Minimizing the sum of job earliness and tardiness in a multimachine system

We provide a heuristic algorithm for minimizing job earliness and tardiness cost in a multimachine scheduling problem. Our formulation explicitly separates machine setup times from processing times, assumes that setup times may depend on the job-to-job sequence, and assumes that processing times may depend on the job-machine combination. The new algorithm can easily provide approximate solutions to problems involving about 10 machines and 100 jobs when using a personal computer. The accuracy of the solutions was measured using a large variety of problem types taken from the literature. Relative accuracy was measured by comparing the new algorithm's results with those from other heuristics, and absolute accuracy was measured by comparing with results obtained using integer programming methods. The new algorithm was significantly more accurate than the other heuristics, and its average deviation was only about 10% when compared to the optimal solutions. In many cases the new algorithm yielded the optimal solution.