A deterministic, multi-item inventory model with supplier selection and imperfect quality. (English) Zbl 1145.90313

Summary: This paper considers the scenario of supply chain with multiple products and multiple suppliers, all of which have limited capacity. We assume that received items from suppliers are not of perfect quality. Items of imperfect quality, not necessarily defective, could be used in another inventory situation. Imperfect items are sold as a single batch, prior to receiving the next shipment, at a discounted price. The demand over a finite planning horizon is known, and an optimal procurement strategy for this multi-period horizon is to be determined. Each of products can be sourced from a set of approved suppliers, a supplier-dependent transaction cost applies for each period in which an order is placed on a supplier. A product-dependent holding cost per period applies for each product in the inventory that is carried across a period in the planning horizon. Also a maximum storage space for the buyer in each period is considered. The decision maker, the buyer, needs to decide what products to order, in what quantities, with which suppliers, and in which periods. Finally, a genetic algorithm (GA) is used to solve the model.


90B05 Inventory, storage, reservoirs
90C10 Integer programming


Full Text: DOI


[1] Burton, T. T., JIT/repetitive sourcing strategies: ‘typing the knot’ with your suppliers, Prod. Inventory Manage. J., 38-41 (1988)
[2] Degraeve, Z.; Roodhooft, F., Improving the efficiency of the purchasing process using total cost of ownership information: the case of heating electrodes at Cockerill Sambre S.A., Eur. J. Oper. Res., 112, 42-53 (1989) · Zbl 0937.90022
[3] Degraeve, Z.; Labro, E.; Roodhooft, F., An evaluation of vendor selection models from a total cost of ownership perspective, Eur. J. Oper. Res., 125, 34-58 (2001) · Zbl 0959.90027
[4] Dickson, G. W., An analysis of vendor selection systems and decisions, J. Purchas., 2, 1, 5-17 (1966)
[5] Jayaraman, V.; Srivastava, R.; Benton, W. C., Supplier selection and order quantity allocation: a comprehensive model, J. Supply Chain Manage., 35, 50-58 (1989)
[6] Patton, W. E., Use of human judgment models in industrial buyers’ vendor selection decisions, Ind. Market. Manage., 25, 135-149 (1986)
[7] Weber, C. A.; Current, J. R., A multi-objective approach to vendor selection, Eur. J. Oper. Res., 68, 173-184 (1983) · Zbl 0800.90587
[8] Weber, C. A.; Current, J. R.; Benton, W. C., Vendor selection criteria and methods, Eur. J. Oper. Res., 50, 2-18 (1980) · Zbl 1403.90061
[9] Weber, C. A.; Current, J. R.; Desai, A., Non-cooperative negotiation strategies for vendor selection, Eur. J. Oper. Res., 108, 208-223 (1988) · Zbl 0952.91049
[10] Buffa, F. P.; Jackson, W. M., A goal programming model for purchase planning, J. Purchas. Mater. Manage., 27-34 (1983)
[11] Bender, P. S.; Brown, R. W.; Isaac, M. H.; Shapiro, J. F., Improving purchasing productivity at IBM with a normative decision support system, Interfaces, 15, 106-115 (1985)
[12] Basnet, C.; Leung, J. M.Y., Inventory lot-sizing with supplier selection, Comput. Oper. Res., 32, 1-14 (2005) · Zbl 1076.90002
[13] Wagner, H. M.; Whitin, T. M., Dynamic version of the economic lot size model, Manage. Sci., 5, 89-96 (1958) · Zbl 0977.90500
[14] Ganeshan, R., Managing supply chain inventories: a multiple retailer, one warehouse, multiple supplier model, Int. J. Prod. Econ., 59, 341-354 (1989)
[15] Kasilingam, R. G.; Lee, C. P., Selection of vendors – a mixed-integer programming approach, Comput. Ind. Eng., 31, 347-350 (1986)
[16] Rosenthal, E. C.; Zydiak, J. L.; Chaudhry, S. S., Vendor selection with bundling, Decision Sci., 26, 35-48 (1985)
[17] Manne, A. S., Programming of economic lot sizes, Manage. Sci., 4, 115-135 (1958)
[18] Benson, H. Y., Optimal pricing and procurement strategies in a supply chain with multiple capacitated suppliers, Comput. Oper. Res., 32, 1, 1-14 (2005)
[19] Porteus, E. L., Optimal lot sizing, process quality improvement and setup cost reduction, Oper. Res., 34, 137-144 (1986) · Zbl 0591.90043
[20] Rosenblat, M. J.; Lee, H. L., Economic production cycles with imperfect production processes, IIE Trans., 18, 48-55 (1986)
[21] Lee, H. L.; Rosenblatt, M. J., Simultaneous determination of production cycles and inspection schedules in a production system, Manage. Sci., 33, 1125-1137 (1987) · Zbl 0628.90032
[22] Salameh, M. K.; Jaber, M. Y., Economic production quantity model for items with imperfect quality, Int. J. Prod. Econ., 64, 59-64 (2000)
[23] Chan, W. M.; Ibrahim, R. N.; Lochert, P. B., A new EPQ model: integrating lower pricing, rework and reject situations, Prod. Plan. Control, 14, 7, 588-595 (2003)
[24] Papachristos, S.; Konstantaras, I., Economic ordering quantity models for items with imperfect quality, Int. J. Prod. Econ., 100, 1, 148-154 (2006)
[25] Hayek, P. A.; Salameh, M. K., Production lot sizing with the reworking of imperfect quality items produced, Prod. Plan. Control, 12, 6, 584-590 (2001)
[26] Zhang, X.; Gerchak, Y., Joint lot sizing and inspection policy in an EOQ model with random yield, IIE Trans., 22, 1, 41-47 (1980)
[27] Wee, H. M.; Yu, J.; Chen, M. C., Optimal inventory model for items with imperfect quality and shortage backordering, Omega, 35, 1, 7-11 (2007)
[28] Ouyang, L. Y.; Chen, C.-K.; Chang, H.-C., Quality improvement, setup cost and lead-time reductions in lot size reorder point models with an imperfect production process, Comput. Oper. Res., 29, 1701-1717 (2002) · Zbl 1259.90005
[29] Francis Leung, K.-N., A generalized geometric-programming solution to An economic production quantity model with flexibility and reliability considerations, Eur. J. Oper. Res., 176, 1, 240-251 (2007) · Zbl 1137.90453
[30] Freimer, M.; Thomas, D.; Tyworth, J., The value of setup cost reduction and process improvement for the economic production quantity model with defects, Eur. J. Oper. Res., 173, 1, 241-251 (2006) · Zbl 1125.90339
[31] Ouyang, L. Y.; Chang, H.-C., Impact of investing in quality improvement on (Q,r,L) model involving the imperfect production process, Prod. Plan. Control, 11, 6, 598-607 (2000)
[32] Chiu, Y. P., Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging, Eng. Optimiz., 35, 4, 427-437 (2003)
[33] Urban, T. L., Deterministic inventory models incorporating marketing decisions, Comput. Ind. Eng., 22, 1, 85-93 (1982)
[34] Ben-Daya, M., Multi-stage lot sizing models with imperfect processes and inspection errors, Prod. Plan. Control, 10, 2, 118-126 (1989)
[35] Lee, H.-H., A cost/benefit model for investments in inventory and preventive maintenance in an imperfect production system, Comput. Ind. Eng., 48, 55-68 (2005)
[36] Ben-Daya, M., The economic production lot-sizing problem with imperfect production processes and imperfect maintenance, Int. J. Prod. Econ., 76, 257-264 (2002)
[37] Goyal, S. K.; Huang, C. K.; Chen, K. C., A simple integrated production policy of an imperfect item for vendor and buyer, Prod. Plan. Control, 14, 7, 596-602 (2003)
[38] Ouyang, L. Y.; Wu, K. S.; Ho, C. H., The integrated inventory models with defective items and controllable lead time, Prod. Plan. Control, 14, 562-578 (2003)
[39] Deb, K., Multi-Objective Optimization Using Evolutionary Algorithms (2001), Wiley: Wiley New York · Zbl 0970.90091
[40] Davis, L., The Handbook of Genetic Algorithms (1991), Van Nostrand Reinhold: Van Nostrand Reinhold New York
[41] Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning (1989), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0721.68056
[42] Holland, J. H., Adaptation in Natural and Artificial Systems (1975), The University of Michigan Press: The University of Michigan Press Ann Arbor, IL
[43] Michalewicz, Z., Genetic Algorithms+Data Structures=Evolution Programs. AI Series (1994), Springer: Springer New York
[44] Homaifar, A.; Lai, S. H.-V.; Qi, X., Constrained optimization via genetic algorithms, Simulation, 62, 4, 242-254 (1994)
[45] Michalewicz, Z.; Schoenauer, M., Evolutionary algorithms for constrained parameter optimization problems, Evol. Comput. J., 4, 1, 1-32 (1996)
[46] Deb, K., Evolutionary algorithm for multi-criterion optimization in engineering design, (Miettinen, K.; Neittaanmäki, P.; Mäkelä, M.; Périaux, J., Evolutionary Algorithms in Engineering and Computer Science (1999), Wiley: Wiley Chichester), 135-161
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