Review of the ordered and proportionate flow shop scheduling research

Panwalkar, S. S.; Smith, Milton L.; Koulamas, Christos

doi:10.1002/nav.21518

Cited by 51 publications

(15 citation statements)

References 65 publications

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“…Using Eqs. (11,16), Eq. (13) becomes C 2 max = 2q n + p 1 + i−1 j=1 p j + P (D) = 2q n + p 1 + i−1 j=1 p j + P (C * ) + P (D) − P (C * ) = 2q n + p 1 + i−1 j=1 p j + P (C * ) + P (C * ) − P (D) ≤ 2q n + p 1 + i−1 j=1 p j + P (C * ) + P (C * ) ≤ C i max + P (C * )…”

Section: Run a (1 + )-Approximation Formentioning

confidence: 99%

“…The scheduling of medical tests in an outpatient health care facility and the scheduling of classes/exams in an academic institution are two typical examples, where the patients (students, respectively) must complete a number of medical tests (academic activities, respectively); some of these activities must be done in a specified sequential order while the others can be finished in any order; and the time-spans for all these activities should not overlap with each other. The proportionate shops were also introduced in the 1980's [10] and they are one of the most specialized shops with respect to the job processing times which have received many studies [11].…”

Section: Introductionmentioning

confidence: 99%

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Approximation algorithms for the three-machine proportionate mixed shop scheduling

Liu

Chen

Dong

et al. 2020

Theoretical Computer Science

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A mixed shop is a manufacturing infrastructure designed to process a mixture of a set of flowshop jobs and a set of open-shop jobs. Mixed shops are in general much more complex to schedule than flow-shops and open-shops, and have been studied since the 1980's. We consider the three machine proportionate mixed shop problem denoted as M 3 | prpt | C max , in which each job has equal processing times on all three machines. Koulamas and Kyparisis [European Journal of Operational Research, 243:70-74,2015] showed that the problem is solvable in polynomial time in some very special cases; for the non-solvable case, they proposed a 5/3-approximation algorithm. In this paper, we present an improved 4/3-approximation algorithm and show that this ratio of 4/3 is asymptotically tight; when the largest job is a flow-shop job, we present a fully polynomialtime approximation scheme (FPTAS). On the negative side, while the F 3 | prpt | C max problem is polynomial-time solvable, we show an interesting hardness result that adding one open-shop job to the job set makes the problem NP-hard if this open-shop job is larger than any flow-shop job. We are able to design an FPTAS for this special case too. Figure 5.1: A feasible schedule π for the constructed instance of the M 3 | prpt | C max problem, when the set S can be partitioned into two equal parts S 1 and S 2 . The partition of the flow-shop jobs {J 1 , J 2 } is correspondingly constructed. In the schedule, the jobs of J 1 and the jobs of J 2 are processed in the LPT order, respectively.

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Section: Run a (1 + )-Approximation Formentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for the three-machine proportionate mixed shop scheduling

Liu

Chen

Dong

et al. 2020

Theoretical Computer Science

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“…We should also point out that the

F m / p r p t / C_{\max}

problem is a special case of the ordered flow shop

F m / o r d r / C_{\max}

problem introduced by Smith et al and reviewed by Panwalkar et al . Smith et al showed that the

F m / o r d r / C_{\max}

problem is solvable in

O (n \log n)

time when each job has its shortest (longest) processing time on

M_{1}

.…”

Section: Discussion‐conclusionmentioning

confidence: 99%

Proportionate flow shop: New complexity results and models with due date assignment

Panwalkar

Koulamas

2015

Naval Research Logistics

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Abstract:It is known that the proportionate flow shop minimum makespan F m/prpt/C max problem is solved optimally by any permutation job sequence. We show that the F m/prpt/C max problem is at least ordinary NP-hard when missing operations are allowed and present some solvable cases. We then consider the standard proportionate flow shop problem (with no missing operations) and show that the solution algorithms for a class of single-machine due date assignment problems can be extended/generalized to the corresponding proportionate flow shop problems.

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“…Numerous comprehensive reviews have been published in the field of production scheduling (Hart et al 2005;Biskup 2008;Koulamas 2010;Panwalkar et al 2013). These studies include many scheduling problems: single-machine scheduling (Koulamas 2010;, parallel machine scheduling (Vallada and Ruiz 2011;Yanga et al 2012), job shop scheduling (Weng and Ren 2006), flow shop scheduling (Panwalkar et al 2013), flexible manufacturing system scheduling (Tomastik et al 1996;, and order scheduling at the company and supply chain levels Guo et al 2013a, b).…”

Section: Previous Studies In Production Schedulingmentioning

confidence: 99%

Intelligent Decision-making Models for Production and Retail Operations

Guo¹

2016

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Review of the ordered and proportionate flow shop scheduling research

Abstract: Ordered flow shop models have appeared in the literature since the mid-1970s and proportionate flow shop models have appeared since the early 1980s. We provide a detailed review of these models along with some analysis and potential topics for future research.

Cited by 51 publications

References 65 publications

Approximation algorithms for the three-machine proportionate mixed shop scheduling

Approximation algorithms for the three-machine proportionate mixed shop scheduling

Proportionate flow shop: New complexity results and models with due date assignment

Intelligent Decision-making Models for Production and Retail Operations

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