Hybrid tabu search for re-entrant permutation flow-shop scheduling problem

The assumption of classical shop scheduling problems that each job visits each machine only once (Baker, 1974) is often violated in practice. A new type of manufacturing shop, the reentrant shop has recently attracted attention. The basic characteristic of a re-entrant shop is that a job visits certain machines more than once. For example, in semiconductor manufacturing, consequently, each wafer re-visits the same machines for multiple processing steps (Vargas-Villamil & Rivera, 2001). The wafer traverses flow lines several times to produce the different layer on each circuit (Bispo & Tayur, 2001). A re-entrant flowshop (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 a re-entrant permutation flow-shop (RPFS) problem. The assumptions made for the RPFS scheduling problems are summarized here. Every job may visit certain machines more than once. Machine order is the same for each of the n jobs. Job order is the same for each of the m machines at each layer. The classical permutation flow-shop scheduling problem can be modified to suit the RPFS scheduling problem by relaxing the assumption that each job visits each machine no more than once. This study considers the RPFS scheduling problems with the objective of minimizing makespan of jobs. Hwang & Sum (1998) addressed a two-machine flow-shop problem with re-entrant workflows and sequence dependent setup times, which have a special structure, to minimize makespan. Demirkol & Uzsoy (2000) proposed a decomposition method to minimize maximum lateness for a RFS with sequence-dependent setup times. Graves et al. (1983) modeled a wafer fabrication as a RFS, where the objective is to minimize average throughput time subject to meeting a given production rate. Drobouchevitch & Strusevich (1999) developed a heuristic algorithm for the two-machine re-entrant shop problem to minimize the makespan. Kubiak et al. (1996) considered a class of re-entrant shops in which jobs followed the route of M1, M2, M1, M3,..., M1, Mm, M1 with the objective of minimizing the mean flow time. They showed that the shortest-processing-time (SPT) rule was optimal