A multi supplier lot sizing strategy using dynamic programming

Abstract: In this paper, the problem of lot sizing for the case of a single item is considered along with supplier selection in a two-stage supply chain. The suppliers are able to offer quantity discounts, which can be either all-unit or incremental discount policies. A mathematical modeling formulation for the proposed problem is presented and a dynamic programming methodology is provided to solve it. Computational experiments are performed in order to examine the accuracy and the performance of the proposed method in terms of running time. The preliminary results indicate that the proposed algorithm is capable of providing optimal solutions within low computational times, high accuracy solutions.

How to cite this paper

 Parsa, I., Khiav, M., Mazdeh, M & Mehrani, S. (2013). A multi supplier lot sizing strategy using dynamic programming.International Journal of Industrial Engineering Computations , 4(1), 61-70.

Refrences

Agarwal, P., Sahai, M., Mishra, V., Bag, M., & Singh, V.(2011). A review of multi-criteria decision making techniques for supplier evaluation and selection, International Journal of Industrial Engineering Computations, 2, 801–810.
Aggarwal, A., & Park, J.K. (1993).Improved algorithms for economic lot-size problems. Operations Research, 41, 549-71.
Agra, A., & Constantino, M. (1999). Lot sizing with backlogging and start-ups: the case of Wagner–
Whitin costs. Operation Research Letters, 25, 81-88.
Babaei, M., Mohammadi, M., Fatemi Ghomi, S.M.T., & Sobhanallahi, M.A. (2012). Two parametertuned metaheuristic algorithms for the multi-level lot sizing and scheduling problem. International Journal of Industrial Engineering Computations, 3, 751-766.
Basnet, C., & Leung, J.M.Y. (2005). Inventory lot-sizing with supplier selection. Computers and Operations Research, 32, 1–14.
Benton, W.C., & Whybark, D.C. (1982). Material requirements planning (MRP) and purchase discounts. Journal of Operations Management, 2, 137-43.
Federgruen, A., & Tzur, M. (1991). A simple forward algorithm to solve general dynamic lot sizing models with n periods in O(n log n) or O(n) time. Management Science, 37, 909-25.
Hassini, E. (2008). Order lot sizing with multiple capacitated suppliers offering leadtime-dependent capacity reservation and unit price discounts. Production Planning & Control, 19, 142–149.
Ho, W., Xu, X., & K. Dey, P.(2010). Multi-criteria decision making approaches for supplier evaluation and selection: A literature review. European Journal of Operational Research, 202, 1, 16-24.
Liao, Z., & Rittscher, J. (2007). Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions. International Journal of Production Economics, 107, 502–510.
Loparic, M., Pochet, Y., & Wolsey, L.A. (2001). The uncapacitated lot-sizing problem with sales and safety stocks. Mathematical Programming, 89, 487-504.
Moqri, M., M., MoshrefJavadi, M., & Yazdian, S., A. (2011). Supplier selection and order lot sizing using dynamic programming. International Journal of Industrial Engineering Computations, 2, 319- 28.
Shaw, D.X., & Wagelmans, A.P.M. (1998). An algorithm for single-item capacitated economic lot sizing with piecewise linear production costs and general holding costs. Management Science, 44, 831-838.
Silver, E.A., & Meal, H.C. (1973). A heuristic for selecting lot size quantities for the case of a deterministic time varying rate and discrete opportunities for replenishment. Production and Inventory Management, 14, 64-74.
Tempelmeier, H. (2002). A simple heuristic for dynamic order sizing and supplier selection with timevarying data. Production and Operations Management, 11, 499–515.
Wagner, H. M., & Whitin, T.M. (1958). Dynamic version of the economic lot-size model. Management Science, 5, 89-96.
Weber, C., & Current, J. (1993).A multi-objective approach to vendor selection. European Journal of
Operational Research, 68, 173-84.
Whybark, D.C., & Williams, J.C. (1976).Material requirements planning under uncertainty. Decision Sciences, 7, 595-606.
Wind, Y., & Robinson, P.J. (1968). The determinants of vendor selection: evaluation function approach. Journal of Purchasing and Materials Management, 17, 29-41.