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New characterizations of finite supersoluble groups

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Scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties

The genus polynomials of cross-ladder digraphs in orientable surfaces

An integral estimate of Bessel function and its application

States on sharply dominating effect algebras

Structure of the spectrum of infinite dimensional Hamiltonian operators

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Scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties

Content Provider	Springer Nature Link
Author	Cheng, CongDian Tang, HengYong Zhao, ChuanLi
Copyright Year	2008
Abstract	This article addresses the problem of scheduling n jobs with a common due date on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties. We investigate the problem under the conditions that the uptimes follow an exponential distribution, and the objective measure in detail is to minimize the expected sum of the absolute deviations of completion times from the common due date. We proceed to study in two versions (the downtime follows an exponential distribution or is a constant entailed for the repeat model job), one of which is the so-called preempt-resume version, the other of which is the preempt-repeat version. Three terms of work have been done. (i) Formulations and Preliminaries. A few of necessary definitions, relations and basic facts are established. In particular, the conclusion that the expectation of the absolute deviation of the completion time about a job with deterministic processing time t from a due date is a semi-V-shape function in t has been proved. (ii) Properties of Optimal Solutions. A few characteristics of optimal solutions are established. Most importantly, the conclusion that optimal solutions possess semi-V-shape property has been proved. (iii) Algorithm. Some computing problems on searching for optimal solutions are discussed.
Starting Page	864
Ending Page	888
Page Count	25
File Format	PDF
ISSN	10069283
Journal	Science in China Series A: Mathematics
Volume Number	51
Issue Number	5
e-ISSN	18622763
Language	English
Publisher	SP Science in China Press
Publisher Date	2008-04-19
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	scheduling stochastic breakdowns due date absolute early-tardy penalty V-shape Scheduling theory, stochastic Performance evaluation; queueing; scheduling Processes in random environments Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Scheduling preempt-repeat version jobs on a machine subject to stochastic breakdowns to minimize quadratic earliness-tardiness penalties (i)

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

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Scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties

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