Parallel machine scheduling under a grade of service provision

Hwang, Ho Jung; Chang, Soo Y.; Lee, Kangbok

doi:10.1016/s0305-0548(03)00164-3

Cited by 99 publications

(46 citation statements)

References 5 publications

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“…If ( ) l  succeeds at this moment, then for 1, 2, , i m =  , ( ) l  schedules the remaining jobs in i  one by one by the list scheduling algorithm [6]: each is assigned to an eligible machine whose current load is the minimum among all the eligible machines of the job. The way that ( ) l  assigns these jobs is similar to the algorithm presented in [2]. Finally, among all feasible schedules, the algorithm outputs the one with the minimum makespan.…”

Section: The Algorithmmentioning

confidence: 99%

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A Simple Algorithm for Scheduling Jobs with GoS Levels

Xiao¹

2017

Proceedings of the 2017 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology (FMSMT 2017

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Abstract. The problem of scheduling jobs with grade of service (GoS) levels is considered, which is motivated from an application in service industry. Jobs and machines are labeled with GoS levels. If the GoS level of a job is greater than or equal to the GoS level of a machine, then this job can be processed on this machine. The objective is to minimize makespan. A simple and fast 3/2-approximation algorithm is presented.

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Section: The Algorithmmentioning

confidence: 99%

“…In this paper, we combine the techniques used in [2] and [14] to get a 3/2-approximation algorithm with running time ( log ) O nm m for max | | P GoS C . The algorithm has a better approximation ratio than the one in [12].…”

Section: Introductionmentioning

confidence: 99%

A Simple Algorithm for Scheduling Jobs with GoS Levels

Xiao¹

2017

Proceedings of the 2017 5th International Conference on Frontiers of Manufacturing Science and Measuring Technology (FMSMT 2017

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“…Correspondence to: C.-L. Li (lgtclli@polyu.edu.hk) and are said to be nested [8,9]; (ii) processing sets that are not only nested but also include one another, and are called inclusive processing sets [8,13]. It is the latter model that this article focuses on.…”

Section: Introductionmentioning

confidence: 99%

“…Inclusive processing sets also arise in the following scenarios [8,13]: Consider the assignment of computer programs to one of several computer processors with identical speed. Each processor has a memory capacity and each job has a memory requirement.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is well worth exploring for solution methods with better worst-case error bounds. Hwang et al [13] have developed a "lowest grade-longest processing time first" (LG-LPT) algorithm for problem P(J , M). They have proven that their algorithm has a worst-case bound of 5 4 for m = 2 and a worst-case bound of 2 − 1 m−1 for m ≥ 3, and they have shown that these bounds are tight for every m ≥ 2.…”

Section: Introductionmentioning

confidence: 99%

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Scheduling parallel machines with inclusive processing set restrictions

Leung

2008

Naval Research Logistics

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Abstract:We consider the problem of assigning a set of jobs to different parallel machines of the same processing speed, where each job is compatible to only a subset of those machines. The machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. The objective is to minimize the makespan of the schedule. This problem is motivated by industrial applications such as cargo handling by cranes with nonidentical weight capacities, computer processor scheduling with memory constraints, and grades of service provision by parallel servers. We develop an efficient algorithm for this problem with a worst-case performance ratio of 4 3 + , where is a positive constant which may be set arbitrarily close to zero. We also present a polynomial time approximation scheme for this problem, which answers an open question in the literature.

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Scheduling parallel machines with inclusive processing set restrictions and job rejection

Zhong

2016

Naval Research Logistics

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In this article, we study a parallel machine scheduling problem with inclusive processing set restrictions and the option of job rejection. In the problem, each job is compatible to a subset of machines, and machines are linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process (but not conversely). To achieve a tight production due date, some of the jobs might be rejected at certain penalty. We first study the problem of minimizing the makespan of all accepted jobs plus the total penalty cost of all rejected jobs, where we develop a ( 5 3 + ε ) ‐approximation algorithm with a time complexity of O ( n 2 / ε 2 ) . We then study two bicriteria variants of the problem. For the variant problem of minimizing the makespan subject to a given bound on the total rejection cost, we develop a ( 5 3 + ε ) ‐approximation algorithm with a time complexity of O ( n m ε 2 · log P ) . For the variant problem of maximizing the total rejection cost of the accepted jobs subject to a given bound on the makespan, we present a 0.5‐approximation algorithm with a time complexity of O ( n log n ) . © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 667–681, 2017

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Parallel machine scheduling under a grade of service provision

Cited by 99 publications

References 5 publications

A Simple Algorithm for Scheduling Jobs with GoS Levels

A Simple Algorithm for Scheduling Jobs with GoS Levels

Scheduling parallel machines with inclusive processing set restrictions

Scheduling parallel machines with inclusive processing set restrictions and job rejection

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