Fast and meta-heuristics for common due-date assignment and scheduling on parallel machines

Abstract

This study considers common due-date assignment and scheduling on parallel machines. The problem has three decision variables: assigning the common-due-date, allocating jobs to parallel machines, and sequencing the jobs assigned to each machine. The objective is to minimise the sum of due-date assignment, earliness and tardiness penalties. A mathematical programming model is presented, and then two types of heuristics are suggested after characterising the optimal solution properties. The two types of heuristics are: (a) a fast two-stage heuristic with obtaining an initial solution and improvement; and (b) two meta-heuristics, tabu search and simulated annealing, with new neighbourhood generation methods. Computational experiments were conducted on a number of test instances, and the results show that each of the heuristic types outperforms the existing one. In particular, the meta-heuristics suggested in this study are significantly better than the existing genetic algorithm.

Keywords:

• parallel machine scheduling
• common due-date assignment
• fast heuristics
• meta-heuristics

Acknowledgements

This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund) (KRF-2007-331-D00547).