Simultaneous lot sizing and scheduling for multi-product multi-level production

The paper deals with the multi-level lot sizing and scheduling problem for job shop production in capacitated, dynamic and deterministic cases. Demand is to be fulfilled without backlogging. The multi-level lot sizing and scheduling models of the literature are small bucket problems such as the discrete lot sizing and scheduling problem (DLSP) and the proportional lot sizing and scheduling problem (PLSP). In contrast we develop a big bucket model for multi-product multi-level production. The multi-level general lot sizing and scheduling problem with multiple machines (MLGLSP_MM) is based on the general lot sizing and scheduling problem (GLSP) for single-level production. Our focus is on minimising the sum of sequence dependent setup costs, inventory costs, production costs and the costs of maintaining the setup conditions of the machines. Inventory costs will be calculated exactly. In addition sequence dependent setup times are considered. Finally, our approach minimises the lead-time of semi-finished goods and the throughput time of finished goods.