Scheduling on a proportionate flowshop to minimise total late work

We study a scheduling problem to minimise total late work, i.e. each job is penalised according to the duration of its parts scheduled after its due-date. The machine setting is an m-machine proportionate flow shop. Two versions of the problem are studied: (i) the case that total late work refers to...

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Bibliographic Details
Published in:International journal of production research Vol. 57; no. 2; pp. 531 - 543
Main Authors: Gerstl, Enrique, Mor, Baruch, Mosheiov, Gur
Format: Journal Article
Language:English
Published: London Taylor & Francis 17.01.2019
Taylor & Francis LLC
Subjects:
Algorithms
combinatorial optimization
Dynamic programming
flow shop
Job shops
Polynomials
Production scheduling
Scheduling
sequencing
total late work
ISSN:0020-7543, 1366-588X
Online Access:Get full text
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Summary:We study a scheduling problem to minimise total late work, i.e. each job is penalised according to the duration of its parts scheduled after its due-date. The machine setting is an m-machine proportionate flow shop. Two versions of the problem are studied: (i) the case that total late work refers to the last operation of the job (i.e. the operation performed on the last machine of the flow shop); (ii) the case that total late work refers to all the operations (on all machines). Both versions are known to be NP-hard. We prove a crucial property of an optimal schedule, and consequently introduce efficient pseudo-polynomial dynamic programming algorithms for the two versions. The dynamic programming algorithms are tested numerically and proved to perform well on large size instances.
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ISSN:0020-7543
1366-588X
DOI:10.1080/00207543.2018.1456693