A tabu search heuristic to solve the scheduling problem for a batch-processing machine with non-identical job sizes

A scheduling problem for the batch-processing machine with non-identical job sizes is investigated. The objective is to minimize the makespan. The problem has been proved to be NP-hard. Hence, a tabu search heuristic is proposed to solve it approximately. Besides the basic neighborhoods, three variable depth neighborhoods which are explored by the filter-and-fan method are proposed and used in the tabu search process for further improvement. The larger neighborhood can be obtained by adjusting the depth of search dynamically in the filter-and-fan method. A group of random instances are generated to test the effectiveness of the heuristic we proposed. The experimental results show that the heuristic can obtain the optimal solutions for most of the instances with small scales. And for all the instances with large scales, the heuristic significantly outperform the standard commercial solver both on run time and quality of solution.