# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.