Scheduling Algorithm for Reentrant Flexible Flow Shop with the Objective Function of Minimizing Orders’ Total Flow Time

This study focuses on a scheduling problem in a flexible flow shop, where there are serial stages, each with identical parallel machines. We suggest heuristic algorithms for the problem to minimize the total flow time of a given set of orders. Each order is composed of multiple lots and is processed on any parallel machines at each stage. This shop has reentrant flows since products for specific orders should visit the processing stages twice. We suggest algorithms of two types. The algorithms of the first type are three-phase algorithms, and the second type's algorithm is one-phase. In the first phase of three-phase algorithms, an initial sequence is obtained using priority dispatching rules, and then a construction algorithm is used to obtain sequences for each stage in the second phase. Finally, in the third phase, lots that visit the stages for the second time are scheduled using priority dispatching rules. Computational experiments are performed on randomly generated test problems to evaluate the performance of the suggested algorithms. Results show that the order-based algorithms perform better than the lot-based algorithms and an algorithm used in practice.