The two-group heuristic to solve the multi-product, economic lot sizing and scheduling problem in flow shops

This paper presents a new and efficient heuristic to solve the multi-product, economic lot sizing and scheduling problem in flow shops. The problem addressed is that of making sequencing, lot sizing and scheduling decisions for a number of products so as to minimize the sum of setup costs, work-in-process inventory holding costs and final-products inventory holding costs while a given demand is fulfilled without backlogging. The proposed heuristic, called the two-group method (TG), assumes that the cycle time of each product is an integer multiple of a basic period and restricts these multiples to take either the value 1 or K where K is a positive integer. The products to be produced once each K basic period are then partitioned into K sub-groups and each sub-group is assigned to one and only one of the K basic periods of the global cycle. This method first determines a value for K and a feasible partition. Then, a production sequence is determined for each sub-group of products and a non-linear program is solved to determine lot sizes and a feasible schedule. We also show how to adapt our method to the case of batch streaming (transportation of sub-batches from one machine to the next). To evaluate its performance, the TG method was compared to both the common cycle method and a reinforced version of El-Najdawi's job-splitting heuristic. Numerical results show that the TG method outperforms both of these methods.