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Dynamic inventory and pricing policy in a capacitated stochastic inventory system with fixed ordering cost. (English) Zbl 1242.90008
Summary: We study a dynamic inventory and pricing optimization problem in a periodic review inventory system with setup cost and finite ordering capacity in each period. We show that the optimal inventory control is characterized by an (\(s,s^{{\prime}},p\)) policy in four regions of the starting inventory level.

MSC:
90B05 Inventory, storage, reservoirs
90C90 Applications of mathematical programming
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[1] Agrawal, V.; Seshadri, S., Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem, Manufacturing and service operations management journal, 2, 410-423, (2000)
[2] Chao, X.; Chen, H.; Zheng, S., Optimal inventory management under stochastically dependent supply capacity, European journal of operational research, 191, 142-155, (2008)
[3] Chao, X.; Seshadri, S.; Pinedo, M., Optimal capacity in a coordinated supply chain, Naval research logistics, 55, 130-141, (2008) · Zbl 1152.90304
[4] Chen, S., The infinite horizon periodic review problem with setup costs and capacity constraints: a partial characterization of the optimal policy, Operations research, 52, 409-421, (2004) · Zbl 1165.90337
[5] Chen, S.; Lambrecht, M., \(X - Y\) band and modified \((s, S)\) policy, Operations research, 44, 1013-1019, (1996) · Zbl 0874.90074
[6] Chen, X.; Simchi-Levi, D., Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the finite horizon case, Operations research, 52, 887-896, (2004) · Zbl 1165.90308
[7] Ciarallo, F.W.; Akella, R.; Morton, T.E., A periodic review, production planning model with uncertain capacity and uncertain demand—optimality of extended myopic policies, Management science, 40, 320-332, (1994) · Zbl 0805.90052
[8] Federgruen, A.; Heching, A., Combined pricing and inventory control under uncertainty, Operations research, 47, 454-475, (1999) · Zbl 0979.90004
[9] Federgruen, A.; Zipkin, P., An inventory model with limited production capacity and uncertain demands I, the average cost criterion, Mathematics of operations research, 11, 193-207, (1986) · Zbl 0602.90053
[10] Federgruen, A.; Zipkin, P., An inventory model with limited production capacity and uncertain demands II, the discounted cost criterion, Mathematics of operations research, 11, 208-215, (1986) · Zbl 0628.90017
[11] Gallego, G.; Scheller-Wolf, A., Capacitated inventory problems with fixed order costs: some optimal policy structure, European journal of operational research, 126, 603-613, (2000) · Zbl 0982.90002
[12] Gallego, G.; Toktay, L.B., All-or-nothing ordering under a capacity constraint, Operations research, 52, 1001-1002, (2004) · Zbl 1165.90314
[13] Li, Q.; Zheng, S., Joint inventory replenishment and pricing control for systems with uncertain yield and demand, Operations research, 54, 696-705, (2006) · Zbl 1167.90342
[14] Ozalp, O.; Wei, W., Inventory control with limited capacity and advanced demand information, Operations research, 52, 998-1000, (2004) · Zbl 1165.90332
[15] Petruzzi, N.C.; Dada, M., Pricing and the newsvendor problem: a review with extensions, Operations research, 47, 183-194, (1999) · Zbl 1005.90546
[16] Puterman, M.L., Markov decision processes, (1994), John Wiley & Sons New York · Zbl 0336.93047
[17] Scarf, H., The optimality of \((S, s)\) policy in the dynamic inventory problem, () · Zbl 0203.22102
[18] Veinott, A., On the optimality of \((s, S)\) policies: new conditions and a new proof, SIAM journal of applied mathematics, 14, 1067-1083, (1966) · Zbl 0173.47603
[19] Wang, Y.; Gerchak, Y., Periodic-review production models with variable capacity, random yield, and uncertain demand, Management science, 42, 130-137, (1996) · Zbl 0851.90059
[20] J. Wijnaard, 1972, An inventory problem with constrained order capacity, TH-Report 72-WSK-63, Eindhoven University of Technology, Eindhoven, The Netherlands.
[21] Whitin, T.T., Inventory control and price theory, Management science, 2, 61-80, (1955)
[22] Yang, J.; Qi, X.; Xia, Y., A production – inventory system with Markovian capacity and outsourcing option, Operations research, 53, 328-349, (2005) · Zbl 1165.90341
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