A simulated annealing algorithm to minimize makespan of parallel batch processing machines with unequal job ready times

Abstract

A simulated annealing (SA) algorithm to minimize the makespan on a group of identical batch processing machines arranged in parallel is presented. We consider the case where each job has an arbitrary processing time, non-identical size, and non-zero ready time. Each machine can process simultaneously several jobs as a batch as long as the machine capacity is not exceeded. The batch processing time is equal to the largest processing time among those jobs in the batch. Similarly, the batch ready time is equal to the largest ready time among all the jobs in the batch. Random instances were used to compare the results of the SA approach against a lower bound, a mathematical model, and two heuristics published in the literature: the Modified Delay (MD) heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP). Computational experiments showed that the SA approach is comparable to GRASP with respect to solution quality, and less computationally costly. Both SA and GRASP comfortably outperformed the MD heuristic.