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Efficient Models, Formulations and Algorithms for Some Variants of Fixed Interval Scheduling Problems

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Data and Decision Sciences in Action

Part of the book series: Lecture Notes in Management and Industrial Engineering ((LNMIE))

Abstract

The fixed interval scheduling problem—also known as the personnel task scheduling problem—optimizes the allocation of available resources (workers, machines, or shifts) to execute a given set of jobs or tasks. We introduce a new approach to solve this problem by decomposing it into separate subproblems. We establish the mathematical basis for optimality of such a decomposition and thereafter develop several new techniques (exact and heuristic) to solve the resulting subproblems. An extensive computational analysis of the new techniques proves the efficacy of these approaches when compared to other established techniques in the literature. Specifically, a hybrid integer programming formulation presented in this paper solves several larger problem instances that were not amenable to exact techniques previously. In addition, a constructive heuristic approach (based on quantification metrics for tasks and resources) gives solutions equal to the optimal. We demonstrate that our decomposition approach is applicable for several important variants within the topic of fixed interval scheduling including tactical fixed interval scheduling problem and operational fixed interval scheduling problem.

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Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Monash University, Clayton, VIC, 3800, Australia

    D. Niraj Ramesh & Mohan Krishnamoorthy

  2. School of Mathematical Sciences, Monash University, Clayton, VIC, 3800, Australia

    Andreas T. Ernst

Authors
  1. D. Niraj Ramesh
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  2. Mohan Krishnamoorthy
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  3. Andreas T. Ernst
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Corresponding author

Correspondence to Mohan Krishnamoorthy .

Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Canberra, Aust Capital Terr, Australia

    Ruhul Sarker

  2. School of Engineering and Information Technology, University of New South Wales, Canberra, Aust Capital Terr, Australia

    Hussein A. Abbass

  3. Data 61, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Melbourne, Victoria, Australia

    Simon Dunstall

  4. Data 61, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Melbourne, Victoria, Australia

    Philip Kilby

  5. Strategic Capability Analysis Department, Defence Science and Technology Group, Canberra, Aust Capital Terr, Australia

    Richard Davis

  6. Department of Defence, War Research Centre, Canberra, Aust Capital Terr, Australia

    Leon Young

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Niraj Ramesh, D., Krishnamoorthy, M., Ernst, A.T. (2018). Efficient Models, Formulations and Algorithms for Some Variants of Fixed Interval Scheduling Problems. In: Sarker, R., Abbass, H., Dunstall, S., Kilby, P., Davis, R., Young, L. (eds) Data and Decision Sciences in Action. Lecture Notes in Management and Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-55914-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-55914-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55913-1

  • Online ISBN: 978-3-319-55914-8

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