Lot sizing with random yields and tardiness costs

Abstract

We consider a single-stage manufacturing problem with random yields, and investigate the impact of yield uncertainty on lot sizing decisions when there is a tardiness cost for not meeting the customer specified due date. We assume that the demand, as well as the customer-specified due date for the product, is known. Due to the limited production capacity, the manufacturer has to produce the product in a single production run and deliver the product in a single shipment. We derive the optimal lot size for some specific yield-rate distributions. We also obtain some distribution free results by assuming that only the mean and variance of the yield-rate distribution are known. Sensitivity of the optimal solution to these parameters is investigated through some numerical examples. Scope and purpose Lot sizing problems deal with determining production and procurement quantities and their timing. Significant amount of research has been done on solving lot sizing problems when demand is known, as well as demand is uncertain. Although considerable research has been done when production yield-rate is known, few researchers have dealt with situations where yield rate is uncertain. Yano and Lee [1] present many variations of lot sizing problem with random yield and review the corresponding literature. Production yield-rate uncertainty can lead to delays in delivery, which may result in penalty costs. When yield-rate is constant, several researchers evaluated the impact of imposing tardiness cost for late delivery on lot sizing decisions. However, no research has been done to date to evaluate the impact of yield uncertainty on lot sizing decisions when there is a tardiness cost associated with delayed delivery. The main emphasis of this paper is to address this issue.