Resource-constrained unrelated parallel machine scheduling problem with sequence dependent setup times, precedence constraints and machine eligibility restrictions

Abstract

This study addresses an unrelated parallel machine scheduling problem with resource constrains, sequence-dependent setup times, different release dates, machine eligibility and precedence constraints. This problem has been inspired from the block erection scheduling problem in a shipyard. Majority of the traditional scheduling problems in parallel machine environment deal with machine as the only resource. However, other resources such as labors, tools, jigs, fixtures, pallets, dies and industrial robots are not only required for processing jobs but also are often restricted. To formulate this complicated problem, a new pure integer mathematical modeling is proposed and makespan is employed as the objective function. Since the problem is strongly NP-hard, exact approaches are intractable for large size problems. Thus, two new meta-heuristic algorithms including genetic algorithm (GA) and artificial immune system (AIS) are developed to find optimal or near optimal solutions. In addition, the parameters of these algorithms are calibrated by using Taguchi method. The performances of the proposed meta-heuristics are evaluated by a number of numerical examples. The computational results demonstrated that in small scale problems both algorithms are effective and efficient, but in large scale problems the suggested AIS statistically outperformed the proposed GA.