An uncertain single machine scheduling problem with periodic maintenance

Shen, Jiayu; Zhu, Kai

doi:10.1016/j.knosys.2017.12.021

Cited by 33 publications

(19 citation statements)

References 18 publications

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“…Likewise, Hong et al suggested optimal periodic maintenance policies to determine the interval between the periodic maintenance activities taking into consideration the maintenance costs [20], while Shen and Zhu studied a single machine scheduling problem with periodic maintenance, in which the processing time and repair time were nondeterministic. They used LPT algorithms to solve the problem [21].…”

Section: Literature Reviementioning

confidence: 99%

An Exact Method and Ant Colony Optimization for Single Machine Scheduling Problem With Time Window Periodic Maintenance

et al. 2020

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This paper considers a time window periodic maintenance strategy with different duration windows and job scheduling activities in a single machine environment. The aim is to minimize the number of tardy jobs through the integration of production scheduling and periodic maintenance intervals. A mixedinteger linear programming model (MILP) is proposed to optimize small-sized test instances. Furthermore, an ant colony optimization (ACO) algorithm is developed to solve larger sized test instances. Subsequently, to measure the efficiency of the solutions obtained by ACO, Moore's algorithm is also developed to benchmark with ACO. To test the efficiency and the effectiveness of the ACO algorithm, a set of data for small and large sized problems was generated in which several parameters were adopted and then ten replicates were solved for each combination. The small sized instances were solved by the MILP. Then, the results obtained showed that the proposed ACO was able to obtain the exact solutions within reasonable CPU times, thus, it outperformed the CPLEX solver with respect to CPU. The large sized instances were solved by the Moore's algorithm and compared to ACO. Then, the results obtained showed that the ACO outperforms Moore's algorithm for all the instances tested. It can be concluded that the developed ACOis very efficient and effective in solving the problem considered in this paper. INDEX TERMS Scheduling, MILP, single machine, periodic Maintenance, ant colony. AHMED BADWELAN received the B.Sc. degree in mechanical engineering from the Faculty of Engineering, University of Aden, in 2012, and the M.S. degree in industrial engineering from King Saud University, Saudi Arabia. He is currently pursuing the Ph.D. degree with the

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Section: Literature Reviementioning

confidence: 99%

An Exact Method and Ant Colony Optimization for Single Machine Scheduling Problem With Time Window Periodic Maintenance

et al. 2020

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“…Some relevant literatures suggested that the LPT algorithm on addressing makespan minimization problem is quite appropriate. 5,29,30,[31][32][33][34][35] LPT algorithm: Sort all jobs in non-increasing order of their processing times. Each job is subsequently assigned to a machine on which it can be finished as early as possible.…”

Section: Worst-case Ratio Analysismentioning

confidence: 99%

A parallel-machine scheduling with periodic constraints under uncertainty

Shen

Zhu

2019

Advances in Mechanical Engineering

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Most studies on scheduling problem have assumed that the machine is continuously available. However, the machine is likely to be unavailable for many practical reasons (e.g. breakdown and planned preventive maintenance). Once a machine is not available, the optimal scheme in the deterministic scenario may not be the optimal choice. To address the actual scenario, a scheduling problem with two identical parallel machines, one of which requires periodic maintenance, is considered in this article. For uncertainties in reality, the processing and maintenance time are considered as uncertain variables. A novel method to study the worst-case ratio in an uncertain scenario is proposed. It is shown that the worst-case ratio of the longest processing time algorithm is 3/2 at a high confidence level. Given theoretical analysis results, an modified algorithm is proposed. Finally, numerical experiments are used to verify the feasibility of the modified algorithm.

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“…To deal with the involved human uncertainty, the uncertainty theory was founded by Liu [12] in 2007 and refined it in 2010 [13]. The uncertainty theory is a branch of axiomatic mathematics for modeling human uncertainty, which has been deeply developed in many fields such as uncertain programming [14][15][16], uncertain scheduling [17][18][19][20][21][22], uncertain risk analysis [23][24][25], uncertain calculus [26][27][28] and uncertain optimal control [29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

A Single Machine Scheduling with Periodic Maintenance and Uncertain Processing Time

Shen¹,

Zhu²

2020

IJCIS

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A single machine scheduling problem with periodic maintenance is studied in this paper. Due to many uncertainties in reality, the processing time is recognized as an uncertain variable. The aim is to minimize the makespan at a confidence level. An uncertain chance-constrained programming model is developed to delve into the impact of uncertainties on decision variables, and an algorithm for calculating the objective function is proposed. According to the theoretical analysis, a novel method named longest shortest processing time (LSPT) rule is proposed. Subsequently, an improved genetic algorithm (GA-M) combined with LSPT rule is proposed. Numerical experiments are used to verify the feasibility of this model and algorithm.

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An uncertain single machine scheduling problem with periodic maintenance

Cited by 33 publications

References 18 publications

An Exact Method and Ant Colony Optimization for Single Machine Scheduling Problem With Time Window Periodic Maintenance

An Exact Method and Ant Colony Optimization for Single Machine Scheduling Problem With Time Window Periodic Maintenance

A parallel-machine scheduling with periodic constraints under uncertainty

A Single Machine Scheduling with Periodic Maintenance and Uncertain Processing Time

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