Minimizing the number of tardy jobs under piecewise-linear deterioration

Authors:
Ghasem Moslehi;Abbasali Jafari
Affiliations:
Department of Industrial and Systems Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran;Department of Industrial and Systems Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran
Venue:
Computers and Industrial Engineering
Year:
2010

Citing 9
Cited 5

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Deteriorating job scheduling to minimize the number of late jobs with setup times

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Short Communication: A note on "Single machine scheduling with time-dependent deterioration and exponential learning effect"

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Minimizing the number of tardy jobs in a single-machine scheduling problem with periodic maintenance

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Joint reply to the erratum and the note on "Single machine scheduling problems under the effects of nonlinear deterioration and time-dependent learning" [Math. Comput. Modelling 50 (2009) 401-406]

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Scheduling linear deteriorating jobs to minimize the number of tardy jobs

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Abstract

In this paper, we consider a single machine scheduling problem with piecewise-linear deterioration where its objective is to minimize the number of tardy jobs, in which the processing time of each job depends on its starting time where all the jobs have a specific deterioration rate. The problem is known to be NP-hard; therefore a Branch and Bound algorithm and a heuristic algorithm with O(n^2) are proposed. The proposed heuristic algorithm has been utilized for solving large scale problems and upper bound of the B&B algorithm. Computational experiments on 1840 problems demonstrate that the Branch and Bound procedure can solve problems with 28 jobs and 85.4% of all the sample problems optimally showing the high capability of the proposed procedure. Also it is shown that the average value of the ratio of optimal answer to the heuristic algorithm result with the objective @?(1-U"i) is at last 1.08 which is more efficient in contrast to other proposed algorithms in related studies in the literature. According to high efficacy of the heuristic algorithm, large scale samples are also being solved and the results are presented. A specific form of this problem is also being considered and it is proven that the B&B procedure can handle problems with more jobs even up to 44 jobs.