Two-stage hybrid flowshop scheduling problem with a product ratio constraint under dynamic job arrivals

Abstract

We consider a two-stage hybrid flowshop scheduling problem with a production ratio constraint in the presence of dynamic job arrivals. The first stage is composed of parallel identical machines and there is a single batch processing machine in the second stage. Also, at the batch processing machine product ratio of product types should be satisfied in order to maintain a required yield rate. The batch processing machine can process multiple jobs up to its capacity simultaneously and the processing time is determined by the longest processing time job in the batch. Since it is very difficult to obtain optimal solution for the problem considered in this study in a reasonable amount of time., we present heuristic algorithms for the problem with the objective of minimizing makespan. A forward approach and a backward approach are proposed along with a few scheduling rules employed in each approach, and these are evaluated with a series of computational experiments on randomly generated test problems. The result shows that the heuristics suggested in the study work better than algorithms used in practice.