Scheduling identical parallel machines to minimize total weighted completion time

Belouadah, Hocine; Potts, Chris N.

doi:10.1016/0166-218x(92)00176-m

Cited by 47 publications

(23 citation statements)

References 18 publications

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“…4, where the processing times are taken uniformly from the interval [5,15] or [35,45] and the weights are determined by choosing the weight to processing time ratio uniformly from the interval [0.8, 1.2]. Since we were not able to receive any data-sets or codes of the existing exact solution methods of Belouadah and Potts (1994) and van den Akker et al (1999), we calculated for a set of smaller instances optimal solutions via some straight forward enumeration method. Additionally, we use a lower bounding method described by Eastman et al (1964) (abbreviated with LB).…”

Section: Computational Resultsmentioning

confidence: 99%

“…in O(n n j =1 p j ) time and space. Computational testing indicates, that the algorithm is capable of solving instances from Belouadah and Potts (1994) in one fourth of the time that their method needs. Moreover, because the algorithm performs better with increasing m, the column generation approach is able to solve instances of size up to n = 100 jobs and m = n/10 machines in at most an hour on a HP 9000/710 computer, which is about twice as fast as the CDC 7600.…”

Section: Introductionmentioning

confidence: 99%

“…For the problem P w j C j Belouadah and Potts (1994) develop a branch and bound algorithm. For receiving lower bounds, they use Lagrangian relaxation on the constraint, that at most m jobs may be processed during any unit time interval.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Matching based very large-scale neighborhoods for parallel machine scheduling

Brueggemann

Hurink

2010

J Heuristics

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In this paper we study very large-scale neighborhoods for the minimum total weighted completion time problem on parallel machines, which is known to be strongly N P-hard. We develop two different ideas leading to very large-scale neighborhoods in which the best improving neighbor can be determined by calculating a weighted matching. The first neighborhood is introduced in a general fashion using combined operations of a basic neighborhood. Several examples for basic neighborhoods are given. The second approach is based on a partitioning of the job sets on the machines and a reassignment of them. In a computational study we evaluate the possibilities and the limitations of the presented very large-scale neighborhoods.

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Section: Computational Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Matching based very large-scale neighborhoods for parallel machine scheduling

Brueggemann

Hurink

2010

J Heuristics

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“…However, an algorithm with such high complexity can only solve problems of small size. Belouadah and Potts [2] use a Lagrangian relaxation based branch and bound algorithm to solve the problem Pm|| w j C j with up to 20 jobs and 5 machines or 30 jobs and 4 machines. By a column generation approach, Chen and Powell [6] and van den Akker, Hoogeveen, and van de Velde [26] are able to solve this same problem with a much larger size (100 jobs and 20 machines).…”

Section: Introductionmentioning

confidence: 99%

Scheduling jobs and maintenance activities on parallel machines

Lee

Chen

2000

Naval Research Logistics

182

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“…Interestingly, all exact algorithms for TWCT in the parallel machine environment are limited to identical machines up until 1999. These include the branch-and-bound (B&B) algorithms of Elmaghraby and Park (1974), Barnes and Brennan (1977), Sarin et al (1988), Belouadah and Potts (1994), and the dynamic programming techniques of Lawler and Moore (1969), Lee and Uzsoy (1992). Unsurprisingly, these papers have very limited success in solving instances of any meaningful size -clearly partly due to the lack of powerful computers back then.…”

Section: Introductionmentioning

confidence: 99%

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

Bülbül

źEn

2016

J Sched

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The plethora of research on NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds.

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Scheduling identical parallel machines to minimize total weighted completion time

Cited by 47 publications

References 18 publications

Matching based very large-scale neighborhoods for parallel machine scheduling

Matching based very large-scale neighborhoods for parallel machine scheduling

Scheduling jobs and maintenance activities on parallel machines

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

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