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

• Published in: Operations research Vol. 56; no. 1; pp. 59 - 68
• Main Authors: Chao, Xiuli, Zipkin, Paul H
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.01.2008; Institute for Operations Research and the Management Sciences
• Subjects: Analysis; Applied sciences; Business orders; Capacity costs; Contracts; convexity; Cost efficiency; Cost functions; Costs; dynamic programming; Exact sciences and technology; Fixed costs; Heuristic; Heuristics; incentives; Inventories; Inventory control; Inventory control, production control. Distribution; K; Logistics; Manufacturers; Mathematical models; Minimization of cost; Operational research and scientific management; Operational research. Management science; optimal control; Optimal policy; Order quantity; periodic-review inventory systems; Poisson distribution; policies; Production control; s, S; Studies; Suppliers; United States; Fixed cost; Optimal policy; Periodicity; Modeling; Periodic control; Delivery (good); Production management; periodic-review inventory systems; optimal control; s; Quota; Lorry; Optimal control; Economic order quantity; Heuristic method; Ordering; Cost function; Inventory control; Convex function; Convexity; Dynamic programming; S policies; K-convexity; incentives; dynamic programming; Contract; Logistics
• DOI: 10.1287/opre.1070.0478
• ISSN: 0030-364X

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.