Lot sizing with random yields and tardiness costs

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.