Bi-Objective Parallel Machine Scheduling Problem with Flexible Maintenance and Jobs’ Release Times
To deal with the needs of machine maintenance activities, an integrated scheduling model in which maintenance activities and job processing are considered simultaneously has been attracted by many researchers. Motivated by the clean operation in the semiconductor manufacturing, in which the machines must to be stopped for changing cleaning agent periodically to avoid that too much the dirt residue in the machine damages the wafer, we addressed in this paper the non-preemptive non-identical parallel machine scheduling problem with jobs’ release times and maintenance activities, and considered a bi-objective of minimizing the total weighted tardiness and the total completion time simultaneously. This is a NP-hard problem. For the problem, we proposed a mixed integer programming model to find all efficient solutions for small problems, which could be benchmarks for evaluating the performances of other heuristic algorithms in the future.
Keywords- Parallel-Machine Scheduling, Flexible Maintenance, Release Time, Bi-Objective.