An Integer Programming Formulation for the Lot Streaming Problem in a Job Shop Environment with Setups

This paper aims at solving the lot streaming problem in a job shop environment, where setup times are involved. The proposed integer programming formulation sufficiently describes the processing dynamics of individual sublots and enables the simultaneous determination of schedules on machines and sublot sizes. Small instances of job shop problems with consistent sublots can thus be optimally solved. Computational results confirm that, by applying the lot streaming strategy, both idling times of machines and completion times of operations are significantly reduced. In view of setups, various types of setups are incorporated in the model. The influence of setup times on the performance of lot streaming is also intensively examined. In addition, the efficiency of the formulation with special constraints is evaluated.