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

Panwalkar, S. S.; Koulamas, Christos

doi:10.1002/nav.21615

Cited by 12 publications

(4 citation statements)

References 27 publications

(53 reference statements)

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“…140). The extension of the optimal

1 / / CD

and

1 / / DD

sequences to the proportionate flow shop was recently shown by Panwalkar and Koulamas . To the best of our knowledge, all other results mentioned above (including the modifications of some of these results as outlined in Baker and Scudder and in Gordon et al ) have not been shown to extend to the proportionate flow shop.…”

Section: Problems With Fixed Job Processing Timesmentioning

confidence: 77%

“…Let [j ] denote the job in the j th position in the sequence and I [j ] denote the idle time on the last machine immediately preceding job [j ]; by assumption, p [0] = 0. Then, as shown in Panwalkar and Koulamas [31],…”

Section: Sufficient Conditions For the Extension Of A Single-machine mentioning

confidence: 85%

“…However, in that case, we must assume that all operations of a job are outsourced when the outsourcing option is exercised by the scheduler. This is because the partial outsourcing of some jobs will result in a proportionate flow shop with missing operations which was shown to be at least ordinary NP‐hard by Panwalkar and Koulamas .…”

Section: Discussion‐conclusionmentioning

confidence: 99%

“…Let

[j]

denote the job in the

j th

position in the sequence and

I_{[j]}

denote the idle time on the last machine immediately preceding job

[j]

; by assumption,

p_{[0]} = 0

. Then, as shown in Panwalkar and Koulamas ,

I_{[j]} = (m - 1) * \max [0, p_{[j]} - \max (p_{[0]}, \dots, p_{[j - 1]})], j = 1, \dots, n

and

\sum_{j = 1}^{n} I_{[j]} = (m - 1) p_{\max} .

…”

Section: Sufficient Conditions For the Extension Of A Single‐machine mentioning

confidence: 99%

See 3 more Smart Citations

On equivalence between the proportionate flow shop and single‐machine scheduling problems

Panwalkar

Koulamas

2015

Naval Research Logistics

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We derive sufficient conditions which, when satisfied, guarantee that an optimal solution for a single‐machine scheduling problem is also optimal for the corresponding proportionate flow shop scheduling problem. We then utilize these sufficient conditions to show the solvability in polynomial time of numerous proportionate flow shop scheduling problems with fixed job processing times, position‐dependent job processing times, controllable job processing times, and also problems with job rejection. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 595–603, 2015

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“…140). The extension of the optimal

1 / / CD

and

1 / / DD

Section: Problems With Fixed Job Processing Timesmentioning

confidence: 77%

Section: Sufficient Conditions For the Extension Of A Single-machine mentioning

confidence: 85%

Section: Discussion‐conclusionmentioning

confidence: 99%

“…Let

[j]

denote the job in the

j th

position in the sequence and

I_{[j]}

denote the idle time on the last machine immediately preceding job

[j]

; by assumption,

p_{[0]} = 0

. Then, as shown in Panwalkar and Koulamas ,

I_{[j]} = (m - 1) * \max [0, p_{[j]} - \max (p_{[0]}, \dots, p_{[j - 1]})], j = 1, \dots, n

and

\sum_{j = 1}^{n} I_{[j]} = (m - 1) p_{\max} .

…”

Section: Sufficient Conditions For the Extension Of A Single‐machine mentioning

confidence: 99%

See 2 more Smart Citations

On equivalence between the proportionate flow shop and single‐machine scheduling problems

Panwalkar

Koulamas

2015

Naval Research Logistics

Self Cite

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Two-agent proportionate flowshop scheduling with deadlines: polynomial-time optimization algorithms

Ying,

Pourhejazy,

Sung

2024

Ann Oper Res

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Volatility in the supply chain of critical products, notably the vaccine shortage during the pandemic, influences livelihoods and may lead to significant delays and long waiting times. Considering the capital- and time-intensive nature of capacity expansion plans, strategic operational production decisions are required best to address the supply-demand mismatches given the limited production resources. This research article investigates the production scenarios where the demand of one agent must be completed within a specified due date, hereinafter referred to as the deadline, while minimizing the maximum or total completion time of another agent's demand. For this purpose, the Two-Agent Proportionate Flowshop Scheduling Problem with deadlines is introduced. Two polynomial-time optimization algorithms are developed to solve these optimization problems. This study will serve as a basis for further developing this practical yet understudied scheduling problem.

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Regular scheduling measures on proportionate flowshop with job rejection

Mor

Shapira

2020

Comp. Appl. Math.

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In this article, we study the method of job rejection in the setting of proportionate flowshop, and focus on minimizing regular performance measures, subject to the constraint that the total rejection cost cannot exceed a given upper bound. In particular, we study total completion time, maximum tardiness, total tardiness, and total weighted number of tardy jobs. All the addressed problems are NP-hard as their single machine counterpart are known to be NPhard. To the best of our knowledge, there are no detailed solutions in scheduling literature to the first two problems, whereas the last two problems were never addressed to date. For each problem, we provide a pseudo-polynomial dynamic programming solution algorithm, and furthermore, we enhance the reported running time of the first two problems. Our extensive numerical study validates the efficiency of the provided solutions.

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

Cited by 12 publications

References 27 publications

On equivalence between the proportionate flow shop and single‐machine scheduling problems

On equivalence between the proportionate flow shop and single‐machine scheduling problems

Two-agent proportionate flowshop scheduling with deadlines: polynomial-time optimization algorithms

Regular scheduling measures on proportionate flowshop with job rejection

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