A Dynamic Inventory Model with the Right of Refusal
We consider a dynamic inventory (production) model with general convex order (production) costs and excess demand that can be accepted or refused by the firm. Excess demand that is accepted is backlogged and results in a backlog cost whereas demand that is refused results in a lost sales charge. Endogenizing the sales decision is appropriate in the presence of general convex order costs so that the firm is not forced to backlog a unit whose subsequent satisfaction would reduce total profits. In each period, the firm must determine the optimal order and sales strategy. We show that the optimal policy is characterized by an optimal buy-up-to level that increases with the initial inventory level and an order quantity that decreases with the initial inventory level. More importantly, we show the optimal sales strategy is characterized by a critical threshold, a backlog limit, that dictates when to stop selling. This threshold is independent of the initial inventory level and the amount purchased. We investigate various properties of this new policy. As demand stochastically increases, the amount purchased increases but the amount backlogged decreases, reflecting a shift in the way excess demand is managed. We develop two regularity conditions, one that ensures some backlogs are allowed in each period, and another that ensures the amount backlogged is nondecreasing in the length of the planning horizon. We illustrate the buy-up-to levels in our model are bounded above by buy-up-to levels from the pure lost sales and pure backlogging models. We explore additional extensions using numerical experiments.
Volume (Year): 56 (2010)
Issue (Month): 12 (December)
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- Samuel Karlin, 1960. "Dynamic Inventory Policy with Varying Stochastic Demands," Management Science, INFORMS, vol. 6(3), pages 231-258, April.
- Alan S. Blinder, 1986.
"Can the Production Smoothing Model of Inventory Behavior be Saved?,"
The Quarterly Journal of Economics,
Oxford University Press, vol. 101(3), pages 431-453.
- Alan S. Blinder, 1984. "Can The Production Smoothing Model of Inventory Behavior be Saved?," NBER Working Papers 1257, National Bureau of Economic Research, Inc.
- Griffin, James M, 1972. "The Process Analysis Alternative to Statistical Cost Functions: An Application to Petroleum Refining," American Economic Review, American Economic Association, vol. 62(1), pages 46-56, March.
- Andrew B. Abel, 1985. "Inventories, Stock-Outs and Production Smoothing," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 283-293.
- Donald M. Topkis, 1968. "Optimal Ordering and Rationing Policies in a Nonstationary Dynamic Inventory Model with n Demand Classes," Management Science, INFORMS, vol. 15(3), pages 160-176, November.
- Mordechai Henig & Yigal Gerchak & Ricardo Ernst & David F. Pyke, 1997. "An Inventory Model Embedded in Designing a Supply Contract," Management Science, INFORMS, vol. 43(2), pages 184-189, February.
- Andrew B. Abel, 1985. "Inventories, Stock-Outs, and Production Smoothing," NBER Working Papers 1563, National Bureau of Economic Research, Inc.
- Jehoshua Eliashberg & Richard Steinberg, 1991. "Competitive Strategies for Two Firms with Asymmetric Production Cost Structures," Management Science, INFORMS, vol. 37(11), pages 1452-1473, November.
- Driskill, Robert, 1997. "Durable-Goods Monopoly, Increasing Marginal Cost and Depreciation," Economica, London School of Economics and Political Science, vol. 64(253), pages 137-54, February.
- Eichenbaum, Martin, 1989.
"Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment,"
American Economic Review,
American Economic Association, vol. 79(4), pages 853-64, September.
- Martin S. Eichenbaum, 1988. "Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment," NBER Working Papers 2523, National Bureau of Economic Research, Inc.
- Kenneth R. Smith, 1970. "Risk and the Optimal Utilization of Capital," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 253-259.
- Spulber, Daniel F, 1993. "Monopoly Pricing of Capacity Usage under Asymmetric Information," Journal of Industrial Economics, Wiley Blackwell, vol. 41(3), pages 241-57, September.
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