Dynamic models of production with multiple operations and general processing times

Traditional integer programming model formulations for job-shops and flow-shops do not easily account for characteristics common to high-technology manufacturing such as high-volume semiconductor manufacturing. These characteristics are: (1) products (wafers) are processed by the same machine type more than once during the operation sequence, (2) many lots of similar type are run, and (3) there can be multiple machines of the same type. In this paper, we present two new integer programming formulations which easily account for these characteristics. The approach is based on restricting the allowed domain of events for the start of lot processing. The first model restricts production starts to the beginning of a planning time period. The second model uses a special time grid at each operation with width equal to the processing time, and allows starts to be scheduled at the grid points. In an example problem replicating a high-volume wafer fabrication process, it is shown that it is computationally practical to obtain solutions for the restricted start models where it is not computationally possible for the traditional integer programming model formulations.