Minimizing the total weighted flow time in a single machine with controllable processing times

Shabtay, Dvir; Kaspi, Moshe

doi:10.1016/s0305-0548(03)00187-4

Cited by 73 publications

(37 citation statements)

References 12 publications

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“…Problem 1|p j = (a j /u j ) k , Σu j ≤ U |Σw j C j was considered in [71]. The problem was reduced to discrete optimization problem, however, the computational complexity of the problem remains an open question.…”

Section: Scheduling Problems With Convex Function Of Job Processing Tmentioning

confidence: 99%

Section: Scheduling Problems With Convex Function Of Job Processing Tmentioning

confidence: 99%

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Resource Management in Machine Scheduling Problems: A Survey

Janiak

Lichtenstein

2007

dmms

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Abstract. The paper is a survey devoted to job scheduling problems with resource allocation. We present the results available in the scientific literature for commonly used models of job processing times and job release dates, i.e., the models in which the job processing time or the job release date is given as a linear or convex function dependent on the amount of the additional resource allotted to the job. The scheduling models with resource dependent processing times or resource dependent release dates extend the classical scheduling models to reflect more precisely scheduling problems that appear in real life. Thus, in this paper we present the computational complexity results and solution algorithms that have been developed for this kind of problems.

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Section: Scheduling Problems With Convex Function Of Job Processing Tmentioning

confidence: 99%

Section: Scheduling Problems With Convex Function Of Job Processing Tmentioning

confidence: 99%

Resource Management in Machine Scheduling Problems: A Survey

Janiak

Lichtenstein

2007

dmms

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“…This problem, i.e. the single-machine scheduling problem with convex resource dependent processing times, has been widely studied in the literature [13][14][15][16][17][18][19][20][21] due to the wide applicability of the convex resource consumption function and its tness for many real problems [22]. However, almost all the existing studies on the problem consider only one resource allocation, and there are very few studies on multiple resources.…”

Section: Introductionmentioning

confidence: 99%

Single machine scheduling problem with convex multi-resource dependent processing times and job deadlines

Ziaee

2017

Scientia Iranica

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Abstract. In this paper, the single-machine scheduling problem with convex multiresource dependent processing times, subject to meeting job deadlines, is considered. The objective is to minimize the total cost, including the resource allocation costs and the xed costs. We assume that the actual processing time of each job (task) is a function of the amount of resources allocated. Therefore, the decision variables of the model are: (1) resources allocated to the jobs; (2) total consumed resources; (3) processing times of the jobs; (4) start/completion times of the jobs. We reformulate and solve the problem using a posynomial geometric programming model. In the proposed exact solution method based on the geometric programming, the original problem of any size is reduced to a two-variable unconstrainted optimization problem, which can be easily solved by a simple grid search.

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“…Most of the existing studies assumed linear processing or compression cost functions. A nonlinear relation between processing time and used resource is considered by Shabtay and Kaspi [3]. They deal with the problem of minimizing total weighted completion time on a single machine under a maximal resource constraint where processing time of each job is a nonlinear function of allocated resource to it.…”

Section: Introductionmentioning

confidence: 99%

Scheduling parallel CNC machines with time/cost trade-off considerations

Gürel

Aktürk

2007

Computers & Operations Research

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When the processing times of jobs are controllable, selected processing times affect both the manufacturing cost and the scheduling performance. A well-known example for such a case that this paper specifically deals with is the turning operation on a CNC machine. Manufacturing cost of a turning operation is a nonlinear convex function of its processing time. We also know that scheduling decisions are quite sensitive to the processing times. Therefore, this paper considers minimizing total manufacturing cost (F 1 ) and total completion time (F 2 ) objectives simultaneously on identical parallel CNC turning machines. Since decreasing processing time of a job increases its manufacturing cost, we cannot minimize both objectives at the same time, so the problem is to generate non-dominated solutions. We consider the problem of minimizing F 1 subject to a given F 2 level and give an effective formulation for the problem. For this problem, we prove some optimality properties which facilitated designing an efficient heuristic algorithm to generate approximate non-dominated solutions. Computational results show that proposed algorithm performs almost equal with the GAMS/MINOS commercial solver although it spends much less computation time. ᭧

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Minimizing the total weighted flow time in a single machine with controllable processing times

Cited by 73 publications

References 12 publications

Resource Management in Machine Scheduling Problems: A Survey

Resource Management in Machine Scheduling Problems: A Survey

Single machine scheduling problem with convex multi-resource dependent processing times and job deadlines

Scheduling parallel CNC machines with time/cost trade-off considerations

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