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Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity. (English) Zbl 1144.90003
Summary: We study a joint optimization problem of replenishment and pricing for a periodic-review inventory system with random supply capacity. When making replenishment and pricing decisions at the beginning of each period, the firm only knows the supplier’s available capacity in the current period, but does not know what will be the available capacity in future periods. The salient feature of our model is that the random supply capacities for different periods are dependent. Several stochastic dependency structures are considered for the supply capacity sequence, including the one-lag and the multi-lag dependency.
We show that the optimal inventory control policy is of the modified base-stock type and the base-stock level is decreasing in the available capacity of the current period and that the optimal pricing policy is a “list-price” coined with markdown and markup. This paper generalizes the work of A. Federgruen and P. Zipkin [Math. Oper. Res. 11, 193–207 (1986; Zbl 0602.90053); ibid. 11, 208–215 (1986; Zbl 0628.90017)] in which the supply capacity and selling price are assumed to be fixed constants, and the work of A. Federgruen and A. Heching [Oper. Res. 47, No. 3, 454–475 (1999; Zbl 0979.90004)] on joint optimization of replenishment and pricing with unlimited supply capacity.

90B05 Inventory, storage, reservoirs
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[1] Aviv, Y., The effect of collaborative forecasting on supply chain performance, Management science, 47, 1-18, (2001)
[2] Brown, R.G., Statistical forecasting for inventory control, (1959), McGraw-Hill New York · Zbl 0095.14606
[3] 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
[4] Chen, X.; Simchi-Levi, D., Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the infinite horizon case, Mathematics of operations research, 29, 698-723, (2004) · Zbl 1082.90025
[5] 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
[6] Federgruen, A.; Heching, A., Combining pricing and inventory control under uncertainty, Operations research, 47, 454-475, (1999) · Zbl 0979.90004
[7] 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
[8] 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
[9] Feng, Y., Chen, F. (2003). Joint pricing and inventory control with setup cost and demand uncertainty. Working paper, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong.
[10] Gallego, G.; Ozalp, O., Integrating replenishment decisions with advanced demand information, Management science, 47, 1344-1360, (2001) · Zbl 1232.90047
[11] Heath, D.C.; Jackson, P.L., Modeling the evolution of demand forecasts with application to safety stock analysis in production/distribution system, IIE transactions, 26, 17-30, (1994)
[12] Johnson, L.A.; Montgomery, D.C., Operations research in production planning, scheduling, and inventory control, (1974), John Wiley & Sons New York
[13] Karlin, S., Optimal inventory policy for the arrow-harris-marschak dynamic model, ()
[14] 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
[15] Nahmias, S., Production and operations analysis, (2001), McGraw-Hill New York
[16] Ozalp, O.; Wei, W., Inventory control with limited capacity and advanced demand information, Operations research, 52, 998-1000, (2004) · Zbl 1165.90332
[17] Puterman, M.L., Markov decision processes, (1994), John Wiley & Sons New York · Zbl 0336.93047
[18] Shaked, M.; Shanthikumar, J.G., Stochastic orders and their applications, (1994), Academic Press Boston · Zbl 0806.62009
[19] Topkis, D.M., Minimizing a submodular function on a lattice, Operations research, 26, 305-321, (1978) · Zbl 0379.90089
[20] 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
[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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