Abstract
The focus of this work is to analyze parallel machine earliness/tardiness (ET) scheduling problem with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we mean that the processing time of a job is defined by an increasing function of its starting time and a decreasing function of the position in the sequence. We develop a mixed integer programming formulation for the problem and show that the optimal sequence is V-shaped: all jobs scheduled before the shortest jobs and all jobs scheduled after the shortest job are in a non-increasing and non-decreasing order of processing times, respectively. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The illustrative example with 11 jobs for 2 machines and 3 machines shows that the model can easily provide the optimal solution, which is V-shaped, for problem.
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Toksarı, M.D., Güner, E. Parallel machine scheduling problem to minimize the earliness/tardiness costs with learning effect and deteriorating jobs. J Intell Manuf 21, 843–851 (2010). https://doi.org/10.1007/s10845-009-0260-3
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DOI: https://doi.org/10.1007/s10845-009-0260-3