# A Mixed Integer Linear Programming approach to minimize the number of late jobs with and without machine availability constraints

* Corresponding author
2 Realopt - Reformulations based algorithms for Combinatorial Optimization
LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This study investigates scheduling problems that occur when the weighted number of late jobs that are subject to deterministic machine availability constraints have to be minimized. These problems can be modeled as a more general job selection problem. Cases with resumable, non-resumable, and semi-resumable jobs as well as cases without availability constraints are investigated. The proposed efficient mixed integer linear programming approach includes possible improvements to the model, notably specialized lifted knapsack cover cuts. The method proves to be competitive compared with existing dedicated methods: numerical experiments on randomly generated instances show that all 350-job instances of the test bed are closed for the well-known problem $1|r_i|\sum w_iU_i$. For all investigated problem types, 98.4% of $500$-job instances can be solved to optimality within one hour.
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Document type :
Journal articles
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https://hal.archives-ouvertes.fr/hal-00880908
Contributor : Boris Detienne <>
Submitted on : Thursday, November 7, 2013 - 9:47:00 AM
Last modification on : Monday, November 26, 2018 - 4:12:05 PM

### Citation

Boris Detienne. 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, 2014, 235 (3), pp.540--552. ⟨10.1016/j.ejor.2013.10.052⟩. ⟨hal-00880908⟩

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