Abstract
The unrelated parallel machine scheduling problem aims to assign jobs to independent machines with sequence-dependent setup times so that the makespan is minimized. When many practical considerations are introduced, solving the resulting problem is challenging, especially when problems of realistic sizes are of interest. In this study, in addition to the conventional objective of minimizing the makespan, we further consider the burn-in (B/I) procedure that is required in practice; we need to ensure that the scheduling results satisfy the B/I ratio constrained by the equipment. To solve the resulting complicated problem, we propose a population-based simulated annealing algorithm embedded with a variable neighborhood descent technique. Empirical results show that the proposed solution strategy outperforms a commonly used commercial optimization package; it can obtain schedules that are better than the schedules used in practice, and it does so in a more efficient manner.
Highlights
Unrelated parallel machine scheduling problems are of significant practical relevance, and they arise in many applications
We developed a population-based simulated annealing (PBSA) algorithm for the unrelated parallel machine scheduling problem considering B/I constraints
The proposed PBSA algorithm integrates the advantages of simulated annealing (SA) and variable neighborhood descent (VND) and was implemented for practical applications
Summary
The unrelated parallel machine scheduling problem aims to assign a set of jobs to a set of unrelated machines that can process the jobs in parallel without affecting each other. As each job has its own suitable B/I equipment, the maximization of B/I equipment utilization can be achieved by making the ratio of completed jobs match the number of B/I equipment available Other than this additional consideration, the conventional constraints (i.e., sequence-dependent setup times) are accommodated in the study. As the unrelated parallel machine scheduling problem possesses non-deterministic polynomial-time (NP)-hard complexity [1], solving problem instances with practical sizes is a challenging task, especially when many practical constraints need to be considered. To address this type of problem, we propose a population-based simulated annealing (PBSA). The final section offers conclusions and provides suggestions for future research
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