Abstract
We study problems of scheduling n unit-time jobs on m identical parallel machines, in which a common due window has to be assigned to all jobs. If a job is completed within the due window, then no scheduling cost incurs. Otherwise, a job-dependent earliness or tardiness cost incurs. The job completion times, the due window location and the size are integer valued decision variables. The objective is to find a job schedule as well as the location and the size of the due window such that a weighted sum or maximum of costs associated with job earliness, job tardiness and due window location and size is minimized. We establish properties of optimal solutions of these min-sum and min-max problems and reduce them to min-sum (traditional) or min-max (bottleneck) assignment problems solvable in O(n 5/m 2) and O(n 4.5log0.5 n/m 2) time, respectively. More efficient solution procedures are given for the case in which the due window size cost does not exceed the due window start time cost, the single machine case, the case of proportional earliness and tardiness costs and the case of equal earliness and tardiness costs.
Highlights
We study problems that combine parallel machine scheduling of unit-time jobs with due window assignment
We have studied problems P-sum and P-max of scheduling n unit-time jobs on m identical parallel machines, in which a common due window has to be assigned to all jobs and there are job-dependent earliness and tardiness costs and due window location and size costs
Our results can be generalized to the case of job—and machine-dependent earliness and tardiness costs
Summary
We study problems that combine parallel machine scheduling of unit-time jobs with due window assignment. The two parties agree about the relative importance of the pallets with respect to their completion before or after the due window because of the relative urgency of the corresponding construction works The latter leads to the earliness and tardiness costs. Kramer and Lee (1994) studied a problem with min-sum objective, in which the due window is given and job processing times are arbitrary. They proved NP-hardness of this problem, presented a dynamic programming algorithm for the two-machine case and a heuristic for the general case.
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