A fresh view on the Discrete Ordered Median Problem based on partial monotonicity
This paper presents new results for the Discrete Ordered Median Problem (DOMP). It exploits properties of k-sum optimization to derive specific formulations for the monotone DOMP (MDOMP), that arises when the λ weights are non-decreasing monotone, and new formulations for the general non-monotone DO...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/162801 |
| Acceso en línea: | https://hdl.handle.net/11441/162801 https://doi.org/10.1016/j.ejor.2020.04.023 |
| Access Level: | acceso abierto |
| Palabra clave: | Location Combinatorial optimization Logistics Ordered Median Problem |
| Sumario: | This paper presents new results for the Discrete Ordered Median Problem (DOMP). It exploits properties of k-sum optimization to derive specific formulations for the monotone DOMP (MDOMP), that arises when the λ weights are non-decreasing monotone, and new formulations for the general non-monotone DOMP. The main idea in our approach is to express ordered weighted averages as telescopic sums whose terms are k-sums, with positive and negative coefficients. Formulations of k-sums with positive coefficients derive from the linear programming representations obtained by Ogryczack and Tamir (2003) and Blanco, Ali, and Puerto (2014). Valid formulations for k-sums with negative coefficients are more elaborated and we present 4 different approaches, all of them based on mixed integer programming formulations. An extensive computational experience based on a collection of well-known instances shows the usefulness of the new formulations to solve difficult problems such as trimmed and anti-trimmed mean. |
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