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Mixed integer formulations using natural variables for single machine scheduling around a common due date

Anne-Elisabeth Falq 1 Pierre Fouilhoux 1 Safia Kedad-Sidhoum 2 
2 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
Abstract : While almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims at minimizing the weighted sum of earliness tardiness penalties around a common due-date. Using natural variables, we provide one compact formulation for the unrestrictive case and, for the general case, a non-compact formulation based on non-overlapping inequalities. We show that the separation problem related to the latter formulation is solved polynomially. In this formulation, solutions are only encoded by extreme points. We establish a theoretical framework to show the validity of such a formulation using non-overlapping inequalities, which could be used for other scheduling problems. A Branch-and-Cut algorithm together with an experimental analysis are proposed to assess the practical relevance of this mixed integer programming based methods.
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Submitted on : Monday, February 15, 2021 - 9:27:47 AM
Last modification on : Wednesday, September 28, 2022 - 5:57:27 AM


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Anne-Elisabeth Falq, Pierre Fouilhoux, Safia Kedad-Sidhoum. Mixed integer formulations using natural variables for single machine scheduling around a common due date. Discrete Applied Mathematics, 2021, 290, pp.36-59. ⟨10.1016/j.dam.2020.08.033⟩. ⟨hal-02074488v2⟩



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