A single machine scheduling problem to minimize total early work

Yoav Ben-Yehoshua; Gur Mosheiov

doi:10.1016/j.cor.2016.03.010

A single machine scheduling problem to minimize total early work

Yoav Ben-Yehoshua, Gur Mosheiov^*

^*Corresponding author for this work

Business Administration

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

We study a single machine scheduling problem, where the objective is minimum total early work. In this setting, a job is penalized according to the duration of the parts of the job completed prior to its due-date. First we prove that the problem is NP-hard. Then, based on a number of properties of an optimal schedule, we introduce a pseudo-polynomial dynamic programming algorithm, verifying NP-hardness in the ordinary sense. Our numerical tests indicate that the dynamic programming solves problems of hundreds of jobs in very reasonable time.

Original language	American English
Pages (from-to)	115-118
Number of pages	4
Journal	Computers and Operations Research
Volume	73
DOIs	https://doi.org/10.1016/j.cor.2016.03.010
State	Published - Sep 2016

Bibliographical note

Funding Information:
This research was supported by the Israel Science Foundation (Grant no. 1286/14 ). The second author was supported in part by the Recanati Fund of The School of Business Administration, and Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem, Israel.

Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.

Keywords

Dynamic programming
Scheduling
Single machine
Total early work

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10.1016/j.cor.2016.03.010

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AU - Mosheiov, Gur

N1 - Funding Information: This research was supported by the Israel Science Foundation (Grant no. 1286/14 ). The second author was supported in part by the Recanati Fund of The School of Business Administration, and Charles I. Rosen Chair of Management, The Hebrew University of Jerusalem, Israel. Publisher Copyright: © 2016 Elsevier Ltd. All rights reserved.

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N2 - We study a single machine scheduling problem, where the objective is minimum total early work. In this setting, a job is penalized according to the duration of the parts of the job completed prior to its due-date. First we prove that the problem is NP-hard. Then, based on a number of properties of an optimal schedule, we introduce a pseudo-polynomial dynamic programming algorithm, verifying NP-hardness in the ordinary sense. Our numerical tests indicate that the dynamic programming solves problems of hundreds of jobs in very reasonable time.

AB - We study a single machine scheduling problem, where the objective is minimum total early work. In this setting, a job is penalized according to the duration of the parts of the job completed prior to its due-date. First we prove that the problem is NP-hard. Then, based on a number of properties of an optimal schedule, we introduce a pseudo-polynomial dynamic programming algorithm, verifying NP-hardness in the ordinary sense. Our numerical tests indicate that the dynamic programming solves problems of hundreds of jobs in very reasonable time.

KW - Dynamic programming

KW - Scheduling

KW - Single machine

KW - Total early work

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DO - 10.1016/j.cor.2016.03.010

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SN - 0305-0548

VL - 73

SP - 115

EP - 118

JO - Computers and Operations Research

JF - Computers and Operations Research

ER -

A single machine scheduling problem to minimize total early work

Abstract

Bibliographical note

Keywords

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