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Optimal Policy for a Periodic-Review Inventory System Under a Supply Capacity Contract

Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109-2117
Fuqua School of Business, Duke University, Durham, North Carolina 27708
xchao{at}umich.edu
paul.zipkin{at}duke.edu

Transportation and production contracts often specify the frequency and volume reserved by the supplier for a particular customer's deliveries. This practice motivated Henig et al. (Henig, M., Y. Gerchak, R. Ernst, D. Pyke. 1997. An inventory model embedded in designing a supply contract. Management Sci. 43 184–189) to study a periodic-review inventory-control model where ordering cost is zero if the order quantity does not exceed a given contract volume and is linear in the excess quantity otherwise. This paper addresses the same problem but with a fixed cost if the order quantity is above the contract volume. The fixed cost may represent the cost of disruption for the supplier (finding more trucks, arranging extra processing capacity, persuading other customers to wait, etc.) as well as additional administrative costs. Also, suppliers may impose such costs simply to induce desired behavior by buyers. This order-cost function is neither convex nor concave. The classical inventory models with fixed costs are special cases with contract volume zero. We partially characterize the optimal policy for this system and develop a simple, effective heuristic policy. We also apply the model to a production-control problem in which an incentive is provided for not ordering over a certain quota.

Subject classifications: periodic-review inventory systems; optimal control; (s, S) policies; K-convexity; incentives; dynamic programming.
History: Received June 2002; revision received December 2005; accepted January 2006.