Single machine stochastic JIT scheduling problem subject to machine breakdowns

Heng-yong, Tang; Zhao, Chengli; Cheng, Chin‐Hsiang

doi:10.1007/s11425-007-0151-z

Cited by 16 publications

(8 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In 1996, Cai and Tu [5] made a further investigation into the problem that was considered by the paper [4] under the condition of jobs with random processing times. In 2008, Tang et al [6] studied a stochastic JIT scheduling problem with a machine subject to a sequence of stochastic breakdowns. 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.…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…In 1996, Cai and Tu [5] made a further investigation into the problem that was considered by the paper [4] under the condition of jobs with random processing times. In 2008, Tang et al [6] studied a stochastic JIT scheduling problem with a machine subject to a sequence of stochastic breakdowns. In 2008, Cheng et al [7] studied the problem of scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties.…”

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…In this model, the setup, cleaning, and transportation time are also considered. Tang et al [10] studied the single machine stochastic just-in-time scheduling problem subject to machine breakdowns for the preemptresume and the preempt-repeat. The objective function of the problem is the sum of squared deviations of the job expected completion time from the due date.…”

Section: Introductionmentioning

confidence: 99%

A Discrete Group Search Optimizer for Hybrid Flowshop Scheduling Problem with Random Breakdown

Cui

2014

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The scheduling problems have been discussed in the literature extensively under the assumption that the machines are permanently available without any breakdown. However, in the real manufacturing environments, the machines could be unavailable inevitably for many reasons. In this paper, the authors introduce the hybrid flowshop scheduling problem with random breakdown (RBHFS) together with a discrete group search optimizer algorithm (DGSO). In particular, two different working cases, preempt-resume case, and preempt-repeat case are considered under random breakdown. The proposed DGSO algorithm adopts the vector representation and several discrete operators, such as insert, swap, differential evolution, destruction, and construction in the producers, scroungers, and rangers phases. In addition, an orthogonal test is applied to configure the adjustable parameters in the DGSO algorithm. The computational results in both cases indicate that the proposed algorithm significantly improves the performances compared with other high performing algorithms in the literature.

show abstract

Single machine stochastic JIT scheduling problem subject to machine breakdowns

Cited by 16 publications

References 12 publications

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 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

A Discrete Group Search Optimizer for Hybrid Flowshop Scheduling Problem with Random Breakdown

Contact Info

Product

Resources

About