Multiple lotsizing in production to order with random yields: Review of recent advances

This article provides a review of models, analytical results and insights pertaining to multiple lotsizing in production to order, with emphasis on recent work on multistage systems and inspection issues. The basic setting consists of an order of fixed size that has to be met in its entirety. Production is in lots and is imperfect, and inspection can take place only when lot has completed a stage. Processing each lot at each stage entails fixed and variable costs. The tradeoff is between running large lots, entailing potentially costly overproduction, and small lots, which may necessitate multiple production runs and their associated setups. Variations of this problem have been explored since the 1950's, but only recently has there been significant progress in solving exactly problems of realistic complexity. We first review single-stage models, including those which compute the variance of costs, those dealing with inspections, those with multiple grades and situations with uncertain demand. We then review multi-stage systems, starting with those with no bottlenecks, and progressing to one, and two bottlenecks. The implications of rework capability in the various systems are then explored.