Planning and Scheduling for Epitaxial Wafer Production Facilities

In this paper we describe production planning and scheduling models for a semiconductor company manufacturing specialty wafers. The production of specialty wafers involves processing a large number of low volume, customer-specific orders which can be classified into a number of product groups. Typically, the literature on scheduling deals with one product and a single objective. In contrast, we propose and test several heuristics for scheduling jobs in a multiproduct parallel reactor (machine) shop with different criteria. We introduce a set of indices to measure the degree of homogeneity in the product set. Based on the results of the computational experiments, we recommend that the choice of the heuristic should be guided by the homogeneity of the product set and the chosen objective criterion. The planning problem relates to the assignment of reactors to the product groups to obtain homogeneous product sets, and can be viewed as an effort to define smaller, independent shops. The significance of the planning exercise is due to the fact that a homogeneous product set enables the use of a simpler heuristic and reduces the complexity of the scheduling system. We examine two variants of the planning model and briefly comment on their application to the design and layout of the facility. Since one of the variants of the problem is difficult to solve, we present a method to obtain an approximate solution. We provide bounds on the performance of this approximate solution and demonstrate that it is asymptotically optimal.