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A hybrid evolutionary model for supplier assessment and selection in inbound logistics
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Journal of Applied Logic www.elsevier.com/locate/jal
A hybrid evolutionary model for supplier assessment and selection in inbound logistics Dragan Simić a,∗ , Vasa Svirčević b , Svetlana Simić c a
University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia b Lames Ltd., Jarački put bb., 22000 Sremska Mitrovica, Serbia c University of Novi Sad, Faculty of Medicine, Hajduk Veljkova 1–9, 21000 Novi Sad, Serbia
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Article history: Available online xxxx Keywords: Supplier assessment Supplier selection Harmony search algorithm Genetic algorithm Inbound logistics
a b s t r a c t Business stability, quality, safety, supply chain flexibility and cost optimization have an increasing role in companies that strive to stay and survive in the market competition. A wise supplier choice becomes ever more important prerequisite for the success of any company. This paper presents a novel hybrid model for supplier assessment and selection, based on hybrid solution including genetic algorithm (GA) and harmony search algorithm (HSA). The chosen data set presents original data which is used for assessment in “Lames” company. The results show that HSA & GA value constraint model is slightly more restricted than other discussed models, and separates, much better and with greater precision, poor companies from the good ones in business environment. © 2014 Published by Elsevier B.V.
1. Introduction Dynamic market changes demand selection of business partners who are logistically and otherwise able to follow changes in company requirements, especially regarding phenomenon of globalization and rapid development of logistics which is in detail presented in [10] and, at the same time, the relationship among enterprises is more competitive than ever. In such circumstances a wise choice of suppliers in inbound logistics becomes increasingly important prerequisite for the success of any company. A firm’s sourcing strategy is characterized by three key decisions [2]: (a) criteria for establishing a supplier base; (b) criteria for supplier selection, a subset of the base, which will receive an order from the firm and (c) the selected quantity of goods to order from each supplier. The most popular intelligence optimization algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO) have been successfully applied to large-scale complicated problems of scientific and engineering computing. However, the harmony search algorithm (HSA) a meta-heuristic random * Corresponding author. E-mail addresses: [email protected] (D. Simić), [email protected] (V. Svirčević), [email protected] (S. Simić). http://dx.doi.org/10.1016/j.jal.2014.11.007 1570-8683/© 2014 Published by Elsevier B.V.
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optimization algorithm, inspired by the process of the musicians’ improvisation of the harmony and proposed in [3] represents a new research field. This paper presents a novel model for supplier assessment and selection based on hybrid evolutionary algorithm that is used in multinational company “Lames LLC” with operations in more than a dozen countries in the world as well as in Serbia. “Lames” company is part of automotive industry, and it produces electrical and manual car window lifters. The proposed model includes soft computing methods in general and harmony search and genetic algorithms in particular into the whole supplier assessment and selection in decision making system. The rest of the paper is organized in the following way. In the following section, Section 2, similar available implementation in supplier assessment and selection domain is overviewed. Section 3 elaborates on a short part of a previous research. Section 4 describes the proposed hybrid genetic algorithm and harmony search performance value constraint model. Section 5 presents experimental results while Section 6 concludes the paper and offers notes on future work. 2. Literature review It is proven that the application of soft computing (SC) has two main advantages. First, it made solving nonlinear problems in which mathematical models are not available, possible. Secondly, it introduced the human knowledge such as cognition, recognition, understanding, learning, and other skills into the fields of computing. The underlying paradigms of SC such as neural computing, fuzzy logic computing and evolutionary computing are known as powerful tools for almost any difficult and complex optimization problem. In the past, some mathematical programming approaches have been used for supplier selection. A multiphase mathematical programming approach for effective supply chain design was presented in 2002 [9]. More specifically, a combination of multi-criteria efficiency models, based on game theory concepts, and linear and integer programming methods was developed and applied. Fuzzy goal programming approach was applied in 2004 to solve the vendor selection problem with multiple objectives [5]. According to recent research work conducted in 2009, the quantitative decision methods for solving the supplier selection problem can be classified into three categories: (1) multi-attribute decision-making, (2) mathematical programming models and (3) intelligent approaches [11]. Furthermore, in the latest literature survey conducted in 2010, it can be seen that the mathematical programming models are grouped into the following five models: (1) linear programming, (2) integer linear programming, (3) integer non-linear programming, (4) goal programming and (5) multi-objective programming [4]. Two implementations of fuzzy supplier selection models, which are critical in contemporary business and management, are presented in: (1) supplier selection strategies on fuzzy decision space [6]; (2) fuzzy logic method adopted in modelling supplier selection process [1]. A review, approach of fuzzy models and applications in logistics is in detail presented in [7]. Hundreds of criteria were proposed, and the most often criterion is quality, followed by delivery, price/cost, manufacturing capability, service, management, research and development, finance, flexibility, reputation, relationship, risk, and safety and environment. Various quality related attributes have been found, such as: “compliance with quality”, “six sigma program or total quality management”, “ISO quality system installed”. The traditional single criterion approach based on lowest cost bidding is no longer supportive and robust enough in contemporary supply management. 3. Supplier assessment and selection in “Lames LLC” Supplier assessment and selection mapping as an essential component of inbound logistics management is usually a multi-criteria decision problem which, in actual business contexts, may have to be solved in
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Fig. 1. Supplier assessment and selection workflow.
the absence of precise information. Supplier assessment and selection workflow in “Lames LLC” is shown in Fig. 1. Corporate decision procurement makers first define procurement categories and all of these are divided into sub-categories. Then, supplier performances groups according to business activities, which represent groups of individual performances, are defined. The individual performances are established by carefully choosing well known quantitative and qualitative criteria including already existing experience with procurement decision makers. In general, individual performances depend on industry branch relevant to supplier assessment and selection process. For every procurement category, corporate target grade for each individual performance is defined. Target grade of every individual performance presents expected value in supplier selection process. The supplier assessment and selection process can begin. Suppliers are continuously evaluated, at least once a year, which means that the supplier base is a time variable category. Suppliers are grouped into procurement categories, and every supplier is assessed in its particular category, that is why it is possible for one supplier to get represented in several procurement categories. Procurement manager evaluates every supplier individual performance separately, and gets supplier assessment grade, also separately for each supplier individual performance. Supplier individual performance assessment grades are compared to appropriate corporate target grades. The supplier’s capability to satisfy the criteria is determined according to the supplier assessment and selection model: “Supplier approved ? ”. If supplier is approved then the supplier gets in general “Status”: “Preferred – (P )” or “Referenced – (R)”, depends on decision making model and scoring model, and it is stored (included) in “Supplier base”. The supplier which is “Not approved” is defined by “Request for corrective actions”, and follow up of “Supplier action plan”. When supplier is improved its individual performances corporate procurement manager once more evaluates separately every supplier individual performance, gets supplier assessment grade for each of them, and the process continues as mentioned before. If supplier did not improve its individual performance gets “Status”: “Disorder – (D)”.
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Table 1 Performance groups and individual performances for supplier assessment. Performance groups
Individual performances
Method of evaluation
Financial
Debt Dependency Profitability
Ratio Debt/Equity % Turnover with Lames/Supplier Global Turnover Net result/Turnover
Logistics
Delivery Distribution Capacity Commitment/Stock Coverage B to B Solutions
Respect of delivery time Ability to manage the distribution chain Capacity to supply required prod./service range Commitment/Availability on supplier stock Supplier’s geographical coverage Ability to implement EDI or B to B solution
Competitiveness
Technical offer Technical know-how Proposition force Price transparency Cost level/market Cost level/competitors
Management of the technical part of its offer Technical/Business know-how Proposition force (process improvement, ability to innovate) Transparency: prices, organization Cost Level compared to the market Price level/competitors
Quality
Quality Certification Quality compliance Corrective actions Sustainable development
ISO certification, control process or various certification Compliance with specifications Ability to implement corrective actions Safety & Environmental information, child labour
Service/Commercialism
K. A. M. approach Reactivity R&D Export turnover Reporting
Is the Key Account Manager approach working adequately? Reactivity towards a demand R&D department existence % of export turnover/Global turnover Reporting
3.1. Procurement categories, groups and individual performances “Lames LLC” company defined the following procurement categories: a) Raw Material; b) Industrial Products & Consumables; c) Industrial Services; d) Utilities; e) Transport Services; f) General Supplies & Services; g) Plants and Equipments; z) Out of Scope. Supplier performances groups represent groups of individual performances that are to be assessed in the following business activities: 1) Finance; 2) Logistics; 3) Competitiveness; 4) Quality; 5) Service/Commercialism. All of individual performances, for supplier assessment represent questions which are assessed and ranked in three supplier assessment grades (1, 2 or 3) respectively. Table 1 shows all performance groups, all individual performances and the method of evaluation for every individual performance. Corporate target grade for supplier performances for every purchase category are defined separately. It is necessary because the importance of one performance is not the same for suppliers in different purchase category. In other words, there is difference between the target grade for suppliers who deal with raw materials and those who supply office supplies or provide the service of cleaning office space. It is important to mention that a supplier can be well placed in one procurement category, and not so well placed in another. 3.2. Empirical model The real world application currently used in a local “Lames LLC” company for supplier assessment and selection, is named “Empirical model”. This model is presented in the following way. For every question concerning supplier individual performance, which consists of 24 questions (Table 1), the supplier assessment grade of performance is set on a scale form 1 to 3 so that the sum of the entire performance set should be 50 (Eq. (1)). It can be seen, that sum = 50 is smaller than maximum possible sum value 72 (24 questions ∗ 3 target grade = 72). i
target gradei = 50
(1)
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Fig. 2. (a) Supplier assessment grade, corporate target grade and the enclosed areas; (b) Graphical surface representation.
% supplier performance =
(target gradei ∗ current gradei ) ∗ 2/3
(2)
i
This should be done in order to apply the following formula for calculating the percentage of supplier performance on a scale from 0% to 100% (Eq. (2)). 3.3. The GA performance value constraint model This subsection presents our previous research which is in detail presented in [8]. As it can be seen supplier individual performance can be lower, equal to, or higher than defined target values (Fig. 2(a)). If supplier assessment grade is lower than the corporate target grade, it means that the supplier has not yet satisfied company requirements. If supplier assessment grade is equal or higher to the target value then the performance of the supplier is as expected. The proposed genetic algorithm performance value constraint model is based on performance value constraints during supplier assessment for one performance on maximum target grade. This limits the possibility of a supplier performance which is not requisite to heighten supplier assessment grade. Further on, the proposed model calculates the area enclosed by the performance values which are lower or equal to target grade on one side, and on the other, by target grade of those supplier assessment grade performances which are higher than the target values. Corporate target grade and supplier assessment grades represent variables in optimization algorithm. The optimization algorithm searches for the best solution, the maximum supplier area enclosed with respect to previously defined conditions between target and assessment grades. The order of all 24 vertices of defined icosikaitetragon, (twenty-four-sided polygon) is assorted to maximize the enclosed area. In this way the estimation of the maximum affected area is completed thus eliminating the possibility of subjectivity in positioning individual performances or groups of performances. 3.4. Surfaces ordered model On one hand, in the graphical representation of the results, as it can be seen, the questions are grouped by 3 (Financial), 4 (Quality), 5 (Service/Commercialism) and 6 (Logistics, Competitiveness). In this way
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Fig. 3. Supplier individual performances, target level performances, enclosed target and supplier areas and the defined enclosed surface.
graphical representation of the results corresponds to five different surfaces. The maximum affected area can be observed in relation to different surfaces, and it can be named surface ordered model. One such example together with supplier performances, groups of performances, and the enclosed area by the proposed methodology is shown in Fig. 2(b). In accordance with what was previously mentioned, light grey colour of enclosed area shows that the criteria was satisfied, grey enclosed area shows where supplier performances are higher than target performance, and black enclosed area indicates where target grade is grater than supplier assessment grade (Fig. 3).
4. The harmony search performance value constraint model
The aim of this research is to find the best solution, and maximize supplier area enclosed, with respect to: (1) previously defined conditions between target and assessment grades; (2) the order of vertices defined by individual performances could be random; (3) the order of surfaces defined by group performances could be random. The new proposed hybrid model includes two different artificial intelligent techniques. Firstly, genetic algorithm is used, soft computing technique, and after that harmony search algorithm, population-based meta-heuristic algorithm. This problem is divided and solved in two steps. In the first phase, group supplier area, each of 5 defined, will be maximized: Financial, Logistics, Competitiveness, Quality, and Service/Commercialism. Good qualities of GA performance value constraint model will be used. In the second phase, supplier area surface will be maximized with respect to position and order of each 5 performance group areas defined in icosikaitetragon. In the second phase, a new metaheuristic algorithm has been added mimicking the improvisation of music players and it is named Harmony Search Algorithm (HSA).
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Fig. 4. Flow chart of the Harmony Search algorithm (Geem, 2000 [3]).
4.1. Harmony Search algorithm Harmony Search (HS) is a relatively new population-based meta-heuristic algorithm which has obtained noticeable results in the field of combinatorial optimization [3]. It mimics the behaviour of a music orchestra when aiming at composing the most harmonious melody, as measured by aesthetic standards. HS maintains a set of solutions in the so-called Harmony Memory (HM). An estimation of the optimal solution is achieved in every iteration by applying a set of optimization parameters to the HM, which produce a new harmony vector every time. Fig. 4 illustrates the flow diagram of the HS algorithm, which can be summarized in four steps: (1) initialization of the HM; (2) improvisation of a new harmony; (3) inclusion of the newly generated harmony in the HM provided that its fitness improves the worst fitness value in the previous HM. (4) returning to step (2) until a termination criteria is satisfied. This procedure is mainly controlled by two different probabilistic parameters, which are sequentially applied to produce a new set of candidate solutions. The parameters that are used in the generation process of a new solution are called Harmony Memory Considering Rate (HMCR) and Pitch Adjusting Rate (PAR). 1. HMCR ∈ [0, 1], establishes the probability that the new value for a certain note is drawn uniformly from the values of this same note in all the remaining solutions. 2. PAR ∈ [0, 1], establishes the probability that the new value xnew for a given note value x is obtained by adding a small random amount to the existing value xold . xnew = xold + ωx · ε where ωx represents the pitch bandwidth, and ε is a random number drawn from a uniform distribution with support [−1, 1]. A low pitch adjusting rate with a narrow bandwidth may restrict the diversification of the algorithm within a small search subspace and consequently, decrease the convergence rate of the overall solver. On the other hand, a high PAR with a high value of ωx may force the algorithm to unnecessarily escape from areas with potentially near optimal solutions.
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Table 2 Experimental results: Empirical model, Surface without constraints, GA value constraint model, HSA & GA value constraint model. No
Year
Company
Empirical model/ Status
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013
DK PACK d.o.o. Manzan 98 OC Elab Ninagro Staklo enterijeri Belem Adamšped system Tele group SIRMIUM PAPIR Lames S.p.A. INTER-HERMES INSTITUT IMS ALBO StandardŠped ALCO FLEXIMA AUTO LL Logist PAPIR DOO Elektro nedex Merkator-S TEHNOLIFT DAJAS SRBOEXPORT YONEX d.o.o. HARCO d.o.o. DK PACK d.o.o. Alatnica Vuletić FESTO Gesellscha Fromm pakovanje Ninagro MIS COMERC Mitroprevoz Medigo M Spektar MB Transport Pro Tea RECA HAHN KOLB Heli Viljuskari Dali d.o.o. Adamšped system Elektromaterijal Tele group SIRMIUM PAPIR Varmedja Metalobox YU GARFILD doo Biroshop Vujasin. Agencija za zaštitu PAKO MD Golf Metalija TR Lames S.p.A.
68.66% 46.66% 80.00% 83.33% 80.66% 73.33% 70.00% 76.66% 81.33% 81.33% 81.33% 84.67% 82.00% 75.33% 75.33% 72.66% 74.00% 80.00% 68.00% 88.66% 79.33% 57.33% 50.66% 77.33% 84.66% 76.66% 78.66% 68.66% 80.66% 56.00% 86.66% 84.66% 74.66% 82.00% 82.00% 76.00% 78.00% 83.33% 84.00% 64.00% 76.66% 72.00% 52.00% 87.33% 76.00% 74.00% 79.33% 77.33% 66.00% 74.66% 79.33% 78.66%
Surface without constraints
GA value constraint
HSA value constraint/ Status
70.58% 40.19% 84.15% 86.27% 92.30% 77.88% 74.50% 96.07% 79.80% 75.47% 84.31% 90.09% 92.30% 90.19% 79.41% 75.49% 80.39% 86.27% 67.92% 98.03% 81.73% 56.86% 44.11% 82.35% 88.23% 84.31% 85.84% 76.41% 93.13% 54.90% 90.19% 95.09% 77.88% 86.53% 80.39% 83.96% 83.33% 85.57% 94.23% 63.72% 83.01% 84.61% 55.76% 99.05% 82.35% 69.23% 84.61% 86.53% 70.19% 82.35% 91.50% 78.30%
69.40% 39.52% 82.94% 84.83% 91.21% 76.60% 72.91% 94.92% 78.86% 74.59% 82.90% 88.80% 91.21% 88.26% 78.08% 74.22% 78.67% 84.83% 67.13% 96.39% 80.02% 55.91% 43.17% 80.97% 86.75% 82.90% 84.85% 75.52% 91.57% 53.98% 88.68% 93.06% 76.96% 85.51% 78.67% 82.98% 81.93% 83.79% 93.11% 62.36% 82.05% 83.61% 55.11% 97.90% 81.36% 68.41% 83.61% 85.51% 69.36% 80.97% 90.44% 77.39%
Distinction HSA & EM
% supplier performance
Preferred – (P)
(P) (D) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (D) (R) (P) (R) (P) (P) (D) (D) (P) (P) (P) (P) (R) (P) (D) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (R) (D) (P) (P) (P) (P) (P) (R) (P) (P) (P)
111.65% 44.66% 126.73% 145.63% 122.11% 101.90% 89.32% 112.74% 131.73% 150.46% 134.95% 140.59% 129.80% 105.82% 116.50% 109.70% 106.79% 133.98% 89.71% 158.25% 110.57% 66.99% 49.51% 123.30% 146.60% 126.21% 113.08% 84.11% 127.18% 59.22% 155.33% 130.09% 113.46% 137.50% 132.03% 108.41% 119.41% 125.00% 130.76% 72.81% 107.47% 100.00% 55.76% 139.25% 115.68% 115.38% 123.07% 122.11% 93.26% 114.56% 119.62% 128.03%
Referenced – (R)
(R) (D) (P) (P) (P) (P) (R) (P) (P) (R) (P) (P) (P) (P) (P) (R) (P) (P) (R) (P) (P) (D) (D) (P) (P) (P) (P) (R) (P) (D) (P) (P) (P) (P) (P) (P) (P) (P) (P) (R) (P) (P) (D) (P) (P) (R) (P) (P) (R) (P) (P) (P)
1.06 −18.07 3.54 1.77 11.56 4.26 3.99 19.86 −3.13 −9.03 +1.8 +4.65 +10.1 +14.65 +3.52 +2.10 +5.93 +5.69 −1.29 +8.01 +0.86 −2.54 −17.35 +4.49 +2.40 +7.52 +7.29 +9.08 +11.91 −3.74 +2.27 +9.02 +2.98 +4.10 −4.23 +8.41 +4.79 +0.54 +9.78 −2.62 +6.56 +13.88 +5.64 +10.79 +6.58 −8.17 +5.11 +9.56 +4.84 +7.97 +12.28 −1.64
Disorder – (D)
5. Experimental results Experimental results (Table 2) show minimum and maximum supplier assessment and selection and supplier performance values and their status: Preferred, Referenced and Disorder. Furthermore, this research shows that new hybrid HSA & GA value constraint model is slightly more restricted than GA value constraint model.
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Table 3 Comparative assessment and selection company analysis in 2012 and 2013. No
Company
Year
Trend
2012
1 2 3 4 5 6
DK PACK d.o.o. Ninagro Adamšped sys. Tele group SIRMIUM PAPIR Lames S.p.A.
2013
Empirical model
Status
Empirical model
Status
Assessment
Status
68.66% 83.33% 70.00% 76.66% 81.33% 81.33%
Preferred Preferred Preferred Preferred Preferred Preferred
76.66% 56.00% 64.00% 72.00% 52.00% 78.66%
Preferred Disorder Preferred Referenced Disorder Preferred
↓ ↓
↔ ↓ ↔ ↓ ↔
Presented results show that the assessment values of HSA & GA model are significantly lower than GA values constraint models of poorer companies which can be seen in the example of the following companies: Manzan 98 OC, DAJAS, SRBOEXPORT. Furthermore, when comparing the hybrid HSA & GA model and GA model, it can be seen that there is a mild decrease when it comes to assessed value of “Tele group” company and that there is a serious decrease in assessment position (Status) from “Preferred” to “Referenced”. On the other hand, by comparing HSA & GA model and GA values constraint model of better companies, that is, those that have “Preferred” status, the assessment value is higher in HSA & GA model. That is the case in the following companies: Papir d.o.o., Merkator-S, Fromm pakovanje. It can thus be concluded that new hybrid HSA & GA values constraint model separates, much better and with greater precision, poor companies from the good ones. Supplier assessment is a continuous process, and its results must be conveyed to the suppliers so they could create a corrective action plan to develop and improve their weaknesses. The main goal of assessment processes is to ensure successful and long-term cooperation between all parties in a logistics supply chain. As this research shows, 11 companies are assessed in 2012 and 6 of them are assessed in 2013. Their comparative analysis is shown in Table 3. The results show dramatic decrease in two companies “Ninagro” and “Sirmium papir” which both lost “Preferred” status and have become “Disorder”. There is also a slight decrease in assessed supplier value in “Tele group” company, and change form “Preferred” status to “Referenced”. The other three companies kept the “Preferred” status, but it has to be stressed that there has been an increase in assessed value in company “DK PACK”. The other two companies “Adamšped system” and “Lames S.p.A.” kept the assessment position – “Preferred” status but slightly decreased assessment value. 6. Conclusion and future work Nowadays, the community requires effective soft computing methods and tools for optimizing large scale complex inbound logistics distribution and supply chain management systems. The hybrid HSA & GA performance value constraint model is presented in this paper. The experimental results of this method are obtained from the realistic data set of the supplier performances of a multinational “Lames” company operating in Serbia. The experimental results were later on compared to the results obtained by our previous research. Presented comparison shows that the values obtained by new hybrid HSA & GA value constraint model are slightly restricted then GA value constraint model, and HSA & GA value constraint model separates, much better and more precisely, poor companies from the good ones in business environment. This research can be classified as empirical multi-attribute decision making model and scoring models are typically used to evaluate suppliers for inclusion in the supplier base. Future development can be directed towards adding weight to every performance group; business con-
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straints can be considered as well as technical, legal, geographical and commercial nature of every individual performance. Acknowledgment The authors acknowledge the support for research project TR 36030, funded by the Ministry of Science and Technological Development of Serbia. References [1] A. Amindoust, S. Ahmed, A. Saghafinia, A. Bahreininejad, Sustainable supplier selection: a ranking model based on fuzzy inference system, Appl. Soft Comput. 12 (6) (2012) 1668–1677. [2] G.J. Burke, E. Carrillo J, A.J. Vakharia, Single versus multiple supplier sourcing strategies, Eur. J. Oper. Res. 182 (1) (2007) 95–112. [3] Z.W. Geem, J.H. Kim, G.V. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation 76 (2) (2001) 60–68. [4] W. Ho, X. Xu, P.K. Dey, Multi-criteria decision making approaches for supplier evaluation and selection: a literature review, Eur. J. Oper. Res. 202 (1) (2010) 16–24. [5] M. Kumar, P. Vrat, R. Shankar, A fuzzy goal programming approach for vendor selection problem in a supply chain, Comput. Ind. Eng. 46 (1) (2004) 69–85. [6] M. Pattnaik, Supplier selection strategies on fuzzy decision space, Gen. Math. Notes 4 (1) (2011) 49–69. [7] D. Simić, S. Simić, A review: approach of fuzzy models applications in logistics, in: R. Burduk, M. Kurzynski, M. Wozniak, A. Zolnierek (Eds.), CORES 2011, in: Adv. Intell. Soft Comput., vol. 95, Springer, Heidelberg, 2011, pp. 717–726. [8] D. Simić, V. Svirčević, S. Simić, An approach of genetic algorithm to model supplier assessment in inbound logistics, in: Soft Computing Models in Industrial and Environmental Applications, in: Advances in Intelligent Systems and Computing, vol. 188, 2012, pp. 83–92. [9] S. Talluri, R.C. Baker, A multi-phase mathematical programming approach for effective supply chain design, Eur. J. Oper. Res. 141 (3) (2002) 544–558. [10] J. Tepić, I. Tanackov, G. Stojić, Ancient logistics – historical timeline and etymology, Teh. Vjesn. – Stroj. Fak. 18 (3) (2011) 379–384. [11] T.Y. Wang, Y.H. Yang, A fuzzy model for supplier selection in quantity discount environments, Expert Syst. Appl. 36 (10) (2009) 12179–12187.
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Contents lists available at ScienceDirect
Journal of Applied Logic www.elsevier.com/locate/jal
A hybrid evolutionary model for supplier assessment and selection in inbound logistics Dragan Simić a,∗ , Vasa Svirčević b , Svetlana Simić c a
University of Novi Sad, Faculty of Technical Sciences, Trg Dositeja Obradovića 6, 21000 Novi Sad, Serbia b Lames Ltd., Jarački put bb., 22000 Sremska Mitrovica, Serbia c University of Novi Sad, Faculty of Medicine, Hajduk Veljkova 1–9, 21000 Novi Sad, Serbia
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Article history: Available online xxxx Keywords: Supplier assessment Supplier selection Harmony search algorithm Genetic algorithm Inbound logistics
a b s t r a c t Business stability, quality, safety, supply chain flexibility and cost optimization have an increasing role in companies that strive to stay and survive in the market competition. A wise supplier choice becomes ever more important prerequisite for the success of any company. This paper presents a novel hybrid model for supplier assessment and selection, based on hybrid solution including genetic algorithm (GA) and harmony search algorithm (HSA). The chosen data set presents original data which is used for assessment in “Lames” company. The results show that HSA & GA value constraint model is slightly more restricted than other discussed models, and separates, much better and with greater precision, poor companies from the good ones in business environment. © 2014 Published by Elsevier B.V.
1. Introduction Dynamic market changes demand selection of business partners who are logistically and otherwise able to follow changes in company requirements, especially regarding phenomenon of globalization and rapid development of logistics which is in detail presented in [10] and, at the same time, the relationship among enterprises is more competitive than ever. In such circumstances a wise choice of suppliers in inbound logistics becomes increasingly important prerequisite for the success of any company. A firm’s sourcing strategy is characterized by three key decisions [2]: (a) criteria for establishing a supplier base; (b) criteria for supplier selection, a subset of the base, which will receive an order from the firm and (c) the selected quantity of goods to order from each supplier. The most popular intelligence optimization algorithms, such as genetic algorithm (GA) and particle swarm optimization (PSO) have been successfully applied to large-scale complicated problems of scientific and engineering computing. However, the harmony search algorithm (HSA) a meta-heuristic random * Corresponding author. E-mail addresses: [email protected] (D. Simić), [email protected] (V. Svirčević), [email protected] (S. Simić). http://dx.doi.org/10.1016/j.jal.2014.11.007 1570-8683/© 2014 Published by Elsevier B.V.
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optimization algorithm, inspired by the process of the musicians’ improvisation of the harmony and proposed in [3] represents a new research field. This paper presents a novel model for supplier assessment and selection based on hybrid evolutionary algorithm that is used in multinational company “Lames LLC” with operations in more than a dozen countries in the world as well as in Serbia. “Lames” company is part of automotive industry, and it produces electrical and manual car window lifters. The proposed model includes soft computing methods in general and harmony search and genetic algorithms in particular into the whole supplier assessment and selection in decision making system. The rest of the paper is organized in the following way. In the following section, Section 2, similar available implementation in supplier assessment and selection domain is overviewed. Section 3 elaborates on a short part of a previous research. Section 4 describes the proposed hybrid genetic algorithm and harmony search performance value constraint model. Section 5 presents experimental results while Section 6 concludes the paper and offers notes on future work. 2. Literature review It is proven that the application of soft computing (SC) has two main advantages. First, it made solving nonlinear problems in which mathematical models are not available, possible. Secondly, it introduced the human knowledge such as cognition, recognition, understanding, learning, and other skills into the fields of computing. The underlying paradigms of SC such as neural computing, fuzzy logic computing and evolutionary computing are known as powerful tools for almost any difficult and complex optimization problem. In the past, some mathematical programming approaches have been used for supplier selection. A multiphase mathematical programming approach for effective supply chain design was presented in 2002 [9]. More specifically, a combination of multi-criteria efficiency models, based on game theory concepts, and linear and integer programming methods was developed and applied. Fuzzy goal programming approach was applied in 2004 to solve the vendor selection problem with multiple objectives [5]. According to recent research work conducted in 2009, the quantitative decision methods for solving the supplier selection problem can be classified into three categories: (1) multi-attribute decision-making, (2) mathematical programming models and (3) intelligent approaches [11]. Furthermore, in the latest literature survey conducted in 2010, it can be seen that the mathematical programming models are grouped into the following five models: (1) linear programming, (2) integer linear programming, (3) integer non-linear programming, (4) goal programming and (5) multi-objective programming [4]. Two implementations of fuzzy supplier selection models, which are critical in contemporary business and management, are presented in: (1) supplier selection strategies on fuzzy decision space [6]; (2) fuzzy logic method adopted in modelling supplier selection process [1]. A review, approach of fuzzy models and applications in logistics is in detail presented in [7]. Hundreds of criteria were proposed, and the most often criterion is quality, followed by delivery, price/cost, manufacturing capability, service, management, research and development, finance, flexibility, reputation, relationship, risk, and safety and environment. Various quality related attributes have been found, such as: “compliance with quality”, “six sigma program or total quality management”, “ISO quality system installed”. The traditional single criterion approach based on lowest cost bidding is no longer supportive and robust enough in contemporary supply management. 3. Supplier assessment and selection in “Lames LLC” Supplier assessment and selection mapping as an essential component of inbound logistics management is usually a multi-criteria decision problem which, in actual business contexts, may have to be solved in
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Fig. 1. Supplier assessment and selection workflow.
the absence of precise information. Supplier assessment and selection workflow in “Lames LLC” is shown in Fig. 1. Corporate decision procurement makers first define procurement categories and all of these are divided into sub-categories. Then, supplier performances groups according to business activities, which represent groups of individual performances, are defined. The individual performances are established by carefully choosing well known quantitative and qualitative criteria including already existing experience with procurement decision makers. In general, individual performances depend on industry branch relevant to supplier assessment and selection process. For every procurement category, corporate target grade for each individual performance is defined. Target grade of every individual performance presents expected value in supplier selection process. The supplier assessment and selection process can begin. Suppliers are continuously evaluated, at least once a year, which means that the supplier base is a time variable category. Suppliers are grouped into procurement categories, and every supplier is assessed in its particular category, that is why it is possible for one supplier to get represented in several procurement categories. Procurement manager evaluates every supplier individual performance separately, and gets supplier assessment grade, also separately for each supplier individual performance. Supplier individual performance assessment grades are compared to appropriate corporate target grades. The supplier’s capability to satisfy the criteria is determined according to the supplier assessment and selection model: “Supplier approved ? ”. If supplier is approved then the supplier gets in general “Status”: “Preferred – (P )” or “Referenced – (R)”, depends on decision making model and scoring model, and it is stored (included) in “Supplier base”. The supplier which is “Not approved” is defined by “Request for corrective actions”, and follow up of “Supplier action plan”. When supplier is improved its individual performances corporate procurement manager once more evaluates separately every supplier individual performance, gets supplier assessment grade for each of them, and the process continues as mentioned before. If supplier did not improve its individual performance gets “Status”: “Disorder – (D)”.
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Table 1 Performance groups and individual performances for supplier assessment. Performance groups
Individual performances
Method of evaluation
Financial
Debt Dependency Profitability
Ratio Debt/Equity % Turnover with Lames/Supplier Global Turnover Net result/Turnover
Logistics
Delivery Distribution Capacity Commitment/Stock Coverage B to B Solutions
Respect of delivery time Ability to manage the distribution chain Capacity to supply required prod./service range Commitment/Availability on supplier stock Supplier’s geographical coverage Ability to implement EDI or B to B solution
Competitiveness
Technical offer Technical know-how Proposition force Price transparency Cost level/market Cost level/competitors
Management of the technical part of its offer Technical/Business know-how Proposition force (process improvement, ability to innovate) Transparency: prices, organization Cost Level compared to the market Price level/competitors
Quality
Quality Certification Quality compliance Corrective actions Sustainable development
ISO certification, control process or various certification Compliance with specifications Ability to implement corrective actions Safety & Environmental information, child labour
Service/Commercialism
K. A. M. approach Reactivity R&D Export turnover Reporting
Is the Key Account Manager approach working adequately? Reactivity towards a demand R&D department existence % of export turnover/Global turnover Reporting
3.1. Procurement categories, groups and individual performances “Lames LLC” company defined the following procurement categories: a) Raw Material; b) Industrial Products & Consumables; c) Industrial Services; d) Utilities; e) Transport Services; f) General Supplies & Services; g) Plants and Equipments; z) Out of Scope. Supplier performances groups represent groups of individual performances that are to be assessed in the following business activities: 1) Finance; 2) Logistics; 3) Competitiveness; 4) Quality; 5) Service/Commercialism. All of individual performances, for supplier assessment represent questions which are assessed and ranked in three supplier assessment grades (1, 2 or 3) respectively. Table 1 shows all performance groups, all individual performances and the method of evaluation for every individual performance. Corporate target grade for supplier performances for every purchase category are defined separately. It is necessary because the importance of one performance is not the same for suppliers in different purchase category. In other words, there is difference between the target grade for suppliers who deal with raw materials and those who supply office supplies or provide the service of cleaning office space. It is important to mention that a supplier can be well placed in one procurement category, and not so well placed in another. 3.2. Empirical model The real world application currently used in a local “Lames LLC” company for supplier assessment and selection, is named “Empirical model”. This model is presented in the following way. For every question concerning supplier individual performance, which consists of 24 questions (Table 1), the supplier assessment grade of performance is set on a scale form 1 to 3 so that the sum of the entire performance set should be 50 (Eq. (1)). It can be seen, that sum = 50 is smaller than maximum possible sum value 72 (24 questions ∗ 3 target grade = 72). i
target gradei = 50
(1)
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Fig. 2. (a) Supplier assessment grade, corporate target grade and the enclosed areas; (b) Graphical surface representation.
% supplier performance =
(target gradei ∗ current gradei ) ∗ 2/3
(2)
i
This should be done in order to apply the following formula for calculating the percentage of supplier performance on a scale from 0% to 100% (Eq. (2)). 3.3. The GA performance value constraint model This subsection presents our previous research which is in detail presented in [8]. As it can be seen supplier individual performance can be lower, equal to, or higher than defined target values (Fig. 2(a)). If supplier assessment grade is lower than the corporate target grade, it means that the supplier has not yet satisfied company requirements. If supplier assessment grade is equal or higher to the target value then the performance of the supplier is as expected. The proposed genetic algorithm performance value constraint model is based on performance value constraints during supplier assessment for one performance on maximum target grade. This limits the possibility of a supplier performance which is not requisite to heighten supplier assessment grade. Further on, the proposed model calculates the area enclosed by the performance values which are lower or equal to target grade on one side, and on the other, by target grade of those supplier assessment grade performances which are higher than the target values. Corporate target grade and supplier assessment grades represent variables in optimization algorithm. The optimization algorithm searches for the best solution, the maximum supplier area enclosed with respect to previously defined conditions between target and assessment grades. The order of all 24 vertices of defined icosikaitetragon, (twenty-four-sided polygon) is assorted to maximize the enclosed area. In this way the estimation of the maximum affected area is completed thus eliminating the possibility of subjectivity in positioning individual performances or groups of performances. 3.4. Surfaces ordered model On one hand, in the graphical representation of the results, as it can be seen, the questions are grouped by 3 (Financial), 4 (Quality), 5 (Service/Commercialism) and 6 (Logistics, Competitiveness). In this way
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Fig. 3. Supplier individual performances, target level performances, enclosed target and supplier areas and the defined enclosed surface.
graphical representation of the results corresponds to five different surfaces. The maximum affected area can be observed in relation to different surfaces, and it can be named surface ordered model. One such example together with supplier performances, groups of performances, and the enclosed area by the proposed methodology is shown in Fig. 2(b). In accordance with what was previously mentioned, light grey colour of enclosed area shows that the criteria was satisfied, grey enclosed area shows where supplier performances are higher than target performance, and black enclosed area indicates where target grade is grater than supplier assessment grade (Fig. 3).
4. The harmony search performance value constraint model
The aim of this research is to find the best solution, and maximize supplier area enclosed, with respect to: (1) previously defined conditions between target and assessment grades; (2) the order of vertices defined by individual performances could be random; (3) the order of surfaces defined by group performances could be random. The new proposed hybrid model includes two different artificial intelligent techniques. Firstly, genetic algorithm is used, soft computing technique, and after that harmony search algorithm, population-based meta-heuristic algorithm. This problem is divided and solved in two steps. In the first phase, group supplier area, each of 5 defined, will be maximized: Financial, Logistics, Competitiveness, Quality, and Service/Commercialism. Good qualities of GA performance value constraint model will be used. In the second phase, supplier area surface will be maximized with respect to position and order of each 5 performance group areas defined in icosikaitetragon. In the second phase, a new metaheuristic algorithm has been added mimicking the improvisation of music players and it is named Harmony Search Algorithm (HSA).
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Fig. 4. Flow chart of the Harmony Search algorithm (Geem, 2000 [3]).
4.1. Harmony Search algorithm Harmony Search (HS) is a relatively new population-based meta-heuristic algorithm which has obtained noticeable results in the field of combinatorial optimization [3]. It mimics the behaviour of a music orchestra when aiming at composing the most harmonious melody, as measured by aesthetic standards. HS maintains a set of solutions in the so-called Harmony Memory (HM). An estimation of the optimal solution is achieved in every iteration by applying a set of optimization parameters to the HM, which produce a new harmony vector every time. Fig. 4 illustrates the flow diagram of the HS algorithm, which can be summarized in four steps: (1) initialization of the HM; (2) improvisation of a new harmony; (3) inclusion of the newly generated harmony in the HM provided that its fitness improves the worst fitness value in the previous HM. (4) returning to step (2) until a termination criteria is satisfied. This procedure is mainly controlled by two different probabilistic parameters, which are sequentially applied to produce a new set of candidate solutions. The parameters that are used in the generation process of a new solution are called Harmony Memory Considering Rate (HMCR) and Pitch Adjusting Rate (PAR). 1. HMCR ∈ [0, 1], establishes the probability that the new value for a certain note is drawn uniformly from the values of this same note in all the remaining solutions. 2. PAR ∈ [0, 1], establishes the probability that the new value xnew for a given note value x is obtained by adding a small random amount to the existing value xold . xnew = xold + ωx · ε where ωx represents the pitch bandwidth, and ε is a random number drawn from a uniform distribution with support [−1, 1]. A low pitch adjusting rate with a narrow bandwidth may restrict the diversification of the algorithm within a small search subspace and consequently, decrease the convergence rate of the overall solver. On the other hand, a high PAR with a high value of ωx may force the algorithm to unnecessarily escape from areas with potentially near optimal solutions.
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Table 2 Experimental results: Empirical model, Surface without constraints, GA value constraint model, HSA & GA value constraint model. No
Year
Company
Empirical model/ Status
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
2012 2012 2012 2012 2012 2012 2012 2012 2012 2012 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013 2013
DK PACK d.o.o. Manzan 98 OC Elab Ninagro Staklo enterijeri Belem Adamšped system Tele group SIRMIUM PAPIR Lames S.p.A. INTER-HERMES INSTITUT IMS ALBO StandardŠped ALCO FLEXIMA AUTO LL Logist PAPIR DOO Elektro nedex Merkator-S TEHNOLIFT DAJAS SRBOEXPORT YONEX d.o.o. HARCO d.o.o. DK PACK d.o.o. Alatnica Vuletić FESTO Gesellscha Fromm pakovanje Ninagro MIS COMERC Mitroprevoz Medigo M Spektar MB Transport Pro Tea RECA HAHN KOLB Heli Viljuskari Dali d.o.o. Adamšped system Elektromaterijal Tele group SIRMIUM PAPIR Varmedja Metalobox YU GARFILD doo Biroshop Vujasin. Agencija za zaštitu PAKO MD Golf Metalija TR Lames S.p.A.
68.66% 46.66% 80.00% 83.33% 80.66% 73.33% 70.00% 76.66% 81.33% 81.33% 81.33% 84.67% 82.00% 75.33% 75.33% 72.66% 74.00% 80.00% 68.00% 88.66% 79.33% 57.33% 50.66% 77.33% 84.66% 76.66% 78.66% 68.66% 80.66% 56.00% 86.66% 84.66% 74.66% 82.00% 82.00% 76.00% 78.00% 83.33% 84.00% 64.00% 76.66% 72.00% 52.00% 87.33% 76.00% 74.00% 79.33% 77.33% 66.00% 74.66% 79.33% 78.66%
Surface without constraints
GA value constraint
HSA value constraint/ Status
70.58% 40.19% 84.15% 86.27% 92.30% 77.88% 74.50% 96.07% 79.80% 75.47% 84.31% 90.09% 92.30% 90.19% 79.41% 75.49% 80.39% 86.27% 67.92% 98.03% 81.73% 56.86% 44.11% 82.35% 88.23% 84.31% 85.84% 76.41% 93.13% 54.90% 90.19% 95.09% 77.88% 86.53% 80.39% 83.96% 83.33% 85.57% 94.23% 63.72% 83.01% 84.61% 55.76% 99.05% 82.35% 69.23% 84.61% 86.53% 70.19% 82.35% 91.50% 78.30%
69.40% 39.52% 82.94% 84.83% 91.21% 76.60% 72.91% 94.92% 78.86% 74.59% 82.90% 88.80% 91.21% 88.26% 78.08% 74.22% 78.67% 84.83% 67.13% 96.39% 80.02% 55.91% 43.17% 80.97% 86.75% 82.90% 84.85% 75.52% 91.57% 53.98% 88.68% 93.06% 76.96% 85.51% 78.67% 82.98% 81.93% 83.79% 93.11% 62.36% 82.05% 83.61% 55.11% 97.90% 81.36% 68.41% 83.61% 85.51% 69.36% 80.97% 90.44% 77.39%
Distinction HSA & EM
% supplier performance
Preferred – (P)
(P) (D) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (D) (R) (P) (R) (P) (P) (D) (D) (P) (P) (P) (P) (R) (P) (D) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (P) (R) (D) (P) (P) (P) (P) (P) (R) (P) (P) (P)
111.65% 44.66% 126.73% 145.63% 122.11% 101.90% 89.32% 112.74% 131.73% 150.46% 134.95% 140.59% 129.80% 105.82% 116.50% 109.70% 106.79% 133.98% 89.71% 158.25% 110.57% 66.99% 49.51% 123.30% 146.60% 126.21% 113.08% 84.11% 127.18% 59.22% 155.33% 130.09% 113.46% 137.50% 132.03% 108.41% 119.41% 125.00% 130.76% 72.81% 107.47% 100.00% 55.76% 139.25% 115.68% 115.38% 123.07% 122.11% 93.26% 114.56% 119.62% 128.03%
Referenced – (R)
(R) (D) (P) (P) (P) (P) (R) (P) (P) (R) (P) (P) (P) (P) (P) (R) (P) (P) (R) (P) (P) (D) (D) (P) (P) (P) (P) (R) (P) (D) (P) (P) (P) (P) (P) (P) (P) (P) (P) (R) (P) (P) (D) (P) (P) (R) (P) (P) (R) (P) (P) (P)
1.06 −18.07 3.54 1.77 11.56 4.26 3.99 19.86 −3.13 −9.03 +1.8 +4.65 +10.1 +14.65 +3.52 +2.10 +5.93 +5.69 −1.29 +8.01 +0.86 −2.54 −17.35 +4.49 +2.40 +7.52 +7.29 +9.08 +11.91 −3.74 +2.27 +9.02 +2.98 +4.10 −4.23 +8.41 +4.79 +0.54 +9.78 −2.62 +6.56 +13.88 +5.64 +10.79 +6.58 −8.17 +5.11 +9.56 +4.84 +7.97 +12.28 −1.64
Disorder – (D)
5. Experimental results Experimental results (Table 2) show minimum and maximum supplier assessment and selection and supplier performance values and their status: Preferred, Referenced and Disorder. Furthermore, this research shows that new hybrid HSA & GA value constraint model is slightly more restricted than GA value constraint model.
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Table 3 Comparative assessment and selection company analysis in 2012 and 2013. No
Company
Year
Trend
2012
1 2 3 4 5 6
DK PACK d.o.o. Ninagro Adamšped sys. Tele group SIRMIUM PAPIR Lames S.p.A.
2013
Empirical model
Status
Empirical model
Status
Assessment
Status
68.66% 83.33% 70.00% 76.66% 81.33% 81.33%
Preferred Preferred Preferred Preferred Preferred Preferred
76.66% 56.00% 64.00% 72.00% 52.00% 78.66%
Preferred Disorder Preferred Referenced Disorder Preferred
↓ ↓
↔ ↓ ↔ ↓ ↔
Presented results show that the assessment values of HSA & GA model are significantly lower than GA values constraint models of poorer companies which can be seen in the example of the following companies: Manzan 98 OC, DAJAS, SRBOEXPORT. Furthermore, when comparing the hybrid HSA & GA model and GA model, it can be seen that there is a mild decrease when it comes to assessed value of “Tele group” company and that there is a serious decrease in assessment position (Status) from “Preferred” to “Referenced”. On the other hand, by comparing HSA & GA model and GA values constraint model of better companies, that is, those that have “Preferred” status, the assessment value is higher in HSA & GA model. That is the case in the following companies: Papir d.o.o., Merkator-S, Fromm pakovanje. It can thus be concluded that new hybrid HSA & GA values constraint model separates, much better and with greater precision, poor companies from the good ones. Supplier assessment is a continuous process, and its results must be conveyed to the suppliers so they could create a corrective action plan to develop and improve their weaknesses. The main goal of assessment processes is to ensure successful and long-term cooperation between all parties in a logistics supply chain. As this research shows, 11 companies are assessed in 2012 and 6 of them are assessed in 2013. Their comparative analysis is shown in Table 3. The results show dramatic decrease in two companies “Ninagro” and “Sirmium papir” which both lost “Preferred” status and have become “Disorder”. There is also a slight decrease in assessed supplier value in “Tele group” company, and change form “Preferred” status to “Referenced”. The other three companies kept the “Preferred” status, but it has to be stressed that there has been an increase in assessed value in company “DK PACK”. The other two companies “Adamšped system” and “Lames S.p.A.” kept the assessment position – “Preferred” status but slightly decreased assessment value. 6. Conclusion and future work Nowadays, the community requires effective soft computing methods and tools for optimizing large scale complex inbound logistics distribution and supply chain management systems. The hybrid HSA & GA performance value constraint model is presented in this paper. The experimental results of this method are obtained from the realistic data set of the supplier performances of a multinational “Lames” company operating in Serbia. The experimental results were later on compared to the results obtained by our previous research. Presented comparison shows that the values obtained by new hybrid HSA & GA value constraint model are slightly restricted then GA value constraint model, and HSA & GA value constraint model separates, much better and more precisely, poor companies from the good ones in business environment. This research can be classified as empirical multi-attribute decision making model and scoring models are typically used to evaluate suppliers for inclusion in the supplier base. Future development can be directed towards adding weight to every performance group; business con-
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straints can be considered as well as technical, legal, geographical and commercial nature of every individual performance. Acknowledgment The authors acknowledge the support for research project TR 36030, funded by the Ministry of Science and Technological Development of Serbia. References [1] A. Amindoust, S. Ahmed, A. Saghafinia, A. Bahreininejad, Sustainable supplier selection: a ranking model based on fuzzy inference system, Appl. Soft Comput. 12 (6) (2012) 1668–1677. [2] G.J. Burke, E. Carrillo J, A.J. Vakharia, Single versus multiple supplier sourcing strategies, Eur. J. Oper. Res. 182 (1) (2007) 95–112. [3] Z.W. Geem, J.H. Kim, G.V. Loganathan, A new heuristic optimization algorithm: harmony search, Simulation 76 (2) (2001) 60–68. [4] W. Ho, X. Xu, P.K. Dey, Multi-criteria decision making approaches for supplier evaluation and selection: a literature review, Eur. J. Oper. Res. 202 (1) (2010) 16–24. [5] M. Kumar, P. Vrat, R. Shankar, A fuzzy goal programming approach for vendor selection problem in a supply chain, Comput. Ind. Eng. 46 (1) (2004) 69–85. [6] M. Pattnaik, Supplier selection strategies on fuzzy decision space, Gen. Math. Notes 4 (1) (2011) 49–69. [7] D. Simić, S. Simić, A review: approach of fuzzy models applications in logistics, in: R. Burduk, M. Kurzynski, M. Wozniak, A. Zolnierek (Eds.), CORES 2011, in: Adv. Intell. Soft Comput., vol. 95, Springer, Heidelberg, 2011, pp. 717–726. [8] D. Simić, V. Svirčević, S. Simić, An approach of genetic algorithm to model supplier assessment in inbound logistics, in: Soft Computing Models in Industrial and Environmental Applications, in: Advances in Intelligent Systems and Computing, vol. 188, 2012, pp. 83–92. [9] S. Talluri, R.C. Baker, A multi-phase mathematical programming approach for effective supply chain design, Eur. J. Oper. Res. 141 (3) (2002) 544–558. [10] J. Tepić, I. Tanackov, G. Stojić, Ancient logistics – historical timeline and etymology, Teh. Vjesn. – Stroj. Fak. 18 (3) (2011) 379–384. [11] T.Y. Wang, Y.H. Yang, A fuzzy model for supplier selection in quantity discount environments, Expert Syst. Appl. 36 (10) (2009) 12179–12187.