A MULTI-OBJECTIVE APPROACH FOR OPTIMUM QUOTA ALLOCATION TO SUPPLIERS IN SUPPLY CHAIN

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1 International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 6, Issue 11, Nov 2015, pp , Article ID: IJARET_06_11_004 Available online at ISSN Print: and ISSN Online: IAEME Publication A MULTI-OBJECTIVE APPROACH FOR OPTIMUM QUOTA ALLOCATION TO SUPPLIERS IN SUPPLY CHAIN M. C. S. Reddy Department of Mechanical Engineering, University College of Engineering, Osmania University, Hyderabad , India ABSTRACT In all industrial firms where a large number of parts and components are supplied by different suppliers to the raw materiel stores. So it is necessary to keep a track of their performances and supplier ratings individually. The shortages of many basic raw materials and unfriendly attitudes on the part of suppliers can seriously jeopardize production units. So supplier evaluation comes a necessary task. The supplier selection in the supply chain is a multicriteria problem for this a problem is formulated. The formulated problem is including three primary objectives such as minimizing the net purchase cost, minimizing the net transportation cost and minimizing the net late deliveries subject to realistic constraints regarding buyer s demand, vendor s capacity, budget allocation to individual vendor, Vendor s quality of the items, vendor s quota flexibility, purchase value of items etc. This paper consists of allocating the quota to suppliers from a set of pre-selected candidates. In this paper the Lexicographic Method is used and solved above three objectives on the priority basis. A real life example is also presented and solved by the MATLAB and results are shown in the paper. Key words: Multi Objective, Optimum Quota, Supply Chain, Linear Programming. Cite this Article: M. C. S. Reddy. A Multi-Objective Approach For Optimum Quota Allocation to Suppliers in Supply Chain. International Journal of Advanced Research in Engineering and Technology, 6(11), 2015, pp INTRODUCTION A supply chain is a set of facilities, supplies, customers, products and methods of controlling inventory, purchasing, and distribution. The chain links suppliers and customers, beginning with the production of raw material by a supplier, and ending 42 editor@iaeme.com

2 A Multi-Objective Approach For Optimum Quota Allocation To Suppliers In Supply Chain with the consumption of a product by the customer. In a supply chain, the flow of goods between a supplier and a customer passes through several echelons, and each echelon may consist of many facilities. The objective of managing the supply chain is to synchronize the requirements of the customers with the flow of materials from suppliers in order to strike a balance between what are often seen as conflicting aims of high customer service, low inventory, and low unit cost. The supplier selection problem deals with issues related to the selection of right supplier and their quota allocations. In designing a supply chain, a decision maker must consider decisions regarding the selection of the right supplier and their quota allocation. The choice of the right supplier is a crucial decision with wide ranging implications in a supply chain. Suppliers play an important role in achieving the objectives of the supply management. Hence, strategic partnership with better performing supplie should be integrated within the supply chain for improving the performance in many directions including reducing costs by eliminating wastages, continuously improving quality to achieve zero defects, improving flexibility to meet the needs of the end-customers, reducing lead time at different stages of the supply chain, etc. In designing a supply chain, decision makers are attempting to involve strategic alliances with the potential supplier. Hence, Supplier selection is a vital strategic issue for evolving an effective supply chain and the right supplier play a significant role in deciding the overall performance. The suppler selection is a complex problem due to several reasons. By nature, the supplier selection in supply chain is a multi-criterion decision making problem. Individual supplier may perform differently on different criteria. A supply chain decision faces many constraints, some of these are related to suuplier s internal policy and externally imposed system requirements. (Manoj Kumara, Prem Vratb, R. Shankarc).. A lot of research has been done on supplier selection problem. (Hongwei Ding, Lyès Benyoucef, Xiaolan Xie) used discrete-event simulation for performance evaluation of a supplier portfolio and a genetic algorithm for optimum portfolio identification based on performance indices estimated by the simulation. This simulation approach will not give exact optimal solution but only give near to optimal solution. (Manoj Kumara, Prem Vratb, R. Shankarc) formulated a fuzzy goal programming for vendor selection problem. This has the capability to handle realistic situations in a fuzzy environment and provides a better decision tool for the vendor selection decision in a supply chain. (Chuda Basnet & Janny M.Y.Leung) was given multi-period inventory lot-sizing model for multiple products and multiple suppliers. By this the decision maker needs to decide what products to order in what quantities with which suppliers in which periods. In this paper a Lexicographic Method is used to solve the multi-objectiveoptimization problems. In Lexicographic Method multi-objectives are solved on the basis of priority of objectives. The vendor selection in the supply chain is a multicriteria problem for this a problem has been formulated that includes three primary objectives shown in the model formulation. A real life example is also presented and solved by the MATLAB and results are shown in the paper. 2. MATLAB MATLAB is an integrated technical computing environment that combines numeric computation, advance graphics and visualization and a high level programming language. The details of which is available in the web site In this software number of toolboxes are available. Among these the SIMULINK tool 43 editor@iaeme.com

3 M. C. S. Reddy box has built-in simlp (), that implements the solution of a linear programming problem and the optimization tool box has an almost identical function called linprog () to solve the problem The simlp () is only suitable for small size problems but the linprog () is suitable for all small size and complex problems. In this paper linprog () is used to solve the supplier selection problem in the supply chain (Brian R. Hunt, Ronald L. Lipsman & Jonathan M. Rosenberg). 3. MULTI- OBJECTIVE LINEAR PROGRAMMING FOR SUPPLIER SELECTION PROBLEM Assumptions 1. Only same type of items is purchased from the vendors. 2. Demand of items is constant and known with certainty. 3. Quantity discounts are not taken into consideration. 4. No Shortage of the item is allowed for any vendor. Index set i index for supplier, for all i = 1, 2,.. N l index for inequality constraints, for all l = 1, 2,.., L m index for equality constraints, for all m=1, 2,.., M k index for objectives, for all k= 1, 2, K Decision variable x i order quantity for the vendor i Parameters D = Aggregate demand of the item over a fixed planning period N = Number of supplier competing for selection p i = Price of a unit item of the ordered quantity xi from the supplier i t i = Transportation cost of a unit item of the ordered quantity xi from the supplier i d i = Percentage of the late delivered units by the supplier i C i = Upper bound of the quantity available with supplier i B i = Budget allocated to each supplier q i = Percentage of the rejected units delivered by the supplier i F i = Supplier quota flexibility for supplier i F = Lower bound of flexibility in supply quota that a supplier should have R i = Supplier rating value for supplier i PV = Lower bound to total purchasing value that a supplier should have Model formulation A multiple-objective linear programming problem can be written as follows: Maximize / Minimize Z k (x i ) = [Z 1 (x i ), Z 2 (x i ), Z 3 (x i ).. Z K (x i )] Subject to G l (x i ) or a l H m (x i ) = b m 44 editor@iaeme.com

4 A Multi-Objective Approach For Optimum Quota Allocation To Suppliers In Supply Chain x i 0 In the above formulation, x i are n decision variables, Z 1 (x i ), Z 2 (x i ), Z 3 (x i ) Z K (x i ); are k distinct objective functions, G n are the inequality constraints and H m are the equality constraints. a n and b m are the right hand side constants for inequality and equality relationships, respectively. The supplier selection problem for three objectives and to the set of system and policy constraints is formulated as follows: Min. Z= (Z 1, Z 2, Z 3 ) Subjected to x i =D (1) x i C i (2) x i B i (3) q i x i Q (4) F i x i F (5) R i x i PV (6) x i 0 and (7) Z 1 = p i x i ; Z 2 = t i x i ; Z 3 = d i x i Objective function (Z 1 ) minimizes the net purchasing cost for all the items. Objective function (Z 2 ) minimizes the net transportation cost for all the items. Objective function (Z 3 ) minimizes the net number of late delivered items from the Suppliers. Constraint (1) puts restrictions due to the overall demand of items. Constraint (2) puts restrictions due to the maximum capacity of the supplier. Constraint (3) puts restrictions on budget amount allocated to the suppliers for supplying the items Constraint (4) puts restrictions on number of rejected items from the suppliers for supplying the items Constraint (5) incorporates flexibility needed with the suppliers quota. Constraint (6) incorporates total purchase value constraint for all the ordered quantities. Constraint (7) puts restrictions on number of items from the supplier purchased should be greater than zero. 4. LEXICOGRAPHIC METHOD In the lexicographic method, the objectives are ranked in order of importance by the problem designer. The optimum solution is then found by minimizing the objective functions starting with the most important and proceeding according to the order of importance of the objectives. Let the subscripts of the objectives indicate not only the objective function number, but also the priorities of the objectives. Thus Z 1 and Z k denotes the most and least important objective functions respectively. The first problem is formulated as Minimize Z 1 (x i ) Subjected to G l (x i ) or a l 45 editor@iaeme.com

5 M. C. S. Reddy H m (x i ) = b m x i 0 and its solution is X1 i and Z 1 (X1 i ) = Z 1 is obtained. Then second problem is formulate as Minimize Z 2 (x i ) Subjected to G l (x i ) or a l H m (x i ) = b m Z 1 (x i ) =Z 1 x i 0 The solution of this problem is obtained as X2 i and Z 2 (X2 i ) = Z 2. This procedure is repeated until all K objectives have been considered. Final values of the x i s will give the optimum solution of the problem (Singiresu S.Rao) 5. A SAMPLE SUPPLIER SELECTION PROBLEM Table 1 Supplier source data of the illustrative example Vendor No. p i Rs. t i Rs d i (%) C i Units B i Rs q i (%) F i R i ,50, ,00, ,50, ,75, The effectiveness of the multi-objective linear approach for the supplier selection problem presented in this paper is demonstrated through a real life data represented in Table-1. The data relates to a realistic situation of a manufacturing sector dealing with any type auto parts (Manoj Kumar, Prem Vrat & R.Shankar). The adopted situation can easily be extended to any other industry. Those suppliers who successfully passed the screening processes were eligible for procurement. A multi objective linear program supplier selection problem is developed for the selection and the quota allocations of the supplier from a list of four potential suppliers under uncertain environments. The objective functions and constraint sets reflect the procurement requirements for a purchased item in the supply chain. The three objectives, viz. minimizing the net purchasing cost, minimizing the transportation cost and minimizing the net late deliveries have been considered subject to few practical constraints regarding demand of the item, suppliers capacity limitations, suppliers budget allocations, etc. We have considered a sample situation faced by a firm. The supplier profiles shown in Table 1 represent the data set for the price quoted (p i in rupees per unit); transportation cost (t i in rupees per unit); the percentage of late deliveries d i ; suppliers capacities C i; units; the budget allocations for the suppliers B i ; the percentage rejections q i ; suppliers quota flexibility F i on a scale of 0 1 and supplier rating R i on a scale of 0 1. If the purchasers following 95.5% (2 Limits) of the accepted policy, therefore maximum limit of rejections should not exceed 4.5%of the demand. Hence the maximum rejections at purchasers are x 0.045=1125 units The least value of flexibility in suppliers quota and least total purchase value of supplied items are policy decisions and depend on the demand. The least value of flexibility in suppliers quota is given as F = F o D and the least total purchase value of supplied items is given as PV =RD: If overall flexibility (F o ) is 0.03 on the scale of editor@iaeme.com

6 A Multi-Objective Approach For Optimum Quota Allocation To Suppliers In Supply Chain 1, the overall supplier rating (R) is 0.92 on the scale of 0 1 and the aggregate demand (D) is 25,000, then the least value of flexibility in suppliers quota (F) and the least total purchase value of supplied items (P) are 750 and 23,000, respectively. Then the formulated multi-objective linear supplier selection problem can be written as for supplier source data of the illustrative real life example Minimize Z 1 =100x x x x 4 Minimize Z 2 = 15x 1 +10x 2 +5x 3 +20x 4 Minimize Z 3 =0.02x x x x 4 Subjected to x 1 +x 2 +x 3 +x 4 =25000 x x x x x x x x x x x x x x x x x x x x x 1, x 2,x 3,x RESULTS & DISCUSSIONS In the above problem first priority is given to minimization of net purchase cost, second priority is given to the net transportation cost and final priority is given to net late deliveries. In lexicographic method objectives are solved on the basis of priorities. The problem is solved by using MATLAB. The minimized values are shown in table-2 and vender quota allocation is shown in the table-3. Table 2 Minimized values of the three objectives Minimized objectives Minimized values Net purchased Cost RS. 60,50,000 Net Transportation cost Rs. 2,42,500 Net Late deliveries Items: editor@iaeme.com

7 M. C. S. Reddy Table 3 Suppliers quota allocation Suppliers No Quota allocated to the suppliers Description regarding allocation The supplier-1 has taken quota up to the maximum capacity because of supplier having less purchase cost, less percentage of late deliveries, less percentage of rejections, moderate flexibility, moderate budget allocation etc. The supplier 2 has taken maximum quota than other suppliers because of supplier having highest budget allocation and able to supply maximum quantity. In addition to this late deliveries with this supplier is less and percentage of rejection, transportation cost, percentage of vender purchase rating are moderate. The supplier 3 has also taken quota up to the maximum capacity because of supplier having highest percentage of flexibility, highest vender purchase rating, less percentage of rejections, moderate purchasing cost, moderate budget allocation etc. The supplier 4 has losses total his quota due to highest purchase cost, highest transportation cost, highest percentage of rejections, moderate percentage of vender purchase rating, moderate late deliveries, less budget allocation etc. 7. CONCLUSIONS 1. Supplier selection is an important goal in supply chain management. For this a multi-objective linear programming problem is successfully formulated and solved. 2. The Lexicographic Method is applied to solve the multi-objectives on the basis of priorities. 3. A Sample Supplier Selection Problem is taken for real life problems and which is solved by built in function linprog () which is available in optimization tool box of the MATLAB. Supplier quota allocations according their performances are shown in table 3 and minimized values of the three objectives are shown in table Any commercially available software such as MATLAB can also be used to solve the proposed multi objective supplier selection problem. REFERENCES [1] Hongwei Ding, Lyès Benyoucef & Xiaolan Xie, A Simulation Optimization Approach Using Genetic Search For Supplier Selection Proceedings of the 2003 Winter Simulation Conference, FRANCE. [2] Manoj Kumar, Prem Vrat & R.Shankar A Fuzzy Goal Programming Approach For Vendor Selection Problem In A Supply Chain, Computers & Industrial engineering, Published by Elsevier Ltd. ( September 2003, 48 editor@iaeme.com

8 A Multi-Objective Approach For Optimum Quota Allocation To Suppliers In Supply Chain [3] Singiresu S. Rao, Engineering optimization Technique: Theory and practice 3 rd Edition, New Age International (p) Ltd & Publishers. [4] Pradip Kumar Krishnadevarajan Deepak Muthukrishnan S. Balasubramanian and N. Kannan Supply Chain in India A Review: Challenges, Solution Framework and Key Best Practices. International Journal of Management, 6(10), 2015, pp [5] Chuda Basnet & Janny M.Y. Leung, Inventory Lot Sizing with Supplier Selection, June 2002 (white paper). [6] D. Siva Kumar and Dr. Jayshree Suresh, Optimization of Supply Chain Logistics Cost. International Journal of Management, 4(1), 2015, pp [7] Brian R. Hunt, Ronald L. Lipsman & Jonathan M. Rosenberg A guide to MATLAB for Beginners and Experienced Users, First South Asian Edition- 2002, CAMBRIDGE University Press. [8] M. Chandra Sekhar Reddy and Talluri Ravi Teja. New Approach to Casting Defects Classification and Optimization by Magma Soft. International Mechanical Engineering and Technology, 5(6), 2014, pp editor@iaeme.com