Dynamic programming solution to the batching problem in just-in-time flow-shops

Mixed-model manufacturing systems are widely used by companies, in order to meet the customers’ demand for a variety of products, in an efficient way. This paper is concerned with a special class of mixed-model manufacturing systems: flow-shops. In a flow-shop, each product has to be processed by a number of machines, following a common route. We study the production smoothing problem under presence of non-zero setup and processing times which also vary among the products. We split the master problem into two sub-problems which are concerned with determining the batch sizes and production sequences, respectively. We develop a dynamic programming procedure to solve the batching problem, and suggest using an existing method from the current literature to solve the sequencing problem. We conduct a computational study and show that our solution approach is effective in meeting the JIT goals and efficient in its computational requirements.