On relaxing the integrality of the allocation variables of the reliability fixed-charge location problem
| Autor: | Jose L. Sainz-Pardo, Mercedes Landete, Juan F. Monge, Javier Alcaraz |
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| Rok vydání: | 2016 |
| Předmět: |
Mathematical optimization
021103 operations research Control and Optimization Applied Mathematics Reliability (computer networking) 0211 other engineering and technologies Binary number 02 engineering and technology Management Science and Operations Research Resolution (logic) Computer Science Applications Constraint (information theory) 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Relaxation (approximation) Set (psychology) Value (mathematics) Integer programming Mathematics |
| Zdroj: | Journal of Global Optimization. 67:787-804 |
| ISSN: | 1573-2916 0925-5001 |
| Popis: | The aim of the reliability fixed-charge location problem is to find robust solutions to the fixed-charge location problem when some facilities might fail with probability q. In this paper we analyze for which allocation variables in the reliability fixed-charge location problem formulation the integrality constraint can be relaxed so that the optimal value matches the optimal value of the binary problem. We prove that we can relax the integrality of all the allocation variables associated to non-failable facilities or of all the allocation variables associated to failable facilities but not of both simultaneously. We also demonstrate that we can relax the integrality of all the allocation variables whenever a family of valid inequalities is added to the set of constraints or whenever the parameters of the problem satisfy certain conditions. Finally, when solving the instances in a data set we discuss which relaxation or which modification of the problem works better in terms of resolution time and we illustrate that relaxing the integrality of the allocation variables inappropriately can alter the objective value considerably. |
| Databáze: | OpenAIRE |
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