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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Vydané v:International journal of production research Ročník 57; číslo 2; s. 531 - 543
Hlavní autori: Gerstl, Enrique, Mor, Baruch, Mosheiov, Gur
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: London Taylor & Francis 17.01.2019
Taylor & Francis LLC
Predmet:
Algorithms
combinatorial optimization
Dynamic programming
flow shop
Job shops
Polynomials
Production scheduling
Scheduling
sequencing
total late work
ISSN:0020-7543, 1366-588X
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Abstract 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.
AbstractList 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.
Author Mor, Baruch
Mosheiov, Gur
Gerstl, Enrique
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  organization: School of Business Administration, The Hebrew University
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SubjectTerms Algorithms
combinatorial optimization
Dynamic programming
flow shop
Job shops
Polynomials
Production scheduling
Scheduling
sequencing
total late work
Title Scheduling on a proportionate flowshop to minimise total late work
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