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

This paper presents a new heuristic to solve the problem of making sequencing, lot sizing and scheduling decisions for a number of products manufactured in a flow shop environment, so as to minimize the sum of setup and inventory holding costs while a given demand is fulfilled without backlogging. The proposed solution method first determines sequencing decisions then lot sizing and scheduling decisions are simultaneously determined. This heuristic, called the G-group method, divides the set of products into G groups and requires that products belonging to the same group have the same cycle time. Also, the cycle time of each group is restricted to be an integer multiple of a basic period. For each basic period of the global cycle, the products to be produced during this period and the production sequence to be used are chosen. Then, a non-linear program is solved to determine lot sizes and to construct a feasible production schedule. To evaluate its performance, the G-group method was compared to four other methods. Numerical results show that the proposed heuristic outperforms all these methods.