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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. Nicola Bianchessi & Michael Drexl & Stefan Irnich, 2019. "The Split Delivery Vehicle Routing Problem with Time Windows and Customer Inconvenience Constraints," Transportation Science, INFORMS, vol. 53(4), pages 1067-1084, March.
    2. 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.
    3. Cacchiani, Valentina & Contreras-Bolton, Carlos & Toth, Paolo, 2020. "Models and algorithms for the Traveling Salesman Problem with Time-dependent Service times," European Journal of Operational Research, Elsevier, vol. 283(3), pages 825-843.
    4. Markus Sinnl, 2021. "Mixed-integer programming approaches for the time-constrained maximal covering routing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 497-542, June.
    5. 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.
    6. 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.
    7. Subramanyam, Anirudh & Gounaris, Chrysanthos E., 2016. "A branch-and-cut framework for the consistent traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 248(2), pages 384-395.
    8. Michael Drexl, 2012. "Branch-and-Cut Algorithms for the Vehicle Routing Problem with Trailers and Transshipments," Working Papers 1210, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    9. Tilk, Christian & Drexl, Michael & Irnich, Stefan, 2019. "Nested branch-and-price-and-cut for vehicle routing problems with multiple resource interdependencies," European Journal of Operational Research, Elsevier, vol. 276(2), pages 549-565.
    10. 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.
    11. Wei Zhang & Kai Wang & Shuaian Wang & Gilbert Laporte, 2020. "Clustered coverage orienteering problem of unmanned surface vehicles for water sampling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(5), pages 353-367, August.
    12. Nicola Bianchessi & Stefan Irnich, 2019. "Branch-and-Cut for the Split Delivery Vehicle Routing Problem with Time Windows," Transportation Science, INFORMS, vol. 53(2), pages 442-462, March.

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