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

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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.

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Authors
  1. Francesco Maffioli
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  2. Anna Sciomachen
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Maffioli, F., Sciomachen, A. A mixed-integer model for solving ordering problems with side constraints. Annals of Operations Research 69, 277–297 (1997). https://doi.org/10.1023/A:1018989130169

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