A branch and bound procedure for the reentrant permutation flow-shop scheduling problem

This investigation considers a reentrant permutation flow-shop (RPFS) scheduling problem whose performance criterion is makespan. A reentrant flow-shop (RFS) refers to situations in which every job must be processed on machines in the order, M1, M2, ..., Mm, M1, M2, ..., Mm, ..., and M1, M2, ..., Mm. Every job can be decomposed into several layers each of which starts on M1 and finishes on Mm. In the RFS case, if the job ordering is the same on any machine at each layer, then no passing is said to be allowed, since no job is allowed to pass any former job. The RFS scheduling problem in which no passing is allowed, is called an RPFS problem. A branch and bound algorithm is presented and an example is also given to illustrate the solution procedure. To compare the proposed algorithm, a series of computational experiments are done on randomly generated test problems and the results show that the developed algorithm is efficient.