Bi-criteria scheduling with machine assignment costs

Leung, Joseph Y.-T.; Lee, Kangbok; Pinedo, Michael

doi:10.1016/j.ijpe.2012.05.016

Cited by 22 publications

(9 citation statements)

References 26 publications

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“…There is some prior work concerning scheduling for multiple criteria. For instance, Leung et al consider two objectives for scheduling: one is time-related such as makespan (as the customer's objective), and the other is total machine cost (as the service provider's objective) [27]. They form different final objectives by combining these two objectives in various ways and analyse the complexity of the scheduling problem for each of these various combinations.…”

Section: Related Workmentioning

confidence: 99%

Energy-Efficient Scheduling: Classification, Bounds, and Algorithms

Agrawal,

Rao

2016

Preprint

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Section: Related Workmentioning

confidence: 99%

Energy-Efficient Scheduling: Classification, Bounds, and Algorithms

Agrawal,

Rao

2016

Preprint

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“…Indeed, this type of job processing flexibility permits the presence of the processing cost in the problem as a decision factor. Several researchers considered this type of processing cost in the literature (e.g., Leung et al, 2012;Yeh et al, 2015;Mokhtari & Hasani, 2017;Kononov et al, 2019;Hasani & Hosseini, 2020). Nonetheless, the literature on the fixed processing cost, which is also the context of the current study, is significantly scarcer than the machine activation cost and controllable processing cost.…”

Section: Introductionmentioning

confidence: 99%

“…Although sometimes the word "cost" is used to name time-driven objectives such as the earliness/tardiness cost, they are different from the intended machine cost, which is not a function of the processing times. Leung et al (2012) and Lee et al (2014) pointed out that the time-driven criteria are mostly the customer's objectives because they are interested in their orders' early or on-time completion times. Meanwhile, Leung et al (2012) and Lee et al (2014) mentioned that the machine cost is a type of the service provider's objectives since it expresses production costs.…”

Section: Introductionmentioning

confidence: 99%

“…Leung et al (2012) and Lee et al (2014) pointed out that the time-driven criteria are mostly the customer's objectives because they are interested in their orders' early or on-time completion times. Meanwhile, Leung et al (2012) and Lee et al (2014) mentioned that the machine cost is a type of the service provider's objectives since it expresses production costs. Furthermore, the machine cost is also a useful concept to model sustainability-oriented costs of the production processes, such as energy consumption and carbon emission.…”

Section: Introductionmentioning

confidence: 99%

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Unrelated parallel machine scheduling with machine processing cost

Safarzadeh¹,

Niaki²

2023

10.5267/j.ijiec

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In practical scheduling problems, some factors such as depreciation cost, green costs like the amount of energy consumption or carbon emission, other resources consumption, raw material cost, etc., are not explicitly related to the machine processing times. Most of these factors can be generally considered as machine costs. Considering the machine cost as another objective alongside the other classical time-driven decision objectives can be an attractive work in scheduling problems. However, this subject has not been discussed thoroughly in the literature for the case the machines have fixed processing costs. This paper investigates a general unrelated parallel machine scheduling problem with the machine processing cost. In this problem, it is assumed that processing a job on a machine incurs a particular cost in addition to processing time. The considered objectives are the makespan and the total cost, which are minimized simultaneously to obtain Pareto optimal solutions. The efficacy of the mathematical programming approach to solve the considered problem is evaluated rigorously in this paper. In this respect, a multiobjective solution procedure is proposed to generate a set of appropriate Pareto solutions for the decision-maker based on the mathematical programming approach. In this procedure, the ϵ-constraint method is first used to convert the bi-objective optimization problem into single-objective problems by transferring the makespan to the set of constraints. Then, the single-objective problems are solved using the CPLEX software. Moreover, some strategies are also used to reduce the solution time of the problem. At the end of the paper, comprehensive numerical experiments are conducted to evaluate the performance of the proposed multiobjective solution procedure. A vast range of problem sizes is selected for the test problems, up to 50 machines and 500 jobs. Furthermore, some rigorous analyses are performed to significantly restrict the patterns of generating processing time and cost parameters for the problem instances. The experimental results demonstrate the mathematical programming solution approach's efficacy in solving the problem. It is observed that even for large-scale problems, a diverse set of uniformly distributed Pareto solutions can be generated in a reasonable time with the gaps from the optimality less than 0.03 most of the time.

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“…In the last few decades, more and more researchers have studied bicriteria parallel machine scheduling problems. Many considered makespan-or total-completion-time-related objectives [1,2,6,8,[10][11][12][14][15][16]19,23,24,38,40], while several of them considered due-date-related objectives [4,25,17,37,38,43]. However, none of them considered release dates.…”

Section: Introductionmentioning

confidence: 99%

Bicriteria scheduling problem for unrelated parallel machines with release dates

Lin

2015

Computers & Operations Research

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Bi-criteria scheduling with machine assignment costs

Cited by 22 publications

References 26 publications

Energy-Efficient Scheduling: Classification, Bounds, and Algorithms

Energy-Efficient Scheduling: Classification, Bounds, and Algorithms

Unrelated parallel machine scheduling with machine processing cost

Bicriteria scheduling problem for unrelated parallel machines with release dates

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