory management has always been a focus in supplychain management. Kacprzyk and Stanieski [3] and Park [4]were the first to introduce fuzzy mathematics into inventorymanagement and extend the classical EconomicOrderQuan-tity (EOQ) model to the fuzzy inventory model under thecondition of ordering cost and holding cost being fuzzyvariables. Sadeghi et al. [5] developed a constrained VMI
model with fuzzy demand for a single-vendor multiretailersupply chain, in which the centroid defuzzification methoddefuzzifies trapezoidal fuzzy numbers of the demand. Janaet al. [6] proposed some multi-item inventory models fordeteriorating items in a random planning horizon underinflation and time value money with space and budget con-straints. In addition, the models were illustrated with somenumerical data and results for different achievement levelswere obtained and sensitivity analysis on expected profitfunction was also presented. Mahata and Goswami [7] con-sidered inventorymodels for itemswith imperfect quality andshortage backordering in fuzzy environments by employingtwo types of fuzzy numbers, which were trapezoidal andtriangular, and two fuzzy models were developed. Finally,numerical examples were provided in order to ascertainthe sensitiveness in the decision variables with respect tofuzziness in the components. De and Sana [8] dealt with abackorder EOQ model with promotional index for fuzzydecision variables and a graphical presentation of numericalillustrations and sensitivity analysis were done to justify thegeneral model. Giannoccaro et al. [9] proposed a fuzzyechelonmethod to solve the inventorymanagement in supplychain. Ouyang and Yao [10] set up a hybrid inventory model,where the annual demand quantity was fuzzy variables and
HindawiMathematical Problems in EngineeringVolume 2017, Article ID 5825912, 11 pageshttps://doi.org/10.1155/2017/5825912
2 Mathematical Problems in Engineering
lead time was a variable. Hsieh [11] studied the optimizationof fuzzy production inventory model.
The application of fuzzy mathematics in the productionmanagement was first studied by Chanas et al. [12] whoused it in the transportation problems. Besides, consideringthe premise of the customer demand quantity and externalsupplied quantity be discrete fuzzy variables, Petrovic etal. [13, 14] determined the order quantity and the lowestsafety stock of the node enterprise so as to optimize theoperation of the whole supply chain, through taking thesatisfaction rate of cost and indent as the control target.Giannoccaro et al. [9] established the multistages inventorystrategy to set up a reasonable inventory safety level in orderto make the material of the whole supply chain hold thelowest cost, when market demand and inventory holdingcost were fuzzy variables. Kannan et al. [15] presented anintegrated approach, of fuzzymultiattribute utility theory andmultiobjective programming, for rating and selecting the bestgreen suppliers according to economic and environmentalcriteria and then allocating the optimum order quantitiesamong them.
With the increasing integration of fuzzy theory andoperations research, fuzzy programming is evolving fromsingle-objective to multiobjective, from single layer to mul-tilayer, and from single stage to multistage. Chen and Lee[16] study the multiobjective optimization problem of mul-tilevel supply chain network under the condition of productdemand and price being uncertain. Lin et al. [17] set up afuzzy multiobjective integrated production planning modelin the steel industry. Aliev et al. [18] developed a fuzzymultiobjective and multiproduct supply chain productionand distribution model and used genetic algorithm to solveit. The experimental simulation demonstrated its efficiencyand effectiveness. Rinks [19] used fuzzy logic method todevelop the supply chain integrated production and planningmodel and problem-solving algorithm. Lee [20] establishedthe fuzzy objective function of the single product integratedproduction plan in the different time stage. Gao et al. [21]used fuzzy reasoning Petri nets to establish a decision analysissystem based on the electronic network supply chain. Finally,a comparative study on Pareto optimality and optimalityunder Lagrangeโs interpolating polynomial function had beenmade illustrating numerical example. Other similar litera-tures are as follows: interactive multicriteria fuzzy intensiveproduction plan [22], double level optimization model forsupply chain distribution system [23], production batchplanning method with fuzzy capacity constraints [24], fuzzymultiobjective order allocation model, and so on [25].
This paper mainly studies multiobjective coordination ofsupply chain network under a fuzzy uncertainty environmentand also explores the centralized decision-making methodof multiobjective coordination of supply chain. The maincontents in the paper focus on the optimization of mutualcompensation in fuzzymultiobjective decision-making, so asto get the global optimization and determine the supply chainoptimization subnet in this state.
The rest is organized as follows: in Section 2, cen-tralized decision-making mode and fuzzy multiobjectiveanalysis of supply chain are discussed. Section 3 proposes
fuzzymultiobjective coordinated optimizationmethodunderthe centralized decision-making method. Subsequently, themodel is applied to a Shaoxing textile supply chain networkand some discussions on the obtained results are also givenin Section 4. Section 5 offers our concluding remarks andpotential extensions of this research.
2. Centralized Decision-MakingMode and Fuzzy Multiobjective Analysis ofSupply Chain
2.1. Centralized Decision-Making Mode of Supply Chain.Supply chain centralized decision mode refers to the advan-tage enterprises in the supply chain network with powerfulstrength, through the effective integration of informationexchange system to integrate the other node enterprises in thesupply chain network into a unified system for highly central-ized decision-making and control management. Advantageenterprises eliminate antagonism between upstream anddownstream enterprises, enhance the ability to resist risks,and achieve the mutual benefits and win-win of partners,through strengthening effective integration management ofraw material supply, product manufacturing, distribution,and the whole sale process control [26]. In the centralizeddecision-making mode of the supply chain, the coordinationof the multiobjective tasks can be realized through theeffective control or influence by the unified decision-makinglayer, so as to improve the core competitiveness of the supplychain.
Multiobjective optimization of supply chain network ismutual coordination of the related steps in the objectivefunction or the node enterprises. The supply chain networkconstruction and optimization studied in this paper belongto the initial stage of supply chain network formation,and multiobjective selection needs to consider the wholesupply chain, because the more objectives the optimizationproblem has, the greater the difficulty is. As a result, acomplex supply chain multiobjective problem has difficultyin obtaining global optimization and can only achieve to thepractical feasible solution after collaboration of all partiesunder practical constraints. Three objectives of optimizedinvestment, setting cost, and satisfaction of customer serviceare considered at the same time when the production costsand node enterprises are into the optimization sub to operate.
2.2. Relevant Parametersโ Definition of Multiobjective Analysisin the Centralized Decision-MakingMode of Supply Chain. Inorder to simplify the supply chain multiobjective model, thefollowing assumptions are made:
(1) Locations of all nodes and various facilities in thesupply chain network and the location are known.
(2) All node enterprises in supply chain network are fullycooperative ones and share information with eachother.
(3) Do not consider the delay and lead time in the processof transportation, production, and distribution.
Mathematical Problems in Engineering 3
ยทยทยท
ยทยทยท
ยทยทยท
ยทยทยท
ยทยทยท
ยทยทยท
ยทยทยท
Polyester factory Distributor Customer
Material flow
0 1 2 3 4 5 6
Information flow
Chemical ๏ฟฝberfactory
Weavingenterprise
Dyeing and๏ฟฝnishing enterprise
Clothing machiningenterprise
Figure 1: Hierarchical structure of textile supply chain.
(4) The performance or capacity of each node in thesupply chain network is known.
In addition, related parameters used in the model areshown in Parameter Definitions.
2.3. Fuzzy Multiobjective Mathematical Model of SupplyChain. This paper takes the Shaoxing textile region networkmanufacturing as background. Shaoxing textile takes the
industry of network organization as characteristics to getlocal industrial clusters, and the new model of regionaleconomic development has been successfully deduced. Atthe same, it forms a complete industrial chain composed ofthe polyester, chemical fiber, weaving, dyeing, and finishing,clothing design andmachining, sales, and so on. Hierarchicalnetwork structure of Shaoxing textile supply chain is shownin Figure 1.
The objective function of the supply chain networkstructure model is
min ๐1 = โ๐โ๐ผ
โ๐โ๐ฝ
๐๐๐๐๐๐ + โ๐โ๐ฝ
โ๐โ๐พ
๏ฟฝ๏ฟฝ๐๐๐๐๐ + โ๐โ๐พ
โ๐โ๐ฟ
๏ฟฝ๏ฟฝ๐๐๐๐๐ + โ๐โ๐ฝ
๐๐๐๐ + โ๐โ๐พ
V๐๐๐. (1)
Under the supply chain network centralized decision-making, the unified decision-making layer always wishesto control the objective function ๐1 to minimize the totalcost.The total cost includes rawmaterials and transportationfuzzy costs of the weaving enterprises โ๐โ๐ผโ๐โ๐ฝ ๐๐๐๐๐๐, thetransportation fuzzy costsโ๐โ๐ฝโ๐โ๐พ ๏ฟฝ๏ฟฝ๐๐๐๐๐ from productionenterprises transferred to the clothing machining ones, thetransportation fuzzy costs โ๐โ๐พโ๐โ๐ฟ ๏ฟฝ๏ฟฝ๐๐๐๐๐ from clothingprocessing enterprises to the distribution centers, the oper-ation fuzzy costs โ๐โ๐ฝ ๐๐๐๐ producing the correspondingproducts in the dyeing and finishing enterprises in the unittime, and the corresponding operation fuzzy cost of clothingmachining enterprises โ๐โ๐พ V๐๐๐.
min ๐2 = โ๐โ๐
๏ฟฝ๏ฟฝ๐๐๐ + โ๐โ๐
๏ฟฝ๏ฟฝ๐๐๐. (2)
In the process of supply chain network integration opti-mization, according to customer demand changes in differentregions, decision-making layer conducts to start using thedyeing and finishing enterprises and clothing processingenterprises. In doing so, some input corresponding to thesenode enterprises will be produced in order to meet thedemand of production or distribution of a particular product.
The objective function ๐2 is defined as the minimum of thetotal running costs.
max ๐3 =โ๐โ๐พโ๐โ๐ฟ๐๐๐
โ๐โ๐ฟ ๐๐. (3)
When the objective function ๐3 gets a maximum, it indi-cates that decision-making layer hopes that the products ofsupply chain networkmaximizationmeet customer demandsfurthest.
The constraint conditions of the above objective functionsare as follows:
๐ โ๐โ๐พ
๐๐๐ โค โ๐โ๐ผ
๐๐๐, (4)
๐ โ๐โ๐พ
๐๐๐ โค ๐๐๐, (5)
where formula (4) indicates that the raw material con-sumption in the production process of dyeing and finishingenterprises is restricted to the purchase quantity of rawmaterials in the weaving enterprises, and it is also affected by
4 Mathematical Problems in Engineering
the actual production capacity constraints of the dyeing andfinishing enterprises, which is shown in formula (5).
โ๐โ๐ฝ
๐๐๐ โค โ๐โ๐ฟ
๐๐๐, โ๐ โ ๐พ, (6)
โ๐โ๐ฟ
๐๐๐ข๐๐ โค ๐๐๐๐, โ๐ โ ๐พ, (7)
๐๐๐ โค ๐๐๐ข๐๐, โ๐ โ ๐พ, ๐ โ ๐ฟ, (8)
โ๐โ๐ฝ
๐๐๐ โค ๐๐, โ๐ โ ๐ฝ, (9)
where formula (6) expresses the constraint of the productionquantity of the clothing enterprise; formula (7) indicates thatthe amount of demand determined by the distribution centershould not be greater than the total capacity of the clothingmachining enterprise; formula (8) indicates that the outputof the goods in the clothing machining enterprise should notbe greater than the total demand quantity of the distributioncenter, so as to avoid producing the inventory. Formula (9) isthe raw material supply capacity constraints of the weavingenterprise.
โ๐โ๐พ
๐ข๐๐ = 1, โ๐ โ ๐ฟ, (10)
โ๐โ๐ฝ
๐๐ โค ๐, (11)
โ๐โ๐พ
๐๐ โค ๐, (12)
where formula (10) ensures that each distribution center canobtain at least one garment processing enterprise service;formulas (11) and (12) are the number of restrictions ofthe available dyeing and finishing enterprises and clothingprocessing enterprises. Formula (13) is the two-dimensionalvariable constraint shown as follows:
๐๐ โ {0, 1} ,
๐๐ โ {0, 1} ,๐ข๐๐ โ {0, 1} ,
โ๐ โ ๐ฝ, ๐ โ ๐พ, ๐ โ ๐ฟ.
(13)
Through discussion mentioned above, formulas (1) to(13) are composed of a fuzzy multiobjective model of supplychain.
min ๐1= โ๐โ๐ผ
โ๐โ๐ฝ
๐๐๐๐๐๐ + โ๐โ๐ฝ
โ๐โ๐พ
๏ฟฝ๏ฟฝ๐๐๐๐๐ + โ๐โ๐พ
โ๐โ๐ฟ
๏ฟฝ๏ฟฝ๐๐๐๐๐
+ โ๐โ๐ฝ
๐๐๐๐ + โ๐โ๐พ
V๐๐๐
min ๐2 = โ๐โ๐
๏ฟฝ๏ฟฝ๐๐๐ + โ๐โ๐
๏ฟฝ๏ฟฝ๐๐๐
max ๐3 =โ๐โ๐พโ๐โ๐ฟ๐๐๐
โ๐โ๐ฟ ๐๐s.t. ๐ โ
๐โ๐พ
๐๐๐ โค โ๐โ๐ผ
๐๐๐,
๐ โ๐โ๐พ
๐๐๐ โค ๐๐๐,
โ๐โ๐ฝ
๐๐๐ โค โ๐โ๐ฟ
๐๐๐, โ๐ โ ๐พ,
โ๐โ๐ฟ
๐๐๐ข๐๐ โค ๐๐๐๐, โ๐ โ ๐พ,
๐๐๐ โค ๐๐๐ข๐๐, โ๐ โ ๐พ, ๐ โ ๐ฟ,
โ๐โ๐ฝ
๐๐๐ โค ๐๐, โ๐ โ ๐ฝ,
โ๐โ๐พ
๐ข๐๐ = 1, โ๐ โ ๐ฟ,
โ๐โ๐ฝ
๐๐ โค ๐,
โ๐โ๐พ
๐๐ โค ๐,
๐๐ โ {0, 1} ,
๐๐ โ {0, 1} ,๐ข๐๐ โ {0, 1} ,โ๐ โ ๐ฝ, ๐ โ ๐พ, ๐ โ ๐ฟ.
(14)
3. Fuzzy Multiobjective CoordinatedOptimization under the CentralizedDecision-Making Method
3.1. General Method of Fuzzy Multiobjective CoordinationOptimization under the Centralized Decision-Making. In theprocess of multiobjective coordinated optimization, theobjectives are conflicting and competing with each other.The optimization process cannot make all of objectivesachieve the best, and the multiobjective problem is always toimprove some objectives at the expense of others. In addition,the result of multiobjective optimization is based on theexpectation of the decision-maker. However, it is difficultfor decision-makers to express their goals or expectationprecisely. Therefore, it belongs to fuzzy concept category.In this paper, the fuzzy theory is introduced to express thetarget satisfaction of the decision-makers by using the targetmembership degree and the feasible solution is also obtainedthrough the coordination among the fuzzy satisfaction degreeof each objective.
Mathematical Problems in Engineering 5
The coordination-solving of fuzzy multiobjective prob-lem can adopt the minimax operator, whose basic idea isthat the decision-maker assigns a fuzzy expectation for eachobjective function in advance and uses the correspondingfuzzy set to represent it. The membership degree of fuzzyexpectation represents the satisfaction of decision-makerwith the corresponding objective and its solution is definedas the intersection of all fuzzy expectations. In doing so, amultiobjective problem can be transformed into an equiva-lent fuzzy single-objective one.
Let a multiobjective problem be
max {๐1 (๐ฅ) , ๐2 (๐ฅ) , . . . , ๐๐ (๐ฅ)}s.t. ๐ฅ โ ๐ = {๐ฅ โ ๐ | ๐ด๐ฅ โค ๐} ,
(15)
where ๐๐(๐ฅ) = ๐๐๐ ๐ฅ (๐ = 1, 2, . . . , ๐พ). Objective optimizationprocess is as follow: set x for ๐๐(๐ฅ) โฅ ๐โ๐ (๐ = 1, 2, . . . , ๐พ, ๐ฅ โ๐), where๐โ๐ is fuzzy expected value of corresponding objec-tive function๐๐(๐ฅ). If the objective of formula (15) is regardedas a fuzzy constraint and the allowable deviation of each fuzzyconstraint is known, then themembership function๐๐(๐ฅ) canbe established. In the definition of โminimizeโ operators, thefeasible solution set is defined as the intersection of all thetarget sets; that is to say,
๐๐ท (๐ฅ) = ๐1 (๐ฅ) โฉ ๐2 (๐ฅ) โฉ โ โ โ โฉ ๐๐พ (๐ฅ)
= min {๐1 (๐ฅ) , ๐2 (๐ฅ) , . . . , ๐๐พ (๐ฅ)} .(16)
If ๐ = ๐๐ท(๐ฅ), then formula (15) has the equivalent formshown as follows:
max ๐s.t. ๐ โค ๐๐ (๐ฅ) , ๐ = 1, 2, . . . , ๐พ,
๐ฅ โ ๐.(17)
At this point, the decision-maker needs to determine thecorresponding membership function of each target. For the๐th objective (๐ = 1, 2, . . . , ๐พ), ๐1๐ = min๐ฅโ๐๐๐(๐ฅ) and ๐0๐ =max๐ฅโ๐๐๐(๐ฅ) should be calculated firstly, and then accordingto the subjective preference the decision-maker chooses oneof the functions from the linear function, the exponentialfunction, the hyperbolic function, and the inverse hyperbolicfunction to construct a membership function. Generally,linear function is adopted. We can obtain
๐๐ (๐ฅ)
={{{{{{{{{{{
1, ๐๐ (๐ฅ) โฅ ๐1๐ (๐ฅ)(๐1๐ (๐ฅ) โ ๐๐ (๐ฅ))
๐1๐ (๐ฅ)
โ ๐0๐ (๐ฅ) , ๐1๐ (๐ฅ) โฅ ๐๐ (๐ฅ) โฅ ๐0๐ (๐ฅ)0, ๐๐ (๐ฅ) โค ๐0๐ (๐ฅ) .
(18)
Note that the precondition of multiobjective problemshown in formula (15) or its equivalent form (shown informula (17)) is the sameweight of each target. In the practicalproblems of supply chain network, the importance of eachtarget is different for the decision-maker. For example, in
formulas (1) to (3), if we set different weights for these threeobjectives, then different optimal results will be obtained. Atthemoment, we introduce the objective weight of importancemeasures. Suppose the weight of the ๐th (๐ = 1, 2, . . . , ๐พ)objective is ๐๐, and โ๐๐ = 1. In addition, set ๐ผ =min{(๐1(๐ฅ))๐1 , (๐2(๐ฅ))๐2 , . . . , (๐๐พ(๐ฅ))๐๐พ}, and formula (17)can be further evolved into
max ๐ผs.t. ๐ผ โค ๐๐ (๐ฅ) , ๐ = 1, 2, . . . , ๐พ,
๐ฅ โ ๐.(19)
In the multiobjective decision-making, the weight is anumber to describe relative importance of objectives, whichoften reflects the understanding of the decision-makers ofdecision-making problem. At the same time, the weightis also comprehensive reflection of the decision-makersโknowledge, experience, preferences, and so on. In centralizeddecision-making of supply chain, decision-makers shouldevaluate the influence degree of each objective for the supplychain operation, so as to reasonably determine the weight ofeach objective according to the actual situation. Because thispaper only discusses the supply chain fuzzy multiobjectiveoptimization to form the supply chain optimization subnet-work, the detailed process to determine the specific targetweights is no longer expansion in the case simulation. In thecentralized decision-making mode of supply chain, all thedecision targets are included in the unified and centralizedconsideration of decision-makers and the weight sum ofobjectives at the same level is also equal to 1; that is to say, wesuppose that the weight of the ๐th (๐ = 1, 2, . . . , ๐พ) objectiveis ๐๐ and โ๐๐ = 1.
3.2. Problem-Solving of Fuzzy Supply Chain MultiobjectiveOptimization with Objective Satisfaction Compensation. Theproblem-solving of fuzzy multiobjective model mentionedabove usually adopts the minimax operator, which onlyensures that the satisfactionminimumgoal inmultiobjectivesis to maximize satisfaction and others will be met by themin-imum satisfaction. Therefore, the result is only a noninferiorsolution. Especially for solving complex multiobjective opti-mization problems which have multiple optimal solutions,this strategy cannot guarantee obtaining efficient solution.The reason is because the maximal and minimal operatorsare not compensatory ones. Subsequently, we integrate theminimal and compensatory arithmetic average operators andget the fuzzy minimal one which has certain compensationshown as follows:
๐๐ (๐ฅ) = ๐ฝmin๐๐ท (๐ฅ) + (1 โ ๐ฝ) 1๐พ๐พ
โ๐=1
๐๐ (๐ฅ) . (20)
Considering the impact of the objectives weight when themultiobjective is coordinated, formula (20) is further evolved,shown as follows:
๐๐ (๐ฅ) = ๐ฝmin๐๐ท (๐ฅ) + (1 โ ๐ฝ)๐พ
โ๐=1
(๐๐ (๐ฅ))๐๐ , (21)
6 Mathematical Problems in Engineering
๏ฟฝํ1
๏ฟฝํ2
๏ฟฝํ3
๏ฟฝํฝ
๏ฟฝํฝ
๏ฟฝํ
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
000.10.20.30.40.50.60.70.80.91
Figure 2: Coordination of fuzzymultiple objective satisfaction levelbased on compensation.
where ๐ฝ is compensation coefficient and 0 โค ๐ฝ โค 1.The main problem in using the compensation algorithm ishow to find an appropriate parameter ๐ฝ applicable to thedecision function. As a result, we introduce the probabilityestimation of satisfactory range in advance for the involvedobjectives so as to achieve different satisfaction levels fordifferent objectives. Figure 2 is the calculation results, whichshow that decision-makers can have better coordination byadjusting the value ๐ฝ until the objectives achieve satisfactionso far.
3.3. Procedure of Supply Chain FuzzyMultiobjective Optimiza-tion Solution. Using formula (21) and considering the impor-tance weights of each objective, we propose optimizationcalculation formula based on compensation and interactivesatisfaction for supply chain network multiobjective problemin formulas (1)โ(13) shown as follows:
max ๐ฝ๐ + (1 โ ๐ฝ)๐พ
โ๐=1
(๐๐ (๐ฅ))๐๐
s.t. ๐ โค ๐๐ (๐ฅ) , ๐ โ 1, 2, . . . , ๐พ,๐, ๐ฝ โ [0, 1] ,๐พ
โ๐=1
๐๐ = 1.
(22)
The detailed procedures of optimization problem-solvingare as follows.
(1) According to formulas (1)โ(3), maximum (๐01 , ๐02 , ๐03 )and minimum (๐11 , ๐12 , ๐13 ) values of objective func-tion are obtained. Obviously, satisfaction solution ofdecision-makers for each objective function shouldbe selected between the maximum and minimumvalues of each objective function under constraints.
(2) The membership of each objective function is con-structed by formula (18), which represents the satis-faction degree of decision-makers to each objective indifferent values.
(3) Decision-makers determine the importance degree ofeach objective in the process of supply chain oper-ation, so as to decide the weight of three objectives๐1, ๐2, ๐3, and ๐1 + ๐2 + ๐3 = 1. At the same time,compensation coefficient ๐พ is also selected.
(4) Use formula (21) to obtain a compromise solutionfor the multiobjective problem. If the decision-makeraccepts the compromise solution, then go to step (6)or continue to step (5).
(5) Compensation coefficient value ๐พ is revised bydecision-maker. After that, go to step (4). At thistime, the decision-maker also can adjust the objectivefunction of maximal and minimal, and go to step (2).
(6) End up: the parameter value obtained by problem-solving standardizes operation relationship of supplychain network node enterprise, which determinesthe multiobjective coordination of the supply chainoptimization subnetwork.The concrete flow is shownin Figure 3.
4. Case Study
Take Shaoxing textile supply chain network as the back-ground; this network includes four levels {3-3-4-3}, that is,weaving enterprises (๐ผ = 3), dyeing and finishing enterprises(๐ฝ = 3), clothing machining enterprises (๐พ = 4), anddistribution center (๐ฟ = 4). Its network structure is shownin Figure 4. The advantage enterprises design supply chainand optimize operation process with the principle of lowestcost, lowest investment, and highest customer satisfaction.The detail parameter descriptions are shown in Table 1.
Under the constraint formulas (4)โ(13), lingo 8.0 softwareis adopted to calculate the maximum and minimum value ofthe objective function in formulas (1)โ(3).Thefinal results areshown in Table 2.
The membership function of each fuzzy objective isobtained by formula (18):
๐1 (๐ฅ)
={{{{{{{{{
0, ๐1 (๐ฅ) โฅ 4252
4252 โ ๐1 (๐ฅ)(4252 โ 3586) , 4252 โฅ ๐1 (๐ฅ) โฅ 3586
1, ๐1 (๐ฅ) โค 3586,
๐2 (๐ฅ)
={{{{{{{{{
0, ๐2 (๐ฅ) โฅ 3360
3360 โ ๐2 (๐ฅ)(3360 โ 2140) , 3360 โฅ ๐2 (๐ฅ) โฅ 2140
1, ๐2 (๐ฅ) โค 2140,
๐3 (๐ฅ) ={{{{{{{{{{{
0, ๐3 (๐ฅ) โฅ 1(๐3 (๐ฅ) โ 0.762)
(1 โ 0.762) , 1 โฅ ๐3 (๐ฅ) โฅ 0.7621, ๐3 (๐ฅ) โค 0.762.
(23)
Mathematical Problems in Engineering 7
Solving the extreme value of each target
Whether is there an optimal solution
No
Determine the satisfaction function of each objective
Determine the weight of each objective
Yes
Yes
Modify the upper and lower values of the objective satisfaction
Modify objective weight
Modify compromise coe๏ฟฝcient
๏ฟฝe solved parameters obtained by multiobjective coordination
Whether to accept the satisfactory solution
Obtain the subnetwork of supply chain by solved parameter value
Establish the multiobjective model of supply chain
Determine the optimization range by the initial supply chain network
Multiobjective task analysis of the initial supply chain network
No
Set initial value and according to Equations (5)โ(13) and (15)โ(22) to obtain
satisfactory solution
Figure 3: Fuzzy multiobjective optimization processes with compensation coefficient.
At first, the general interaction method is introducedto solve the optimization problem, and the membershipfunctions of three objectives are substituted for formula (17).We can obtain the optimal satisfaction of decision-makers๐โ = 0.5103, and the objectives are ๐1 = 3863, ๐2 = 2737,and ๐3 = 0.883. If the decision-maker accepts the result, thenend up; otherwise the maximum range and the membershipfunction of each objective are adjusted to resolve until thedecision-maker is satisfied. But, as previouslymentioned, thismethod has not considered the relative importance of eachtarget and satisfaction compensation in the objectives, so
that the coordination effect of multiple objectives has somelimitation.
Suppose the weights of three objectives are๐1 = 0.4,๐2 =0.25, and ๐3 = 0.35. We can obtain different results throughchanging the value of ๐พby calculating formula (21). It is shownin Table 3. The variation process of compensation coefficientcan be expressed in Figure 2. Obviously, due to consideringthe weight and the compensation factor, the change rateof the satisfaction level in each objective is not the samewith the change of ๐พ. At this time, it is helpful for decision-maker to search for optimization in the global scope. If
8 Mathematical Problems in Engineering
Chemical ๏ฟฝberfactory
Weaving enterpriseI Distributor L
Information ๏ฟฝow
Material ๏ฟฝow
enterprise KClothing machining
enterprise JDyeing and ๏ฟฝnishing
1000TS
1220TS
1410TS
1830TM
1860TM
1140TM
450TM1590TM
2030TM 1500TM
530TM300
250
320
260 90, 120, 140
120, 150, 170
110, 150, 180
350
300
450
180
120
1.1
2.1 3.1 4.1
5.2
4.2
4.3
4.4
5.1
5.32.3
2.2 3.2
3.3
100
Figure 4: Supply chain network structure of Shaoxing textile. Note: TM means thousand meters and TS means thousand sets.
Table 1: Example of basic data table.
(a)
๐ ๐๐ ๐ = 1 ๐ = 2 ๐ = 3 ๐๐๐ = 1 0.6, 0.8, 1.0 0.4, 0.6, 0.8 0.4, 0.7, 1.1 3202 0.5, 0.7, 0.9 0.6, 0.8, 1.0 0.6, 0.9, 1.2 2503 0.7, 0.9, 1.1 0.3, 0.7, 0.9 0.5, 0.7, 0.9 300๐๐ 300 350 260 The material of each
dress is 1.5 meters so๐ = 0.67
๐๐ 320, 350, 380 300, 320, 340 280, 300, 320๏ฟฝ๏ฟฝ๐ 650, 700, 750 630, 660, 700 620, 650, 680
(b)
๏ฟฝ๏ฟฝ๐๐ ๐ = 1 ๐ = 2 ๐ = 3 ๐๐ ๐๐๐ = 1 1.0, 1.2, 1.4 0.8, 1.0, 1.2 1.2, 1.5, 1.8 180, 200, 220 1002 1.2, 1.4, 1.6 1.2, 1.4, 1.6 0.9, 1.2, 1.5 220, 240, 260 1503 0.9, 1.2, 1.5 1.6, 1.8, 2.0 0.8, 1.0, 1.2 200, 230, 250 1804 1.0, 1.2, 1.4 1.1, 1.4, 1.7 1.1, 1.3, 1.5 230, 250, 270 120
(c)
๏ฟฝ๏ฟฝ๐๐ ๐ = 1 ๐ = 2 ๐ = 3 ๏ฟฝ๏ฟฝ๐๐ = 1 1.5, 1.8, 2.0 1.6, 1.8, 2.0 1.2, 1.4, 1.6 250, 270, 3002 1.2, 1.4, 1.6 1.1, 1.4, 1.7 1.1, 1.3, 1.5 280, 300, 3203 1.1, 1.3, 1.5 1.5, 1.7, 1.9 1.0, 1.2, 1.4 340, 360, 3804 1.0, 1.2, 1.4 1.0, 1.2, 1.4 0.9, 1.1, 1.3 320, 350, 370๐๐ 110, 150, 180 120, 150, 170 90, 120, 140
Mathematical Problems in Engineering 9
Table 2:Themaximum andminimum values ofmultiple objectives.
Objective Maximum value ๐0๐ Minimum value ๐1๐Cost ๐1 4252 3586Investment costs ๐2 3360 2140Customer satisfaction f 3 1.00 (100%) 0.762 (6.2%)
decision-maker considers that the solution of ๐พ = 0.3 canbe accepted (that is to say, ๐1 = 3818, ๐2 = 2826, and ๐3 =0.902), then process-solving is over. The decision variablescorresponding to multiobjective equations are shown inTable 4.
5. Conclusions
This paper analyzes the centralized decision-making modeof supply chain network and illustrates the decision-makingprocess and characteristics of the centralized decision-making. Based on the background of centralized decision,a fuzzy multiobjective model of supply chain has beenestablished, which is based on the objective conditions andconstraints of the initial optimization of the supply chainnetwork.Themultiple objectives of the supply chain networkare all in the same optimization level in the centralizeddecision-making mode and the main difference lies in theimportant degree of each objective; that is to say, theobjectiveโs weight is different. Due to the limited resourcesof supply chain network, there are a lot of conflicts withmultiobjective coordination. When exploring the generalfuzzy multiobjective optimization methods, we focus on theequilibrium and compensation problem of multiobjectives,which means that proper adjustment of individual goal sat-isfaction level will make other goal satisfaction levels changegreatly so as to achieve the better objective coordination.In the mathematics realization, decision-maker continuouslychanges the satisfaction level of each objective through thechange of compensation coefficient in order to optimize andcoordinate. Finally, the simulation results have testified thatthe model proposed in this paper is efficient and effective.Hence, we may conclude that this model is exclusively fittedfor dealing with multiobjective decision-making optimiza-tion under fuzzy uncertain environment and centralizeddecision-making mode.
The potential extensions of this research may considerstochastic demand and imperfect supply chain systems in theproposed model. Other decision-making methods like groupdecision, multilevel decision, and so on may be included inthis model in the future.
Parameter Definitions
๐ผ, ๐: Weaving enterprise set, weaving enterpriseidentification
๐ฝ, ๐: Dyeing and finishing enterprise set, dyeingand finishing enterprise identification
๐พ, ๐: Clothing machining enterprises set, clothingmachining enterprises identification
๐ฟ, ๐: Distribution center set, distribution centeridentification
๐: Actual available set of dyeing and finishingenterprises (๐ โ ๐ฝ)
๐: Actual available set of clothing machiningenterprises (๐ โ ๐พ)
๐๐: Operation cost fuzzy number of dyeing andfinishing enterprise ๐ in the unit time (tenthousand Yuan)
V๐: Operation cost fuzzy number of clothingmachining enterprise ๐ in the unit time (tenthousand Yuan)
๐๐๐: Fuzzy number of unit product transportationcost from the weaving enterprise ๐ to thedyeing and finishing enterprises ๐ (Yuan)
๏ฟฝ๏ฟฝ๐๐: Fuzzy number of unit product transportationcost from the dyeing and finishing enterprise๐ to the clothing machining enterprise ๐(Yuan)
๏ฟฝ๏ฟฝ๐๐: Fuzzy number of unit product transportationcost from the clothing processing enterprise๐ to the distribution center ๐ (Yuan)
๐๐: Raw material supply ability of weavingenterprise ๐
๐๐: Unit production capacity of dyeing andfinishing enterprises ๐
๐: Production needed raw materialconsumption per unit product
๐: Total number of dyeing and finishingenterprises that can be available or investedin construction
๐: Total number of clothing machiningenterprises that can be available or investedin construction
๐๐: The unit time quantity product demandfuzzy number of distribution center ๐ (tenthousand sets)
๏ฟฝ๏ฟฝ๐: The operation cost fuzzy number of dyeingand finishing enterprises ๐
๏ฟฝ๏ฟฝ๐: The operation cost fuzzy number of clothingmachining enterprises ๐
๐๐๐: Raw material transportation volume pertime from the weaving enterprise ๐ to thedyeing and finishing enterprises ๐
๐๐๐: Product transportation volume per timefrom the dyeing and finishing enterprise ๐ tothe clothing machining enterprises ๐
๐๐๐: Product transportation volume per timefrom the clothing machining enterprise ๐ tothe distribution center ๐
๐๐: 0-1 variable, where 1 indicates that themanufacturing plant is available; otherwisenot
๐๐: 0-1 variable, where 1 indicates that theclothing machining enterprise is available;otherwise not
๐ข๐๐: 0-1 variable, where 1 indicates the clothingmachining enterprise service distributor ๐;otherwise not.
10 Mathematical Problems in Engineering
Table 3: Corresponding compensation changes of the satisfaction degree of each objective.
๐พ ๐ ๐1 ๐2 ๐3 ๐1 ๐2 ๐31 0.5037 3917 2745 0.881 0.5037 0.5037 0.50370.9โ0.8 0.4875 3897 2780 0.884 0.5321 0.4752 0.51270.7โ0.6 0.4291 3866 2795 0.886 0.5797 0.4635 0.52090.5 0.3625 3843 2809 0.888 0.6138 0.4517 0.53110.4 0.2936 3682 2807 0.897 0.6516 0.4531 0.56780.3 0.1886 3818 2826 0.902 0.6969 0.4375 0.58700.2โ0.1 0.0628 3770 2869 0.905 0.7233 0.4022 0.60120 0.0000 3744 2914 0.910 0.7624 0.3653 0.6236
Table 4:The parameters of the fuzzy multiobjective equation basedon compensation.
(a)
๐๐๐, ๐๐ ๐ = 1 ๐ = 2 ๐ = 3๐ = 1 203/1 / /2 / 45/1 /3 / 114/1 186/1 ๐๐๐, ๐ข๐๐
(b)
๐๐๐, ๐๐ ๐ = 1 ๐ = 2 ๐ = 3 ๐ = 1 ๐ = 2 ๐ = 3๐ = 1 150/1 53/1 / 100/1 / / /2 / 159/1 / / 141/1 / /3 / / 183/1 / / 122/1 /4 / / / / / /
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgments
This research is supported by the National Natural ScienceFund Project of China (Grant no. 71401156) and HigherEducation Classroom Teaching Reform Project of ZhejiangProvince in 2016 (Grant no. kg20160151) as well as Con-temporary Business and Trade Research Center and Centerfor Collaborative Innovation Studies of Modern Businessof Zhejiang Gongshang University of China (Grant no.14SMXY05YB).
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