A Periodic Review, Production Planning Model with Uncertain Capacity and Uncertain Demand—Optimality of Extended Myopic Policies

TLDR

Production planning must account for uncertainties such as unplanned maintenance, variable yields, and rework that arise from increasing product complexity, environmental factors, and quality demands. The study addresses aggregate planning for a single product under random demand and random capacity. The authors model the problem as an infinite‑horizon planning task and introduce extended myopic policies that incorporate uncertain review periods. They show that random capacity does not alter the optimal policy in a single period but creates a unimodal nonconvex cost, while in multi‑period and infinite‑horizon settings order‑up‑to policies based on capacity distribution remain optimal and the extended myopic policies achieve this optimality despite nonconvexity.

Abstract

Increasing product complexity, manufacturing environment complexity and an increased emphasis on product quality are all factors leading to uncertainties in production processes. These uncertainties are in the form of unplanned machine maintenance, varying production yields and rework, among others. In planning for production, an adequate model must incorporate these uncertainties into the representation of the production process. This paper treats the aggregate planning problem for a single product with random demand and random capacity. In the single-period problem, random capacity does not affect the optimal policy but results in a unimodal, nonconvex cost function. In the multiple-period and infinite-horizon settings order-up-to policies that are dependent on the distribution of capacity are shown to be optimal in spite of a nonconvex cost. In the infinite-horizon setting an intuitive description of the situation leads to the notion of a class of extended myopic policies, requiring the consideration of review periods of uncertain length.