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A note on ow-based formulations for solving resource constrained scheduling problems.

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Title: A note on ow-based formulations for solving resource constrained scheduling problems.
Authors: Terblanche, S. E.1 fanie.terblanche@nwu.ac.za, Van Vuuren, J. H.2 vuuren@sun.ac.za
Source: Orion. 2017, Vol. 33 Issue 1, p21-34. 14p.
Subjects: Mixed integer linear programming, Mathematical inequalities, Computer scheduling, Graph theory, Computational complexity
Abstract: The resource constrained scheduling problem involves the scheduling of a number of activities over time, where each activity consumes one or more resources per time period. For a feasible solution to exist, the total resource consumption per time period must not exceed the available resources. In addition, the order in which activities may be scheduled is determined by a precedence graph. In this paper, valid inequalities proposed for the resource flow-based formulation in previous studies are investigated to determine what effect they may have on computing times. It is shown empirically that improved computing times may be obtained if these valid inequalities are, in fact, omitted from the resource ow-based formulation. In addition, a heuristic is proposed for the generation of initial starting solutions and for estimating the extent of the scheduling horizon which, in turn, is required to calculate the latest starting times of activities. The computational results are based on well-known problem test instances as well as new randomly generated problem instances. [ABSTRACT FROM AUTHOR]
Copyright of Orion is the property of Operations Research Society of South Africa and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="JN" term="%22Orion%22">Orion</searchLink>. 2017, Vol. 33 Issue 1, p21-34. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+inequalities%22">Mathematical inequalities</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+scheduling%22">Computer scheduling</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Computational+complexity%22">Computational complexity</searchLink>
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  Data: The resource constrained scheduling problem involves the scheduling of a number of activities over time, where each activity consumes one or more resources per time period. For a feasible solution to exist, the total resource consumption per time period must not exceed the available resources. In addition, the order in which activities may be scheduled is determined by a precedence graph. In this paper, valid inequalities proposed for the resource flow-based formulation in previous studies are investigated to determine what effect they may have on computing times. It is shown empirically that improved computing times may be obtained if these valid inequalities are, in fact, omitted from the resource ow-based formulation. In addition, a heuristic is proposed for the generation of initial starting solutions and for estimating the extent of the scheduling horizon which, in turn, is required to calculate the latest starting times of activities. The computational results are based on well-known problem test instances as well as new randomly generated problem instances. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Orion is the property of Operations Research Society of South Africa and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Mixed integer linear programming
        Type: general
      – SubjectFull: Mathematical inequalities
        Type: general
      – SubjectFull: Computer scheduling
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      – SubjectFull: Graph theory
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      – SubjectFull: Computational complexity
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