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On scheduling a single machine to minimize a piecewise linear objective function: A compact MIP formulation

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  • Philippe Baptiste
  • Ruslan Sadykov

Abstract

We study the scheduling situation in which a set of jobs subjected to release dates and deadlines are to be performed on a single machine. The objective is to minimize a piecewise linear objective function ∑jFj where Fj(Cj) corresponds to the cost of the completion of job j at time Cj. This class of function is very large and thus interesting both from a theoretical and practical point of view: It can be used to model total (weighted) completion time, total (weighted) tardiness, earliness and tardiness, etc. We introduce a new Mixed Integer Program (MIP) based on time interval decomposition. Our MIP is closely related to the well‐known time‐indexed MIP formulation but uses much less variables and constraints. Experiments on academic benchmarks as well as on real‐life industrial problems show that our generic MIP formulation is efficient. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

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  • Philippe Baptiste & Ruslan Sadykov, 2009. "On scheduling a single machine to minimize a piecewise linear objective function: A compact MIP formulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 487-502, September.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:6:p:487-502
    DOI: 10.1002/nav.20352
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    2. Detienne, Boris, 2014. "A mixed integer linear programming approach to minimize the number of late jobs with and without machine availability constraints," European Journal of Operational Research, Elsevier, vol. 235(3), pages 540-552.
    3. Davari, Morteza & Ranjbar, Mohammad & De Causmaecker, Patrick & Leus, Roel, 2020. "Minimizing makespan on a single machine with release dates and inventory constraints," European Journal of Operational Research, Elsevier, vol. 286(1), pages 115-128.

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