A matheuristic for making order acceptance decisions in multi-product, multi-stage manufacturing systems

Abstract

We discuss a planning model with load-dependent lead times for making order acceptance decisions in multi-product, multi-stage manufacturing systems. Semiconductor wafer fabrication facilities (wafer fabs) belong to this class of manufacturing systems. A profit-based objective function is considered. Clearing functions are used in the planning formulation to correctly represent the lead time behavior in the case of a congested system. Order acceptance decisions are made with respect to flexible due dates, i.e., it is possible to reject certain orders if there is not enough capacity. Such acceptance decisions are important, for instance, in short-term demand supply matching algorithms that are crucial for demand fulfillment and available to promise decisions in semiconductor manufacturing. The resulting planning problem is formulated as a mixed integer linear program. We first show that the resulting planning problem is NP-hard. Hence, computationally tractable approaches must be designed. Therefore, variable neighborhood search is hybridized with linear programming to solve large-sized problem instances in reasonable amount of computing time in the present paper. Results of computational experiments for problem instances that are derived from a scaled-down wafer fab simulation model are provided and analyzed. The computational results demonstrate that the proposed matheuristic outperforms time-based decomposition approaches from the literature.