Planning and scheduling for epitaxial wafer production facilities

In this paper we describe models that formed the basis for a scheduling system developed and implemented at a semiconductor company manufacturing speciality epitaxial wafers. The production characteristics of speciality wafers is similar to that of a flow shop with customized orders requiring job specific processing at some stages. Based on similarities in key resource requirements we classified jobs into product groups. A detailed analysis of the capacity at various stages revealed that the epitaxial growth in the reactors was a bottleneck operation. This paper describes the models used for scheduling jobs at this stage. It should be noted that the facility is equipped with a number of reactors with varying capability. This results in restrictions on the type of jobs that can be processed on each reactor. In addition, since the number of jobs is large, scheduling at this stage is a complex problem. We model the scheduling problem by a single-stage, parallel-machine facility. Traditional approaches in scheduling typically consider a homogeneous job stream and a single objective. In contrast, we consider a facility with different product groups and propose several heuristics for two criteria: makespan and tardiness. Computational experiments were performed with realistic data to test the heuristics. The results suggest that a two phased hierarchical procedure proposed performs reasonably well under a variety of conditions for both objectives. An exception to this is the case when the due dates are dependent on the product groups and are tight. In this instance we recommend the use of two heuristics depending on the objective. Further, we classify the product mix as "homogeneous" or "heterogeneous', and suggest measures to do so. The experimental results suggest that while a simpler heuristic is adequate for homogeneous products, a more elaborate algorithm is required for the heterogeneous case. We formulate a non-linear programming problem to assign reactors to product groups to obtain homogeneous product mix. The significance of this model is due to the fact that homogeneous product set enables use of a simpler heuristic and reduces the complexity of the scheduling system. The non-linear program can be interpreted as an attempt to identify, within the facility, smaller independent shops with homogeneous product groups. We examine two variants of this model and briefly comment on their application to the design and layout of the facility. Since one of the variants is hard 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.