A mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints

•A generic model is proposed for minimizing the number of late jobs on one machine.•Machine availability constraints, non-resumable and resumable jobs are considered.•An efficient mixed integer linear program is described as well as improvements.•Most 500-job instances can be solved to optimality wi...

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Bibliographic Details
Published inEuropean journal of operational research Vol. 235; no. 3; pp. 540 - 552
Main Author Detienne, Boris
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 16.06.2014
Elsevier Sequoia S.A
Elsevier
Subjects
Availability
Availability constraints
Computer Science
Exact method
Integer programming
Knapsack problem
Late jobs
Linear programming
Mathematical models
Mathematics
Mixed integer
Modeling
Numerical analysis
Operational research
Operations Research
Optimization
Optimization and Control
Production scheduling
Scheduling
Studies
Integer programming
Scheduling
Availability constraints
Late jobs
Modeling
Exact method
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Summary:•A generic model is proposed for minimizing the number of late jobs on one machine.•Machine availability constraints, non-resumable and resumable jobs are considered.•An efficient mixed integer linear program is described as well as improvements.•Most 500-job instances can be solved to optimality within 1hour. This study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized. These problems can be modeled as a more general job selection problem. Cases with resumable, non-resumable, and semi-resumable jobs as well as cases without availability constraints are investigated. The proposed efficient mixed integer linear programming approach includes possible improvements to the model, notably specialized lifted knapsack cover cuts. The method proves to be competitive compared with existing dedicated methods: numerical experiments on randomly generated instances show that all 350-job instances of the test bed are closed for the well-known problem 1|ri|∑wiUi. For all investigated problem types, 98.4% of 500-job instances can be solved to optimality within 1hour.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2013.10.052