The single-manufacturer single-retailer integrated production-delivery lot sizing model with production capacity under stochastic lead time demand

This paper develops an integrated production-delivery lot sizing model in which a manufacturer supplies a product a retailer. The manufacturer produces the product at a finite rate and the production rate is assumed to be smaller than market demand rate. Meanwhile, we assume that the lead time demand is stochastic and that shortages are permitted. The lead time and the reorder point are in this model as decision variables. The objective is to determine the optimal ordering quantity, reorder point, lead time and the delivery number during each production cycle which minimize the expected total cost per unit time of the manufacturer and the retailer by giving an effective iterative algorithm. A numerical example is given as an illustration of this algorithm for the integrated system.