The LPT heuristic for minimizing total load on a proportionate openshop

Enrique Gerstl; Gur Mosheiov

doi:https://doi.org/10.1016/j.dam.2023.05.027

The LPT heuristic for minimizing total load on a proportionate openshop

Enrique Gerstl, Gur Mosheiov

Specialization in Operations Research

The Hebrew University of Jerusalem

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

Abstract

We study the problem of minimizing total load on a proportionate openshop. The problem is proved to be NP-hard. A simple LPT (Longest Processing Time first)-based heuristic is proposed, and a bound on the worst-case relative error is introduced: (where m is the number of machines). The proposed bound is smaller than the classical bound on the relative error of LPT when minimizing makespan on parallel identical machines. The algorithm is tested numerically and is shown to produce very close-to-optimal schedules.

Original language	English
Pages (from-to)	190-198
Number of pages	9
Journal	Discrete Applied Mathematics
Volume	338
DOIs	https://doi.org/10.1016/j.dam.2023.05.027
State	Published - 30 Oct 2023

Keywords

Heuristic
Proportionate openshop
Scheduling
Total load
Worst case bound

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Applied Mathematics

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https://doi.org/10.1016/j.dam.2023.05.027

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N2 - We study the problem of minimizing total load on a proportionate openshop. The problem is proved to be NP-hard. A simple LPT (Longest Processing Time first)-based heuristic is proposed, and a bound on the worst-case relative error is introduced: (where m is the number of machines). The proposed bound is smaller than the classical bound on the relative error of LPT when minimizing makespan on parallel identical machines. The algorithm is tested numerically and is shown to produce very close-to-optimal schedules.

AB - We study the problem of minimizing total load on a proportionate openshop. The problem is proved to be NP-hard. A simple LPT (Longest Processing Time first)-based heuristic is proposed, and a bound on the worst-case relative error is introduced: (where m is the number of machines). The proposed bound is smaller than the classical bound on the relative error of LPT when minimizing makespan on parallel identical machines. The algorithm is tested numerically and is shown to produce very close-to-optimal schedules.

KW - Heuristic

KW - Proportionate openshop

KW - Scheduling

KW - Total load

KW - Worst case bound

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SP - 190

EP - 198

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

The LPT heuristic for minimizing total load on a proportionate openshop

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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