Scheduling with processing set restrictions: A literature update

Leung, Joseph Y.-T.; Li, Chung‐Lun

doi:10.1016/j.ijpe.2014.09.038

Cited by 43 publications

(18 citation statements)

References 82 publications

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“…They consider the problem with equal processing times Shabtay, Karhi, and Oron (2015) present an algorithm allowing also the rejection of jobs. Recently, Leung and Li (2016) provide an expository update of this kind of problems, as according to them there has been a significant increase interest…”

Section: Aq5mentioning

confidence: 99%

A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs

Mateo

Teghem

Tuyttens

2017

International Journal of Production Research

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The scheduling of parallel machines is a well-known problem in many companies. Nevertheless, not always all the jobs can be manufactured in any machine and the eligibility appears. Based on a real-life problem, we present a model which has m parallel machines with different level of quality from the highest level for the first machine till the lowest level for the last 10 machine. The set of jobs to be scheduled on these m parallel machines are also distributed among these m levels: one job from a level can be manufactured in a machine of the same or higher level but a penalty, depending on the level, appears when a job is manufactured in a machine different from the highest level i.e. different from the first machine. Besides, there are release dates and delivery times associated to each job. The tackled problem is bi-objective with the criteria: minimisation of the final date -i.e. the maximum for all the jobs of their completion time plus the delivery time -and the minimisation 15 of the total penalty generated by the jobs. In a first step, we analyse the sub-problem of minimisation of the final date on a single machine for jobs with release dates and delivery times. Four heuristics and an improvement algorithm are proposed and compared on didactic examples and on a large set of instances. In a second step an algorithm is proposed to approximate the set of efficient solutions and the Pareto front of the bi-objective problem. This algorithm contains two phases: the first is a depth search phase and the second is a backtracking phase. The procedure is illustrated in detail on an instance with 20 20 jobs and 3 machines. Then extensive numerical experiments are realised on two different sets of instances, with 20, 30 and 50 jobs, 3 or 4 machines and various values of penalties. Except for the case of 50 jobs, the results are compared with the exact Pareto front.

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Section: Aq5mentioning

confidence: 99%

A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs

Mateo

Teghem

Tuyttens

2017

International Journal of Production Research

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“…One special case of processing set restrictions, that has been studied very thoroughly, is the case of nested processing sets . In this case, one and only one of the following four conditions must hold for any two jobs i and j :

\begin{matrix} left \\ (i) M_{i} = M_{j}, \\ (ii) M_{i} \subset M_{j}, \\ (iii) M_{i} \supset M_{j}, \\ (iv) M_{i} and M_{j} are disjoint . \end{matrix}

Scheduling problems with machine eligibility constraints and processing set restrictions are of interest to industrial engineers, operations researchers as well as computer scientists, and have many applications in practice (see, e.g., and the recent surveys ). In this article, we consider the problem

P m | M_{j} (nested) | \sum w_{j} T_{j}

.…”

Section: Introductionmentioning

confidence: 99%

“…In the past, researchers have mainly focused on the problems

P m | M_{j} (nested) | C_{\max}

and

P m | M_{j} (nested) | \sum C_{j}

, where

C_{\max}

denotes the makespan and

\sum C_{j}

denotes the total completion time, see Ou et al , Huo and Leung and Muratore et al . Leung and Li and provided extensive surveys of the literature. However, little research has considered the performance criteria such as the total weighted tardiness.…”

Section: Introductionmentioning

confidence: 99%

Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness

Pinedo

Wan

2017

Naval Research Logistics

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We study a parallel machine scheduling problem, where a job j can only be processed on a specific subset of machines Mj, and the Mj subsets of the n jobs are nested. We develop a two‐phase heuristic for minimizing the total weighted tardiness subject to the machine eligibility constraints. In the first phase, we compute the factors and statistics that characterize a problem instance. In the second phase, we propose a new composite dispatching rule, the Apparent Tardiness Cost with Flexibility considerations (ATCF) rule, which is governed by several scaling parameters of which the values are determined by the factors obtained in the first phase. The ATCF rule is a generalization of the well‐known ATC rule which is very widely used in practice. We further discuss how to improve the dispatching rule using some simple but powerful properties without requiring additional computation time, and the improvement is quite satisfactory. We apply the Sequential Uniform Design Method to design our experiments and conduct an extensive computational study, and we perform tests on the performance of the ATCF rule using a real data set from a large hospital in China. We further compare its performance with that of the classical ATC rule. We also compare the schedules improved by the ATCF rule with what we believe are Near Optimal schedules generated by a general search procedure. The computational results show that especially with a low due date tightness, the ATCF rule performs significantly better than the well‐known ATC rule generating much improved schedules that are close to the Near Optimal schedules. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 249–267, 2017

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“…Each job j has to be processed by a machine that belongs to a specific subset j  of the m machines called its eligible set. See [3] for a recent survey on machine scheduling with processing set restrictions. The survey covers five types of processing set restrictions, namely inclusive, nested, interval, tree-hierarchical, and arbitrary.…”

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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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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Scheduling with processing set restrictions: A literature update

Cited by 43 publications

References 82 publications

A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs

A bi-objective parallel machine problem with eligibility, release dates and delivery times of the jobs

Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness

A Simple Algorithm for Scheduling Jobs with GoS Levels

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