Multi-Criteria Supplier Selection and Purchase Problem
* Author to whom correspondence should be addressed.
Sigma Journal of Engineering and Natural Sciences 2018, Vol. 36, Issue 4, pp. 1255-1264; doi.org/10.62051/ytu.sigma-journal-of-engineering-and-natural-sciences-multi-criteria-supplier-selection-and-purchase-problem
Abstract
Keywords: Supply chain management; single-product multi-echelon supply chain network design; optimization; multi-criteria supplier selection and purchase problem.
1. Introduction
Due to today’s challenging and competitive business environment, reducing costs has become crucial and a lot of effort should be taken by firms. For example, they can choose the best supplier(s) to realize this goal. As the supply chain is an interconnected system requiring in cooperation of collaborators, the selection of collaborators plays an important role in supply chain management (SCM) [1]. Selecting the appropriate collaborators can effectively reduce the major cost for a product which consists of two basic components: raw material cost and raw material parts and strengthens the business competitiveness. In particular, most firms consume *
Corresponding Author: e-mail: senyigit@erciyes.edu.tr, tel: (352) 207 66 66 / 32455
considerable amount of their incomes on purchasing. For these reasons, the supplier selection process (SSP) has gained attention [2]. However, selecting the supplier that proposes the lowest price is not enough and multi-criteria need to be focused when choosing suppliers. In the literature, there are many different criteria in the multi-criteria supplier selection [3-11]. In this paper, we consider the case where purchasing product raw materials from the best suppliers, at the most competitive prices, producing in the most suitable quantities, storing the produced items in the most appropriate quantities and delivering the products to the customers from distribution centres (DCs) according to the size of the defect between echelons under deterministic conditions [5-8]. There are two phases in the solution of the proposed problem. In the first phase, the best supplier according to the Ng model (supplier selection phase) is selected. After this phase, the total cost of single-product multi-echelon supply chain network of the enterprise XYZ (system cost optimization phase) are minimized. The problem is solved in two phases because the units of criteria are different. For that reason, we cannot use these criteria together in system cost optimization phase. The chairmodel-1 as single product is investigated. The chairmodel-1 has four raw materials. These are in carcass groups (S1); seat groups (S2), sponges (S3) and packages (S4). We assume that each of the raw materials has two suppliers. We focus on three different criteria (quality, price and distance) for supplier selection phase in this study. These criteria are already being used by the enterprise. For this reason, we used these criteria in the application. The quality of the purchased parts is also a critical criterion for an enterprise in supplier selection. The distance is about delivery efficiency. The ‘‘delivery’’ criterion measures the percentage of on time deliveries. Finally, the price denotes the calculated price level offered by a supplier as compared to the average market price [3]. When the suppliers are selected then the total cost of single-product multi-echelon supply chain network of the enterprise XYZ with the mixed integer linear programming (MILP)is optimised by using LINDO software. Finally, the amount of purchased raw materials from related suppliers and the suppliers which we collaborate for each raw material is determined by the getting solution of multi-criteria supplier selection purchase problem. The difference of this study from studies in the literature is selecting suppliers according to the multi-criteria with the optimization of supply chain network. The significant contribution of this study is that it proposes a new type supplier selection and purchase problem and the solution of this new problem with an application. SCM and SSP have large-scale consideration in the literature and the methods to address the supplier selection problem have grouped into three types of models as mathematical programming, cost-based, and categorical [2]. There are also studies with genetic algorithms; artificial intelligence techniques, etc. (see references [10, 12]) for SCM and SSP. The literature about this study can be divided into two parts: the defective supply chain system (DSCS) and the supplier selection and purchase problem (SSPP). In DSCS, unequal input and output may occur; therefore, the case should be taken into account to make the production system more realistic. Early studies discussed reject allowances, which are extra inputs required to fulfil the order. Much of the literature concerning different yield rate systems has covered only the single-order system [4, 5]. A supply chain which has defects with at least one echelon is called the multi-echelon defective supply chain (MDSC) system [5-8]. Burke et al. analysed single period, single product sourcing decisions under demand uncertainty [6, 13]. Awasthi et al. studied a supplier selection problem for a single manufacturer/retailer that faces a random demand with a limitation on minimum and maximum order sizes [6, 14]. Zhang and Zhang [6, 15] studied supplier selection and purchase problem considering minimal ordering quantity and suppliers’ limitation on capacity under stochastic demand. Our study focuses on multi criteria supplier selection while Zhang and Zhang’s study is focus on stochastic demands.
Senyigit and Golec proposed a new heuristic for SSPP for MDSC systems with stochastic demand. They investigated the performance of the proposed H1 heuristic using 4 cases. They assumed that supplier s’ capacities are infinite. Their paper was the first study about SSPP for MDSC system with stochastic demand in the literature [5]. Senyigit studied the purchasing costs of raw materials, production costs, fixed operation costs, transportation costs and lost sales costs in his study similar to his earlier study with Golec. ProModel simulation software was used to model the heuristics and MDSCN system. Senyigit extended the work he did with Golec with finite supplier capacity and a new heuristic. Additionally, a real case study using of these heuristics in the Turkish furniture firm was presented [6]. Senyigit and Soylemez focused on the multi-echelon multi-product defective supply chain network (MMDSCN) of firm X in Kayseri, Turkey which produces chairs under uncertain demand. This manuscript was a proceeding paper. Our aim is to differentiate Senyigit and Soylemez’s proceeding paper with a new perspective. They assumed that the demands of customers were stochastic and normally distributed. They noted that Benny1 and Maksim chairs as products. They proposed two heuristics for the solution of this problem. They formed an MMDSCN system of firm X with the mixed integer linear programming (MILP) by using LINDO. The heuristics and MMDSCN system were modelled by ARENA 4.0. Simulation experiments showed that the proposed H2 heuristic outperformed the H1 heuristic [7]. Senyigit proposed a new problem called the lot-sizing with supplier selection problem (LSSP) in the MDSCN. He showed the multi-product MDSCN of enterprise X [8]. Ho et al. investigated 78 different studies about supplier selection and evaluation. One of the results of their studies was to establish the three most commonly used criteria are quality, price and lead time [9]. Alfares and Turnadi show a realistic multi-item lot-sizing problem with multiple suppliers, multiple time periods, quantity discounts, and backordering of shortages by using MILP [10]. Hamdi et al. review the literature in the field of supplier selection under supply chain risk management [12]. The rest of the paper is as follows. Section 1 of the study presents introduction and earlier studies on multi-criteria supplier selection and purchase problems. Section 2 gives information about proposed mathematical models for the problem (Ng Model, Mixed integer linear programming, etc.) and application. Section 3 presents the results of the study. The last section gives information about the concluding remarks and future studies.
2. Methods
In this section, the notation is described to be used in this model, firstly. Ng model are presented for multi-criteria supplier selection. Finally, the mathematical model of the SMSCN system which we differentiated our earlier study is proposed by using multi-criteria in supplier selection process. The notations used in the model and their meanings are listed as below [7]: Indices/Sets: I Suppliers. S Raw materials. M Distributions Centres (DC) N Customers. J Criteria. Parameters: P The production capacity limits on the factory. Km The capacity limits of the distribution centre m. Ksi The capacity limits on raw material s of supplier i Dn The total demand of customer n. 1257
Csi The transportation cost of raw material s from supplier i to factory. SCsi The purchasing cost of raw material s from supplier i to factory. Cm Unit transportation cost of product from factory to distribution centre m. Cmn Unit transportation cost of product from distribution centre m to customer n. F The fixed operating cost of factory. Fm The fixed operating cost of distribution centre m. 𝝎𝒔 Units of raw material s required to produce one unit of product according to the product bill of material. U The average defect rate of factory. Vm The average defect rate of distribution centre m. Tsi The average defect rate of supplier i for raw material s. PC The production cost. TC Total cost. Decision Variables: Xsi The total units of raw material s purchased from supplier i Ym The amount of product from factory to distribution centre m. Zmn Total units of product distributed from DC m to customer zone n. The score of jth criteria of supplier i. The weight of criteria j of supplier i. Transformed measures of criteria j of supplier i. The score of supplier i for raw material s.
Binary Variable: 1, 𝑖𝑓 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 𝑖 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑠 𝑓𝑜𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑖𝑠 𝑢𝑠𝑒𝑑 ∝𝒔𝒊 = { 0, 𝑖𝑓 𝑠𝑢𝑝𝑝𝑙𝑖𝑒𝑟 𝑖 𝑓𝑜𝑟 𝑐𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡 𝑠 𝑓𝑜𝑟 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑖𝑠 𝑛𝑜𝑡 𝑢𝑠𝑒𝑑
2.1. NG MODEL
The MCSSPP are in a SMSCN based on two parts. First, the best supplier for each raw material is determined. Ng model is for the multi-criteria supplier selection. Wij represents the weight of criteria j of supplier i. Yij is transformed measures of criteria j of supplier i. Second, the SMSCN of enterprise XYZ are optimised by MILP. The total cost of the system is obtained from the optimization solution. The best supplier for each raw material and the optimum purchasing quantities from these best suppliers are determined. Ng model can be given below [3]:
The objective function of the Ng model is presented by equation (1). The goal of this objective function is to maximise the score of the best supplier. Constraint (2) ensures the weight values are in the same sequence as the ranking. Constraint (3) is about normalisation. Xij is the score of jth criteria of supplier i as shown in table-1.The converted values used in the study are calculated using equation (5) for normalisation (see Table-2) [3].
X ij Mini 1, 2,...,J ( X ij ) Maxi 1, 2,...,J ( X ij ) Mini 1, 2,...,J ( X ij )
2.2. APPLICATION
We consider a supply chain network of enterprise XYZ. The manufacturer which produces chairs. The data used are as in Şenyiğit and Soylemez study [7]. Enterprise XYZ has a 30.000 units capacity and 20.000 TLs for fixed operating costs for the product. The production cost for XYZ for each chairmodel-1 is 7 TLs. The enterprise has 3 distribution centres (DCs) in three different countries (Turkey, Iran and France). There are three groups of customers which are in the same country as the DCs are assumed. All suppliers have finite capacities. All raw materials have to purchase from related suppliers for the production of Chairmodel-1. Chairmodel-1 has four different raw materials (carcass groups, seat groups, sponges and packages). There are two different suppliers for each raw material (8 suppliers (4x2)). Only one supplier from two suppliers for each raw material must be chosen (4 suppliers from 8 suppliers). For this reason, the best supplier for each raw material of the Chairmodel-1 by the Ng model (𝑣𝑖𝑎 𝜷𝒔𝒊) is selected. The data of suppliers for different criteria are shown in table-1. As is seen, the units of each criterion are different. Quality (J1) is a supplier selection criterion indicating what percentage of the Chairmodel-1s supplied by the supplier firms are in good condition. Price (J2) indicates the purchase price of the product. The unit is Turkish Liras. Distance (J3) is the distance of the suppliers to the firm in the unit of km. Ng [3] emphasized that all measures were positively related to the score of a supplier. If there was a negatively related criterion, the transformation of negativity or reciprocal taking could be applied for conversions. A common scale for all measures was also an important issue. Ng stated that a particular criterion measure on a large scale might dominate the score. A reciprocal transformation of price and distance measures is taken so that the transformed values are positively related to the desired scores as in the Ng study [3]. The data are normalised which is shown in table-1 by equation (5). Table-2 showed the normalization results, the score of supplier i for raw material s and selected suppliers. The 0 and 1 values in table-2 were calculated by equation (5) for normalization. The score values in table-2 were found by Ng model. For example, there were two suppliers of sponge for the Chairmodel-1 (see table-2). The score of I31 was 0.5 and the score of I32 is 0. The result showed I31 to be better than I32. Therefore, we selected I31 as the supplier of sponge for the Chairmodel-1. This example had been shown to facilitate understanding of the problem. The manufacturer faces the optimization problem of determining the best supplier and purchasing amount from the best supplier while satisfying customers’ demands and minimising the total cost (TC) of the SMSCN system. Thus, in this problem there are four kinds of costs must involve. These are; purchasing costs, transportation costs, production costs and fixed operating costs. The customer demands balance, product balance and raw materials’ balance constraints are ensured by, in order, Constraint (7), Constraint (8) and Constraint (9).
Table 2. Transformed and normalised measures of suppliers under criteria and results of Ng model S S1 S2 S3 S4
2.3. MIXED INTEGER LINEAR PROGRAMMING
The objective function is TC of the SMSCN system and all intermediate variables 1260inimization (Equation (6)). The objective functions and constraints of the model are listed below as: Min ∑𝑠 ∑𝑖 𝐶𝑠𝑖 𝑋𝑠𝑖 𝛽𝑠𝑖 + ∑𝑠 ∑𝑖 𝑆𝐶𝑠𝑖 𝑋𝑠𝑖 𝛽𝑠𝑖 + ∑𝑚 𝐶𝑚 𝑌𝑚 + ∑𝑚 ∑𝑛 𝐶𝑚𝑛 𝑍𝑚𝑛 + ∑𝑚 𝑃𝐶𝑚 𝑌𝑚 + ∑𝑚 𝐹𝑚 + 𝐹
DCs, factory production and suppliers’ capacity limits constraints are maintained by, in order, Constraint (10), Constraint (11) and Constraint (12). Constraint (13) provides that decision variables must be greater than 0. Constraint (14) is about binary variables. The capacity limits on raw material s of supplier i, the transportation cost of raw material s from supplier i to factory,
the purchasing cost of raw material s from supplier i to the factory and the average defect rate of supplier i for raw material s are shown in table-3. Table 3. The parameters of suppliers according to the raw materials [7] S S1 S2 S3 S4
Ksi (Units) 25.000 25.000 25.000 25.000 25.000 25.000 25.000 25.000
The parameters such as transportation, purchasing, production, fixed operating costs, average defect rates, capacities of suppliers, factory and DCs and the customer demands of enterprise XYZ are shown in table-4. Table 4. The parameters of DCs and customers [7] M Cm (TL) Um (%) Km (Units) Fm (TL) Cmn (TL) N Dn (Units) Vm (%)
3. Results
The calculated total quantities of raw material s purchased from supplier i for the best and worst models were presented in Table-5. The result of the 1261ptimization of the MILP model of SMSCN of enterprise XYZ showed that I12, I21, I31 and I42 suppliers are the best suppliers while I11, I22, I32 and I41 suppliers are the worst suppliers. 17324.4 units carcass groups (S1), 17142.4 units seat groups (S2), 17324.4 units sponges (S3) and 17324.4 units packages (S4) are purchased from the best suppliers for each raw material. 16963.85 units S1, 16963.85 units S2, 17142.4 units S3 and 17142.4 S4 are purchased from the worst suppliers for each raw material for getting the worst model solution. The reason for the diversity in the number of seat groups is the average defect rate of the best supplier of the seat group raw material (5%). The total cost of the best model for SMSCN of enterprise XYZ is 553926. 6 TLs whereas total cost of the worst model is 562834.9 TLs. Table-6 presents the calculated quantities for DCs and customers for the best model and worst model. 16,285.3 Chairmodel-1s must be produced at the factory for all models. As there was no fractional transportation, it turned into an integer-valued solution by rounding up. For that reason, we had to revise the solution that we obtained from MILP.
Table 5. The calculated total quantities of raw material s purchased from supplier i Best Model 0 17324.4 17142.4 0 17324.8 0 0 17324.8
Table 8. The corrected total quantities of raw material s purchased from supplier i
The corrected quantities for DCs and customers are shown in Table-7. Table-8 presents the corrected total quantities of raw material s purchased from supplier i both best model and worst model. In the application, 16288 units product must be produced to satisfy the total demands of customers.
4. Concluding Remarks And Future Studies
As the enterprises continue to exist, it is essential for them work with the suppliers that reduce the total system costs. Besides suppliers offering the lowest prices which are not generally accepted as ‘‘efficient sourcing’’, multi-criteria must be in supplier selection with optimum purchasing amount to reduce the total costs and satisfy all customer demands. The motivation of
this study and the multi-criteria supplier selection and purchase problem (MCSSPP) are stemmed from the request of the enterprise XYZ which is a firm from the Turkish furniture industry in Kayseri, Turkey. This paper addressed the problem and presented the solution approach proposed to the problem. To apply the solution approach to MCSSPP, a chair model that has four different raw materials was selected as an application product from the products of enterprise XYZ. For each raw material, the enterprise XYZ had two suppliers. So, each raw material must be procured from one of the suppliers. The problem was modelled by supplier selection and system cost optimization phases. In supplier selection phase, the best supplier was determined by the Ng model for each raw material. It was found that I12, I21, I31 and I42 were the best suppliers while I11, I22, I32 and I41 were the worst suppliers. After the best and worst suppliers were determined, the single-product multi-echelon supply chain network (SMSCN) of enterprise XYZ was first formed by mixed integer linear programming (MILP) in the system cost optimization phase. Then, the SMSCN was optimized, and the optimum results were corrected to integer values according to the defect rates among echelons. The final model was accepted as the best model. The total cost of the best model was 553926.6 TLs. Same procedure were applied for the worst suppliers. The total cost of the worst model was calculated as 562834.9 TLs. As a conclusion, the total cost of SMSCN of enterprise XYZ was reduced by 8908.3 TLs (%1.61). As a future research, it is planned to improve this study by multi products, sustainability, and green supplier selection perspectives. The proposed approach can be applied to wide range of firms to solve their MCSSPPs and to improve their competitiveness.
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ŞENYİĞİT, E.; BABAYİĞİT, B. Multi-Criteria Supplier Selection and Purchase Problem. Sigma Journal of Engineering and Natural Sciences 2018, Vol. 36, pp. 1255-1264. https://doi.org/10.62051/ytu.sigma-journal-of-engineering-and-natural-sciences-multi-criteria-supplier-selection-and-purchase-problem