Capacitated lot sizing with alternative routings and overtime decisions

Material requirements planning (MRP) is a basic tool for performing detailed material planning function in the manufacture of component parts and their assembly into finished items. MRP's managerial objective is to provide 'the right part at the right time' to meet the schedules for completed products. However satisfying end customer demands faster with lower inventories implies smarter scheduling which must simultaneously reflect actual capacity conditions. Therefore, the need is to schedule both capacity and materials simultaneously. Since MRP does not consider the availability of capacity resources to schedule production, consequently the schedules so developed are usually capacity infeasible. This paper proposes a three-step procedure to develop capacity feasible material and production schedules in a finite capacity environment. In the first step, an LP model produces capacity feasible but lot size relaxed planned order releases for all end products and assembly components which are then fed into a MRP processor, where a bill of material (BOM) explosion process generates material plans. Finally, these material plans are introduced to another LP model which assures that capacity feasibility is again restored. The mathematical models developed consider restrictions on lot sizes as well as alternative production routings and overtime decisions. A numerical example also is provided and some future research directions are outlined.