Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties

Cai, Xiaoqiang; Tu, Fengsheng

doi:10.1002/(sici)1520-6750(199612)43:8<1127::aid-nav5>3.0.co;2-g

Cited by 33 publications

(27 citation statements)

References 3 publications

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“…Appendix A of [6]), the difference between the ESSD function and the SSDE function is only i∈N j∈Bi(π) ρ 2 j . It is dependent on the variances of the job processing times.…”

Section: Contrasting Ssde With Essdmentioning

confidence: 99%

“…Cai and Tu [6] researched the ESSD problem for the preemptive-resume model. In their problem, jobs processing times are stochastic.…”

Section: Corollary 2 If the Deviations Of All Jobs Processing Times mentioning

confidence: 99%

“…So, our work also is the supplement for the work of Cai and Tu. The complexity of the algorithm given by Cai and Tu is O(nΨ n Φ n |S|) [6] , where Φ i = i j=1 ρ 2 j . The complexity of our algorithm is only O(nΨ n |S|).…”

Section: Corollary 2 If the Deviations Of All Jobs Processing Times mentioning

confidence: 99%

“…Scheduling problems involving stochastic machine breakdowns have received increasing attention in recent years. A number of results have been published in the [3][4][5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…They derived the V-shaped property of the optimal solutions for these two problems. Cai and Tu [6] extended the model of Mittenthal and Raghavachari to the case where the processing times are random variables. A sufficient condition is derived under which optimal sequences are V-shaped.…”

Section: Introductionmentioning

confidence: 99%

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Single machine stochastic JIT scheduling problem subject to machine breakdowns

Heng-yong

Zhao

Cheng

2008

Sci. China Ser. A-Math.

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In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat. The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date. For preemptive-resume, we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times. And a dynamic programming algorithm with the pseudopolynomial time complexity is given. We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem, and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions. For preemptive-repeat, the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed. We replace the ESSD problem by the SSDE problem. We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times. And a dynamic programming algorithm with the pseudopolynomial time complexity is given. A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem. Keywords:stochastic JIT scheduling, machine breakdowns, preemptive-resume, preemptiverepeat, sum of squared deviations of the expected completion times from the due date MSC(2000): 90B36, 68M20

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“…Appendix A of [6]), the difference between the ESSD function and the SSDE function is only i∈N j∈Bi(π) ρ 2 j . It is dependent on the variances of the job processing times.…”

Section: Contrasting Ssde With Essdmentioning

confidence: 99%

“…Cai and Tu [6] researched the ESSD problem for the preemptive-resume model. In their problem, jobs processing times are stochastic.…”

Section: Corollary 2 If the Deviations Of All Jobs Processing Times mentioning

confidence: 99%

Section: Corollary 2 If the Deviations Of All Jobs Processing Times mentioning

confidence: 99%