Synchronization in common cycle lot size scheduling for a multi-product serial supply chain

In many manufacturing industries multiple products are processed through serial multiple stages. Although, in the past, attempts have been made to control the work-in-process inventory, synchronization of the production flow by overlapping production between stages has not been considered in detail. Two streams of research are brought together here to develop economic lot sizing schedules for this situation. The first is the production of a single product through serial multiple stages by introducing synchronization with overlapping production between different stages and allowing the transfer of the product as several sub-batches before the production run on the former stage has been completed. The second is the common cycle approach of scheduling many products through a single facility. In this paper, a single-product multi-stage model is extended to a multi-product multi-stage case by assuming that all products are produced in a common cycle. The total cost is shown to be a non-convex function of the common cycle time. A heuristic solution procedure, in the form of an algorithm using a directed search technique is developed. The potential value of synchronization of production in reducing cost is illustrated by applying this procedure to an example previously presented in the literature. Some practical issues are also addressed.