Single-machine scheduling with an availability constraint to minimize the weighted sum of the completion times

Kacem, Imed; Chen, Chu; Souissi, Ahmed

doi:10.1016/j.cor.2006.04.010

Cited by 66 publications

(23 citation statements)

References 14 publications

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“…We generate parameters of test problems as used by Kacem, et al [5], Yang, et al [11], and Chen [13] as examples. Our experiment is performed using 16 di erent problem sizes of n 2 f10, 20, 30, 50, 100, 200, 300, 500, 700, 1000, 2000, 4000, 6000, 8000, 12000, 14000g.…”

Section: Numerical Examples and Resultsmentioning

confidence: 99%

“…Kacem et al [5] developed a Mixed Integer Programming (MIP) model for the problem with the objective of minimizing the total completion time (i.e., 1; h 1 k C i ) and used two methods of dynamic programming and a branch-and-bound algorithm. Molaee [6] studied the problem with other separate objectives of minimizing the maximum earliness and minimizing the number of tardy jobs (respectively denoted by 1; h 1 kE max and 1; h 1 k U i ).…”

Section: Introductionmentioning

confidence: 99%

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Minimizing maximum earliness in single-machine scheduling with flexible maintenance time

2017

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Abstract. We consider minimizing the maximum earliness in the single-machine scheduling problem with exible maintenance. In this problem, preemptive operations are not allowed, the machine should be shut down to perform maintenance, tool changing or resetting takes a constant time, and the time window inside which maintenance should be performed is prede ned. We show that the problem is NP-hard. Afterward, we propose some dominance properties and an e cient heuristic method to solve the problem. Also, we propose a branch-and-bound algorithm, in which our heuristic method, the lower bound, and the dominance properties are incorporated. The algorithm is computationally examined using 3,840 instances up to 14,000 jobs. The results impressively show that the proposed heuristic algorithm obtains the optimal solution in about 99.5% of the cases using an ordinary processor in a matter of seconds at most.

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Section: Numerical Examples and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Minimizing maximum earliness in single-machine scheduling with flexible maintenance time

2017

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“…Processing times for problem instances are randomly generated using the discrete uniform distribution in the range [1,10]. According to [11,13,15], due dates are randomly generated from the discrete uniform distribution in the range…”

Section: Data Generationmentioning

confidence: 99%

“…Either of the two values 0.2 and 0.6 is assumed for the two parameters and . According to [8,10], to evaluate the impact of start times of the non-availability period on the performance of algorithms, the values 1 and 2 are generated from the following data sets. possible combinations of the start time of the unavailability period, tardiness factor, and due date factor 12 (2 × 2 × 3) series are generated with a total number of 2680 instances.…”

Section: Data Generationmentioning

confidence: 99%

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Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Molaee

Moslehi

2014

Journal of Industrial Engineering

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Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.

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A Survey on Approximation Algorithms for Scheduling with Machine Unavailability

Diedrich¹,

Jansen²,

Schwarz³

et al. 2009

Lecture Notes in Computer Science

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Single-machine scheduling with an availability constraint to minimize the weighted sum of the completion times

Cited by 66 publications

References 14 publications

Minimizing maximum earliness in single-machine scheduling with flexible maintenance time

Minimizing maximum earliness in single-machine scheduling with flexible maintenance time

Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

A Survey on Approximation Algorithms for Scheduling with Machine Unavailability

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