Total completion time minimization on multiple machines subject to machine availability and makespan constraints

•We study bi-criteria scheduling with limited machine availability.•Our goal is to minimize ∑Cj subject to the condition that Cmax ≤ T.•We show the problem, Pm(t)|m(t + Δ) ≥ m(t) − 1, r − a, prmt|∑Cj/Cmax ≤ T, 0 ≤ Δ < ce: paraid = "para0005" > is in P. This paper studies preemptive...

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Published in:	European journal of operational research Vol. 243; no. 2; pp. 547 - 554
Main Authors:	Huo, Yumei, Zhao, Hairong
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.06.2015 Elsevier Sequoia S.A
Subjects:	Bi-criteria Limited machine availability Operations research Optimization algorithms Parallel machine Polynomial time algorithm Polynomials Production scheduling Scheduling Studies Parallel machine Limited machine availability Scheduling Bi-criteria Polynomial time algorithm
ISSN:	0377-2217, 1872-6860
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Abstract	•We study bi-criteria scheduling with limited machine availability.•Our goal is to minimize ∑Cj subject to the condition that Cmax ≤ T.•We show the problem, Pm(t)\|m(t + Δ) ≥ m(t) − 1, r − a, prmt\|∑Cj/Cmax ≤ T, 0 ≤ Δ < ce: paraid = "para0005" > is in P. This paper studies preemptive bi-criteria scheduling on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T. We study the unavailability model such that the number of available machines cannot go down by 2 within any period of pmax where pmax is the maximum processing time among all jobs. We show that there is an optimal polynomial time algorithm.
AbstractList	This paper studies preemptive bi-criteria scheduling on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T. We study the unavailability model such that the number of available machines cannot go down by 2 within any period of pmax where pmax is the maximum processing time among all jobs. We show that there is an optimal polynomial time algorithm. •We study bi-criteria scheduling with limited machine availability.•Our goal is to minimize ∑Cj subject to the condition that Cmax ≤ T.•We show the problem, Pm(t)\|m(t + Δ) ≥ m(t) − 1, r − a, prmt\|∑Cj/Cmax ≤ T, 0 ≤ Δ < ce: paraid = "para0005" > is in P. This paper studies preemptive bi-criteria scheduling on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion time subject to the constraint that the makespan is at most a constant T. We study the unavailability model such that the number of available machines cannot go down by 2 within any period of pmax where pmax is the maximum processing time among all jobs. We show that there is an optimal polynomial time algorithm.
Author	Huo, Yumei Zhao, Hairong
Author_xml	– sequence: 1 givenname: Yumei surname: Huo fullname: Huo, Yumei email: huo@mail.csi.cuny.edu, yumei.huo@csi.cuny.edu organization: Department of Computer Science, College of Staten Island, City University of New York, Staten Island, NY 10314, USA – sequence: 2 givenname: Hairong surname: Zhao fullname: Zhao, Hairong email: hairong@purduecal.edu organization: Department of Mathematics, Computer Science & Statistics, Purdue University Calumet, Hammond, IN 46323, USA
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Snippet	•We study bi-criteria scheduling with limited machine availability.•Our goal is to minimize ∑Cj subject to the condition that Cmax ≤ T.•We show the problem,... This paper studies preemptive bi-criteria scheduling on m parallel machines with machine unavailable intervals. The goal is to minimize the total completion...
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SubjectTerms	Bi-criteria Limited machine availability Operations research Optimization algorithms Parallel machine Polynomial time algorithm Polynomials Production scheduling Scheduling Studies
Title	Total completion time minimization on multiple machines subject to machine availability and makespan constraints
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