An optimization approach to capacity expansion in semiconductor manufacturing facilities

For a given demand and planning horizon, the general facility design problem faced by semiconductor manufacturers is to decide how much capacity to build into their systems. When the technology is known and only a small number of products is to be manufactured, the specific problem is to find a tool-set configuration that minimizes the average cycle time within a prescribed budget. In this paper, it is shown that this version of the capacity expansion problem can be modelled as a nonlinear integer program in which the decision variables correspond to the number of tools at a workstation. The major difficulty encountered in trying to find solutions is that no closed form expressions exist for the waiting time, primarily due to the presence of re-entrant flow. This means that it has to be approximated. At the outset, it was observed that previously proposed approximation methods based on parametric decomposition provided extremely poor results. In response, a new set of expressions, in the form of simultaneous equations, has been devised for approximating the average waiting time in a multiserver batch queuing system. When the number of batch servers is fixed, these equations become linear and are easy to solve. This fact is exploited in the development of a series of algorithms. The first two are greedy in nature, the third is based on simulated annealing, and the fourth is an exact method centring on implicit enumeration. Each is used to solve a large sample of test problems generated from data (compiled by Sematech) reflecting current technology, costs, and process routings. The results indicate that high quality solutions can be obtained with little computational effort.