Models for Scheduling Batch Production of Items with Lot Streaming in Hybrid Flow Shops

Being a common concern faced by nowadays production managers, the problem of minimizing the makespan of batch production schedules of items by using the lot streaming strategy in hybrid flow shops is insufficiently studied by operations researchers. To address to the limitations found in the literature on this subject, this paper formulates two comprehensive mathematical models to solve the problem, a linear programming model and an enumeration model. The following general production conditions are supposed to exist by the models: a processing cycle time limit prescribed for the batch production of item; no-idling of batch operations; not-negligible times for transportation of streamed lots between processing stages; a multi-machine or a single-machine processing of lots at the parallel machine group in each stage; not-negligible times for set-up the stage operations; an anticipative or a reactive scheduling of the setup work; a fixed number of equal-size lots used for streaming the batch production. Under these conditions, the models minimize the length of batch production schedule by minimizing the start time lag between pairs of successive process operations. OpenSolver add-in for Microsoft Office Excel was used for implementing the linear programming model, and a Visual Basic for Applications procedure was coded in Excel for the enumeration model. A numerical example for the utilization of the models was used to discuss the quality of scheduling solutions under different models’ settings, and also to compare in terms of quality and feasibility the solutions implying equal-size lots with other possible scheduling solutions, assuming optimally-sized, different-in-size lots.