An optimization approach to capacity expansion in semiconductor manufacturing facilities

For a given demand and planning horizon, the general facility design proble m faced by semiconductor manufacturers is to decide how much capacity to bu ild into their systems. When the technology is known and only a small numbe r of products is to be manufactured, the specific problem is to find a tool -set configuration that minimizes the average cycle time within a prescribe d budget. In this paper, it is shown that this version of the capacity expa nsion problem can be modelled as a nonlinear integer program in which the d ecision variables correspond to the number of tools at a workstation. The m ajor difficulty encountered in trying to find solutions is that no closed f orm expressions exist for the waiting time, primarily due to the presence o f re-entrant flow. This means that it has to be approximated. At the outset , it was observed that previously proposed approximation methods based on p arametric decomposition provided extremely poor results. In response, a new set of expressions, in the form of simultaneous equations, has been devise d 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 ba sed on simulated annealing, and the fourth is an exact method centring on i mplicit enumeration. Each is used to solve a large sample of test problems generated from data (complied by Sematech) reflecting current technology, c osts, and process routings. The results indicate that high quality solution s can br obtained with little computational effort.