Minimizing total weighted late work on a single-machine with non-availability intervals

Li, Shi‐Sheng; Chen, Ren-Xia

doi:10.1007/s10878-022-00890-x

Cited by 5 publications

(6 citation statements)

References 39 publications

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“…Chen, Yuan, Ng, and Cheng (2019) showed that problem

1\mid {\overline{d}}_j\mid \sum {Y}_j

is unary

NP

‐hard, and problem

1\mid {p}_j=p,{\overline{d}}_j\mid \sum {w}_j{Y}_j

is solvable in

O\left({n}^3\right)

time, where

{\overline{d}}_j

is the deadline of job

{J}_j

. Recently, other variants of scheduling related to the late work criteria are also well‐studied, such as parallel machine scheduling (Chen et al, 2015; Chen, Liang, et al, 2020), nonavailability interval(s) (Li & Chen, 2022; Yin et al, 2016), generalized due dates (Mosheiov et al, 2021), and job rejection (Mor & Shabtay, 2022).…”

Section: Literature Reviewmentioning

confidence: 99%

“…As a criterion related to due dates, late work has been studied for more than 35 years and a large body of literature has been produced. For studies in recent years, see, for example, Chen et al (2015), Chen et al (2021), Chen, Kovalev, et al (2020), Sterna (2011Sterna ( , 2021, Mosheiov et al (2021), Li and Chen (2022), and Mor and Shabtay (2022). Smith (1956) and Emmons (1975) pioneered research on multi-criterion scheduling.…”

Section: Introductionmentioning

confidence: 99%

“…For problem 1|| ∑ Y j , Van Wassenhove (1992a, 1992b) ) time, where d j is the deadline of job J j . Recently, other variants of scheduling related to the late work criteria are also well-studied, such as parallel machine scheduling (Chen et al, 2015;Chen, Liang, et al, 2020), nonavailability interval(s) (Li & Chen, 2022;Yin et al, 2016), generalized due dates (Mosheiov et al, 2021), and job rejection (Mor & Shabtay, 2022).…”

mentioning

confidence: 99%

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Bicriterion Pareto‐scheduling of equal‐length jobs on a single machine related to the total weighted late work

Chen

Yuan

Zhao

et al. 2023

Naval Research Logistics

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In this article, we study bicriterion Pareto‐scheduling on a single machine of equal‐length jobs, where one of the criteria is the total weighted late work. Motivated by two Pareto‐scheduling open problems where one criterion is the total (weighted) late work and the other criterion is the weighted number of tardy jobs, we show that 12 constrained scheduling problems unaddressed in the literature are binary ‐hard, implying that the Pareto‐scheduling versions of these problems are also binary ‐hard. Moreover, we introduce the concept of dummy due dates (DDD) for equal‐length jobs to be scheduled in equal‐length intervals. Intriguingly, we find that a DDD‐based technique outperforms the existing solution methods and improves the known time complexities of the related problems. In addition, we extend our research to the two‐agent scheduling model under the assumption of equal‐length or partially equal‐length jobs by including the total weighted late work as the criterion of one agent. For these problems, our results also improve the known time complexity results.

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“…Chen, Yuan, Ng, and Cheng (2019) showed that problem

1\mid {\overline{d}}_j\mid \sum {Y}_j

is unary

NP

‐hard, and problem

1\mid {p}_j=p,{\overline{d}}_j\mid \sum {w}_j{Y}_j

is solvable in

O\left({n}^3\right)

time, where

{\overline{d}}_j

is the deadline of job

{J}_j

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Bicriterion Pareto‐scheduling of equal‐length jobs on a single machine related to the total weighted late work

Chen

Yuan

Zhao

et al. 2023

Naval Research Logistics

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show abstract

“…In 2008, Cheng et al [7] studied the problem that scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties. In 2022, Li and Chen [8] explored the problem of minimizing total weighted late work on a single machine with non-availability intervals. In 2022, Choi and Park [9] considered a single-machine ) is minimized.…”

Section: Introductionmentioning

confidence: 99%

The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown

Li¹,

Cheng²

2023

Preprint

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We consider the problem of scheduling tasks on a single machine subject to an uncertain breakdown to minimize the flowtime. Assume the machine is unavailable during the breakdown; the starting time of the breakdown is a random variable s with distribution function D(s) and the terminating time of the breakdown has no any other information; jobs are non-resumable. Under the assumptions, starting from the perspective of statistical optimization, we first define the expected competitive ratio of an algorithm to find the optimized solution with the considered problem. Further, we propose and prove a certain result on the expected competitive ratio of the SPT rule. In particular, we show that under a quite loose condition the expected competitive ratio of the SPT rule is no more than 5/4. Meanwhile, we also make some discussions about our studies. What we have done will rich and improve the studying results on the area of scheduling to minimize flowtime and advance the development of online optimization and statistical optimization.

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“…Currently, the research on the machine with breakdowns is still in progress. In 2022, Li and Chen [8] explored the problem of minimizing total weighted late work on a single machine with non-availability intervals. In 2022, Choi and Park [9] considered a single-machine scheduling problem with resource-dependent processing times and multiple unavailability periods.…”

Section: Introductionmentioning

confidence: 99%

The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown

Cheng

2023

Mathematics

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We consider the problem of scheduling jobs on a single machine subject to an uncertain breakdown to minimize the flowtime. Assuming the machine is unavailable during the breakdown, the starting time of the breakdown is a random variable s with distribution function D(s) and the terminating time of the breakdown has no any other information; jobs are non-resumable. Under these assumptions and starting from the perspective of statistical optimization, we first establish the scheduling problem HSONRP, which contains deterministic information, stochastic information, and online information and then define the expected competitive ratio of an algorithm to find the optimized solution of the problem HSONRP. In addition, then, we propose and prove certain results on the expected competitive ratio of the SPT rule. In particular, we prove the expected competitive ratio of SPT rule is less than 1+max{pi}2P when s is the uniform distribution on interval (0,P], where pi is the processing time of job i, P=∑i=1npi, and show that it is no more than 54 under a quite loose condition. Meanwhile, we also make some discussions about our studies. What we have performed will enrich and improve the research results on the area of scheduling to minimize flowtime and advance the development of online optimization and stochastic optimization.

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Minimizing total weighted late work on a single-machine with non-availability intervals

Cited by 5 publications

References 39 publications

Bicriterion Pareto‐scheduling of equal‐length jobs on a single machine related to the total weighted late work

Bicriterion Pareto‐scheduling of equal‐length jobs on a single machine related to the total weighted late work

The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown

The Expected Competitive Ratio on a Kind of Stochastic-Online Flowtime Scheduling with Machine Subject to an Uncertain Breakdown

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