Solving a Multi-Objective No-Wait Flow Shop Problem by a Hybrid Multi-Objective Immune Algorithm

Abstract

A frequently occurring operational problem is one of processing a given number of jobs (commodities) on a specified number of machines (facilities) referred to by various investigators as scheduling, dispatching, sequencing, or combinations thereof (Gupta and Stafford, 2006). In most manufacturing environments, a set of processes is needed to be serially performed in several stages before a job is completed. Such system is referred to as the flow shop environment that is one class of scheduling problems. In a flow shop problem, we consider n different jobs that need to be processed on m machines in the same order. Each job has one operation on each machine and the operation of job i on machine j has processing time pij (Baker, 1974). The early groups of flow shop researchers were quite small and these people were concentrated in a few US academic and research institutions. However, today’s flow shop research community is global and from every continent and every geographical region (Gupta and Stafford, 2006). Recently, flow shop scheduling problems have been one of the most renowned problems in the area of scheduling and there are numerous papers that have investigated this issue (Murata et al., 1996). For instance, Gupta and Stafford (2006) investigated the evolution of flow shop scheduling problems and possible approaches for their solution over the last fifty years. They introduced the current flow shop problems and the approaches were used to solve them optimally or approximately. Suliman (2000) considered the permutation flow shop scheduling problem by makespan as objective and he proposed a two-phase heuristic approach to solve it. Cheng et al. (2001) addressed the three machine permutation flow shop scheduling problem with release times where the objective is to minimize maximum completion time. They proposed a branch and bound algorithm for solving this problem. Grabowski and Wodecki (2004) proposed a tabu search based algorithm for the permutation flow shop problem with makespan criterion. Solimanpur et al., (2004) proposed a neural networks-based tabu search method for the flow shop scheduling problem, in which the objective is to minimize makespan. Whang et al. (2006) dealt with a two machine flow shop scheduling problem with deteriorating jobs by minimizing the total completion time.