Meta-heuristics for unrelated parallel machines scheduling with random rework to minimize expected total weighted tardiness

Abstract

Unrelated parallel machines scheduling problems with random rework have many industrial applications. Since the problem has been proven to be NP hard in a strong sense, we concentrate on the implementation of efficient approximate methods based on deterministic optimization techniques. Two mixed integer programming models are formulated based on aggregate and separate task estimation, respectively. In order to obtain an approximate solution of a large-scale instance, we further propose modified genetic algorithm and simulated annealing algorithm. The initial solutions of the algorithms are obtained by effective priority rules. Computational experiments based on randomly generated instances demonstrate that the proposed aggregate task estimation is more efficient and more stable than the existing separate task estimation. The proposed meta-heuristics are superior to classical priority rules and close to the exact method. Specifically, simulated annealing algorithm is preferred due to higher computational efficiency than that of genetic algorithm.