Scheduling resumable deteriorating jobs on a single machine with non-availability constraints

Fan, Baoqiang; Li, Shisheng; Zhou, Li; Zhang, Liqi

doi:10.1016/j.tcs.2010.09.017

Cited by 21 publications

(7 citation statements)

References 10 publications

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“…Gawiejnowicz and Kononov [10] considered the complexity and approximability of scheduling resumable proportionally deteriorating jobs. Fan et al [11] considered the scheduling resumable deteriorating jobs on a single machine with nonavailability constraints. Li and Fan [12] addressed the nonresumable scheduling problem 1| − , = | ∑ .…”

Section: Introductionmentioning

confidence: 99%

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

Miao

Zou

2015

Mathematical Problems in Engineering

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We consider the parallel-machine scheduling problem in which the machines have availability constraints and the processing time of each job is simple linear increasing function of its starting times. For the makespan minimization problem, which is NP-hard in the strong sense, we discuss the Longest Deteriorating Rate algorithm and List Scheduling algorithm; we also provide a lower bound of any optimal schedule. For the total completion time minimization problem, we analyze the strong NP-hardness, and we present a dynamic programming algorithm and a fully polynomial time approximation scheme for the two-machine problem. Furthermore, we extended the dynamic programming algorithm to the total weighted completion time minimization problem.

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Section: Introductionmentioning

confidence: 99%

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

Miao

Zou

2015

Mathematical Problems in Engineering

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“…Wu and Lee [6] first studied the deteriorating job scheduling problem under the machine availability constraint condition. For more papers about this topic, the reader is referred to Fan et al [7], Ji et al [8], and Li and Fan [9].…”

Section: Introductionmentioning

confidence: 99%

A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

Wan

2013

Mathematical Problems in Engineering

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In (1998), Kovalyov and Kubiak studied the problem of scheduling n deteriorating jobs on a single machine to minimize makespan. They presented a fully polynomial-time approximation scheme which is based on a dynamic programming. Unfortunately, their dynamic programming is incorrect. So the fully polynomial-time approximation scheme is also invalid. In this paper, we construct an instance to show how their dynamic programming does not work and provide a correct dynamic programming, based on which a new fully polynomial-time approximation scheme is derived.

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“…In the past, there have been many studies of job 19 scheduling with constraints that jobs can be splittable 20 into many sub-jobs such as resumable studies [1][2][3] , lot 21 sizing studies [4][5][6][7] , capacitated machine studies 8-11 , 22 etc. and there have been also many studies on 23 scheduling in available time windows [12][13][14] .…”

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confidence: 99%

“…and there have been also many studies on 23 scheduling in available time windows [12][13][14] . As a pioneering result among [1][2][3] , Min and Cheng 2 considered a cheduling resumable simple linear deteriorating jobs on a single machine with an availability constraint to minimize makespan. The authors showed this problem is equivalent to a binary integer programming problem and proved it is NP-hard in the ordinary sense, and then show there exists an FPTAS for it by applied the technique of Woeginger.…”

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confidence: 99%

A mathematical model for teamwork scheduling problem in available time-windows

Trang

Tran²,

Huynh

2020

Sci. Tech. Dev. J.- Eng. Tech.

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This paper deals with teamwork scheduling problem in available time windows. This problem has been posed by combining the three constraints are the jobs can split into some sub-jobs which should not be less than a threshold called splitmin, the jobs are only assigned into available time windows and the jobs can be assigned into many people in the organization. Since then the four properties of this problem considered are everyone handles any jobs; a job can be handled by some person at the same time; jobs can be broken down into some sub-jobs; the size of the job/sub-job should not be less than splitmin. The goal aims to determine a feasible schedule that minimizes makespan. And a numerical example is presented to demonstrate the essential constraint with given input data to well define this scheduling problem. Besides the authors proposed a mathematical model to determine the optimal solution by using solvers to solve it and some simple heuristics with computing time less than one second to find the good solutions such as Assignment approach, SPT/LPT rules. All experiments were evaluated on two criteria are the maximum completion time for all jobs and runtime in seconds to determine the solution. These experiments were conducted by the comparison of the lower bound, the exact method based on using CPLEX solver to solve the MILP model, and proposed heuristics. The experimental results show it is very time consuming to determine the optimal solution by CPLEX solver, while the solution found by heuristic algorithms is only good enough.

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Scheduling resumable deteriorating jobs on a single machine with non-availability constraints

Cited by 21 publications

References 10 publications

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

Parallel-Machine Scheduling with Time-Dependent and Machine Availability Constraints

A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

A mathematical model for teamwork scheduling problem in available time-windows

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