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Supplier Selection and Demand Allocation Amol Singh IIM Rohtak

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Presentation Plan Humanitarian Supply chain Literature Review Research Issues and objectives of the study Hybrid Fuzzy, TOPSIS and MILP Methodology Case Study Results and discussion Conclusion and future research directions

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Humanitarian Supply chain The process of planning Implementing and Controlling the efficient and cost effective flow of goods of humanitarian SCM network Includes procurement of goods Storage of goods and distribution of goods in such a way that it alleviates the suffering of the vulnerable peoples as efficiently as possible.

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Commercial versus Humanitarian Supply Chains Characteristics of Commercial versus Humanitarian Supply Chains Commercial Supply ChainHumanitarian Supply Chain Demand PatternRelatively stable, predictable. Demands. occur at ﬁxed locations in set quantities. Demand is generated from random events that are unpredictable in terms of timing, type, and size. Demands are estimated after they are needed, based on an assessment of disaster characteristics Inventory ControlUses well-deﬁned methods for determining inventory levels based on lead time, demand and target customer service levels Inventory control is challenging due to high variations in lead times, demands, and demand locations. Lead TimeLead time determined by the Supplier- Manufacturer-DC-Retailer-chain Zero time between the occurrence of the demand and the need for it. Network Conﬁguration There exist methods for supply chain network design. Challenging due to the nature of unknowns (locations, type and size of events, politics, culture) and “last mile” considerations. Information Systems Typically, well-deﬁned, making use of advanced technology Information is often unreliable, incomplete or non-existent. Performance Measurement System Historically, focused on resource performance measures, such as maximizing proﬁt or minimizing costs. Primary focus on output performance measures, such as the time required to respond to a disaster or ability to meet the needs of the disaster victims. Strategic GoalsUsually, to produce high quality products at low cost in order to maximize proﬁtability and achieve customer satisfaction Minimize the loss of life and alleviate suﬀering.

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Background of the Research work Purchasing is an important function of humanitarian supply chain management. The demand is generated from random events that are unpredictable in terms of timing, type and size. The literature focused on choosing the right suppliers and allocating the appropriate demand. The opportunities in this research area include determining the number of suppliers, managing supplier buyer supplier relationship, sourcing strategies and outsourcing decisions. The main objective of the present research work is to address the problem of optimal allocation of demand among candidate suppliers in order to maximize the purchase value of items.

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Literature review Literature review shows that supplier selection is a multi-criteria decision making process involving cost, quality, lead time reliability etc. These criteria can be defined variously as buyers take into account numerous conflicting factors. Dickson identified 23 criteria in his study of various supplier selection problems. Butta (2003) presented a review of 154 articles and showed a variety of methodology and approaches used for supplier selection. Traditionally, linear weighing models, total cost approach multiple attribute theory, and total cost ownership used for supplier selection. In last one decade researchers focused on optimization techniques, multi-objective programming, AHP, DEA, AI, and hybrid approaches. Each approach has its own limitation.

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Research Issues and Objective of the study A critical review of literature brings to the fore some crucial issues for research. A humanitarian supply chain deals with the pool of supplies rather than a single supplier. Supplier selection is a multi-criteria decision making problem encompassing risk and uncertainties. Existing studies have not devoted much attention to this aspect of supplier selection environment. Supplier selection models based on fuzzy set theory adopt the practice of data defuzzified into a crisp one in the initial stage. This approach undermines the advantage of collecting the fuzzy data (opinion of all decision makers). In literature multi-period demand aspect of the supplier evaluation process have not received much attention.

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A complex problem of multi-period customer demand allocation is considered and the rating of the suppliers is integrated with the MILP process in order to maximize the value of procurement. Qualitative and quantitative criteria applies in the computation of the supplier rating. A hybrid Fuzzy TOPSIS algorithm tackles the risk of supplier selection environment. It defuzzifies the fuzzy data in the final step of the ranking process. The hybrid Fuzzy TOPSIS algorithm is integrated with the MILP process for optimal multi-period demand allocation among suppliers. Research Issues and Objective of the study Taking cues from the critical research issues identified in the literature review, the present study aims at addressing the following tasks.

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Hybrid Fuzzy, TOPSIS and MILP Methodology The steps of methodology is explained below: 1.A group of k decision makers is identified and this group defines a set of relevant criteria for supplier evaluation. The scores of the suppliers with respect to the criteria and weight of each criteria is considered as linguistic variables. 2. Each decision maker assigns fuzzy score to the supplier against a criterion and similarly assigns the fuzzy score to each criterion. These fuzzy scores are expressed in the fuzzy matrix format. Very Poor (VP)[(0, 0); 0; (1, 1.5)] Poor (P)[(0, 0.5); 1; (2.5, 3.5)] Moderately Poor (MP)[(0, 1.5); 3; (4.5, 5.5)] Fair (F)[(2.5, 3.5); 5; (6.5, 7.5)] Moderately Good (MG)[(4.5, 5.5); 7; (8, 9.5)] Good (G)[(5.5, 7.5); 9; (9.5, 10)] Very Good (VG)[(8.5, 9.5); 10; (10, 10)] Table : Linguistic variables for the rating of the suppliers Very Low (VL)[(0, 0); 0; (.1,.15)] Low (L)[(0, 0.05); 0.1; (0.25, 0.35)] Medium Low (ML)[(0, 0.15); 0.3; (0.45, 0.55)] Medium (M)[(0.25, 0.35); 0.5; (0.65, 0.75)] Medium High (MH)[(0.45, 0.55); 0.7; (0.8, 0.95)] High (H)[(0.55, 0.75); 0.9; (0.95, 1)] Very High (VH)[(0.85, 0.95); 1; (1, 1)] Table : Linguistic variables for the importance of the criterion

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Hybrid Fuzzy, TOPSIS and MILP Methodology 3. Compute average score of each supplier with respect to a criterion and average weight of each criterion. The average scores of each supplier with respect to a criterion and importance of each criterion are computed by using the following relations: 4. The fuzzy scores computed in step 3 are in different units hence, these scores are normalized by converting them into non-dimensional ratio for comparison. Fuzzy scores x ij = [(a ij, a ij ’ ); b ij ; (c ij c ij ’ )] computed in step 3 are converted into non-dimensional ratio by using the following equations:, i = 1, 2, ………m, j ϵ Ω b, i = 1, 2, ……….m, j ϵ Ω c

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Hybrid Fuzzy, TOPSIS and MILP Methodology 5. Convert the normalized fuzzy decision matrix computed in step 4 into weightage normalized fuzzy decision matrix (v = [v ij ] n×m, where v ij = r ij × w j ) by using the following relation: v ij = [(r 1ij × w 1j, r 1ij × w 1j ’ ); r 2j × w 2j ; (r 3ij × w 3j ’, r 3ij × w 3j ) = [(g ij, g ij ’ ); h ij ; (l ij, l ij ’ )]. 6. Determine positive ideal (A+) and negative ideal (A-) solutions by using the following equations: A+ = [(1, 1); 1; (1, 1)] for j ϵ Ωb A- = [(0, 0); 0; (0, 0)] for j ϵ Ωc 7. Compute the separation measures (Euclidean distances) of each supplier from the positive ideal (A+) and negative ideal (A-) solutions by using the following relations:

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Hybrid Fuzzy, TOPSIS and MILP Methodology Where, D - (N, M) and D + (N, M) are the primary and secondary separation measures hence, the separation measure of each supplier (D + i1, D + i2 ) from the positive ideal solution is computed by using the following equations: Similarly, the separation measure of each supplier (D i1 -, D i2 - ) from the negative ideal solution is computed by using the following relations:

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Hybrid Fuzzy, TOPSIS and MILP Methodology 8. Compute the fuzzy relative closeness of each supplier by using the each pair of separation measure as computed in step 7. The fuzzy relative closeness of supplier A i is computed by using the following equations: 9. Compute crisp value of fuzzy relative closeness as computed in step 8 of each supplier by using the following relation:

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Hybrid Fuzzy, TOPSIS and MILP Methodology 10. Finally, the output of fuzzy TOPSIS model as computed in step 9 is integrated with MILP. The multi-period optimal demand allocation model is formulated by using the following equations: for i = 1 to n th supplier and j = 1 to 4 th quarter Subject to: Budget Constraint Demand Constraint Delivery lead time constraint Supplier Capacity constraint

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Case study 4 Potential suppliers were considered S 1, S 2, S 3, and S 4. These 4 suppliers were evaluated by four decision makers M 1, M 2, M 3, and M 4 based on four criteria, namely quality (C 1 ), price (C 2 ), on time delivery (C 3 ) and consistency (C 4 ). The expected demand, available capacity of suppliers, their lead times and cost for the next 4 quarters are as follow; company wants to purchase at least 5000 but less than 5500 units of an item in each quarter. The unit material cost for supplier S 1, S 2, S 3 and S 4 are $9, $8, $10, $12 respectively and the quarterly capacity of candidate suppliers are 3000, 3500, 2500, and 3200 units respectively. The annual budget for purchasing the items is $200000. The quarterly delivery times of suppliers are 2, 4, 6, 3 days respectively. According to company’s policy, average delivery time should not be more than 4 days.

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Results and discussions Table: Interval value of relative closeness and the final relative closeness of each supplier The demand allocation to the suppliers and their optimum values calculated by the Lindo software are Q 11 = 2667, Q 12 = 2898, Q 13 = 0, Q 14 = 2435, Q 21 = 333, Q 22 = 530, Q 23 = 3000, Q 24 = 2137, Q 31 = 2500, Q 32 = 2072, Q 33 = 2500, Q 34 = 928, Q 41 = 0, Q 42 = 0, Q 43 = 0, Q 44 = 0. The value of the binary variables are X 11 = 1, X 12 = 1, X 13 = 0, X 14 = 1, X 21 = 1, X 22 = 1, X 23 = 1, X 24 = 1, X 31 = 1, X 32 = 1, X 33 = 0, X 34 = 1, X 41 = 0, X 42 = 0, X 43 = 0, X 44 = 0. Total purchase value Z = 12528. SuppliersInterval of relative closeness Final score of suppliers (Rc * ) S1 (0.51, 0.59).551 S2 (0.53, 0.60).564 S3 (0.55, 0.63).592 S4 (0.52, 0.60).557

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Results and discussions According to the relative closeness computed by single approach (i. e. TOPSIS), supplier S 3 is the best supplier. However, a total of 8000, 6000, 8000, and 0 units are assigned to suppliers S 1, S 2, S 3, and S 4 by using the hybrid algorithm, which maximize the total value of the procurement. The maximum units are assigned to supplier S 1 and S 3, 8000 to each. This allocation of the units maximizes the value of procurement. On the contrary, the individual approach (i. e. TOPSIS) assigns the lowest rating to the Supplier S 1. In this context, it may be concluded that the hybrid approach improves the efficacy of the individual approaches. However, the wide applicability of individual approach in literature is due to its simplicity, ease of use and great flexibility. These observations support the literature findings to develop more hybrid approaches for the supplier selection problems.

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Conclusions The present research work aimed at providing a new scenario to the supplier selection problem pertinent to the humanitarian supply chain management. Rating of the suppliers was computed and the demand allocated optimally among the suppliers. This should be encouraging to the SCM managers interested in improving the reliability of the suppliers as well as quality of the items, maximization their value of procurement, and switch over to the demand from one supplier to another supplier when the first supplier is not capable of supplying the items due to unavoidable circumstances. The present research work will be helpful for the Humanitarian SCM managers who are interested to reconfigure their supply chain under the failure of any supply chain partner or in a changing environment. The suitability of the proposed hybrid model to the supplier selection problem derives from four distinctive characteristics: (i) its ability to capture qualitative as well as quantitative criteria consistent with the real supplier selection environment, (ii) its ability not only assign the rating of the suppliers but also they can assess the status of all possible suppliers, (iii) its ability to capture the subjective estimates of the decision makers in terms of linguistic variables, and (iv) its ability to optimal demand allocation among suppliers. The proposed hybrid model provides more objective information for supplier evaluation and demand allocation among suppliers in supply chain.

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Conclusions If a supplier declines to supply the units in a particular quarter then the proposed model is supportive for the managers as they can adjust the value of variables in the model as per their choices and determine the optimal quantity for allocation among rest of the suppliers. The model provides flexibility to the managers for evaluation of the different available alternatives in order to take a decision of optimal demand allocation among the suppliers. The supply chain network is witnessing a changing business environment due to government policies aimed promoting new small manufacturing enterprises (SMEs) for intermediate parts and components. Hence, the managers have an option to select the new group of suppliers and allocate the optimal multi-period demand among new group of suppliers in order to maximize their purchase value. In this context, the proposed hybrid model would be beneficial for the managers to operate their supply chain effectively and efficiently.

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Future research directions The study on supplier evaluation and multi-period demand allocation among suppliers presented in this research paper could be extended in various ways. Firstly, more case studies could underline the practical usefulness of the hybrid methodology as derived from the experimental results. Secondly, future research could consider the transportation cost during demand allocation among suppliers. Thirdly, uncertainty of multi-period demand instead of fixed multi-period demand in supplier selection problem could be taken up. Finally, research can be extended by developing more hybrid approaches for uncertain multi-period demand allocation among suppliers.

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