Heuristics for a multi-machine multi-objective job scheduling problem with smoothing costs

We propose a new multi-objective job scheduling problem on non-identical machines involving job and machine dependent setup costs and times, as well as smoothing costs. Smoothing issues are very important in several settings, such as for example car production, since they allow to balance resource utilization over an assembly line. In this paper, we describe the problem, give a mixed integer linear programming formulation, and propose several heuristics: three greedy procedures, two descent approaches, and a tabu search. Experiments, performed on realistic and challenging instances with up to 500 jobs and 8 machines, show that tabu search is a powerful method: it gives the best results for the large instances and is very competitive on the small instances. General Terms Metaheuristics, job scheduling, multi-resource