The Economic Lot Sizes in Multistage Production Systems

Abstract This article develops a model for a single-product multistage production-inventory system with static deterministic demand, where the product moves between the stages in a serial fashion. In this model, it is assumed that the unfilled demand of the finished product is backlogged. Overproduction (with limitation) is allowed at the different stages so that each stage t may produce ki batches once every ki cycles. The decision variables for each stage i are the number of batches per run ki the batch size Qi , and the shortage quantity of the finished product Qs . These are determined by minimizing the total cost per unit time which includes the inventory holding cost, the shortage cost, and the setup cost. The problem is also considered for the case with storage constraints at the different stages.