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A mixed-integer model for solving ordering problems with side constraints

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  • Francesco Maffioli
  • Anna Sciomachen

Abstract

We present an exact approach for solving the Sequential Ordering Problem (SOP). In this problem, a set of jobs has to be processed on a single machine; a time window (deadline - release date) is associated with each job, and precedence relationships between jobs are given. Moreover, a setup time (possibly zero) before processing a job is assigned. The prob-lem consists in finding an ordering of the jobs such that the completion time of the job sequenced last is minimized. Starting from a 0-1 formulation of the problem, we translate the model into a linear Mixed Integer Program (MIP) problem by adding some variables representing the idle time of the machine, in such a way that both the subtour elimination constraints and the due forcing constraints are implicitly satisfied. Some computational experience is reported along with the analysis of a simple case study. The main goal of this work is to assess the suitability of the mathematical models presented with respect to avail-able MIP software like OSL. Copyright Kluwer Academic Publishers 1997

Suggested Citation

  • Francesco Maffioli & Anna Sciomachen, 1997. "A mixed-integer model for solving ordering problems with side constraints," Annals of Operations Research, Springer, vol. 69(0), pages 277-297, January.
  • Handle: RePEc:spr:annopr:v:69:y:1997:i:0:p:277-297:10.1023/a:1018989130169
    DOI: 10.1023/A:1018989130169
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    Cited by:

    1. Fügenschuh, Armin, 2009. "Solving a school bus scheduling problem with integer programming," European Journal of Operational Research, Elsevier, vol. 193(3), pages 867-884, March.
    2. Nicola Bianchessi & Michael Drexl & Stefan Irnich, 2017. "The Split Delivery Vehicle Routing Problem with Time Windows and Customer Inconvenience Constraints," Working Papers 1706, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    3. Christian Tilk & Michael Drexl & Stefan Irnich, 2018. "Nested Branch-and-Price-and-Cut for Vehicle Routing Problems with Multiple Resource Interdependencies," Working Papers 1801, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    4. Nicola Bianchessi & Stefan Irnich, 2016. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Working Papers 1620, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.

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