Production Lot Sizing with Machine Breakdowns

Abstract

Economic lot sizing and batching models often assume reliable manufacturing facilities. In this research, we focus on the effects of machine breakdowns and corrective maintenance on the economic lot sizing decisions. Two production control policies are proposed for coping with these stochastic interferences. The first policy assumes that production of the interrupted lots is not resumed after a breakdown. Instead, the on-hand inventory is depleted before a new cycle is initiated. Under the second policy studied here, production is immediately resumed after a breakdown, if the current on-hand inventory is below a certain threshold level. It is shown that this control structure is optimal among all stationary policies. We show that under both policies the optimal lot sizes will always be bigger than the ones in a corresponding deterministic case, and that the optimal lot size increases with the failure rate. We also provide exact optimal and closed form approximate lot sizing formulas and derive tight bounds on the average cost per unit time for the approximations. In addition, we present various structural properties for these policies and operational insights relevant to such management decisions as machine replacement or maintenance schedules.