Production-Inventory Decisions under Order-Occurrence Risk: The Deterministic Order Quantity Case

This paper examines the problem of production-inventory decisions under order-occurrence risk. To characterize this problem briefly, let the number of periods which elapse between the receipt of orders n and n + 1 for an item be described by a probability mass function f_n(s). If f_n(∞) > 0, then order-occurrence risk is said to exist. That is, upon receiving order n for an item, there exists a positive probability that no future orders will occur. Assuming deterministic order quantities, the order-occurrence risk problem is formulated as a dynamic program. Optimal production-inventory disposal policies are characterized for the case of piecewise-linear production-disposal costs and concave increasing holding costs. The production cost is assumed to include a setup cost, and demand backlogging is not permitted. The production and disposal lead times are assumed to be zero.