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Dynamic location problem under uncertainty with a regret‐based measure of robustness
Author(s) -
Marques Maria do Céu,
Dias Joana Matos
Publication year - 2018
Publication title -
international transactions in operational research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.032
H-Index - 52
eISSN - 1475-3995
pISSN - 0969-6016
DOI - 10.1111/itor.12183
Subject(s) - regret , subgradient method , mathematical optimization , robustness (evolution) , facility location problem , measure (data warehouse) , robust optimization , computer science , integer programming , bounded function , stochastic programming , dynamic programming , set (abstract data type) , relaxation (psychology) , mathematics , psychology , mathematical analysis , biochemistry , chemistry , social psychology , database , machine learning , gene , programming language
In this paper, we present a dynamic uncapacitated facility location problem that considers uncertainty in fixed and assignment costs as well as in the sets of potential facility locations and possible customers. Uncertainty is represented via a set of scenarios. Our aim is to minimize the expected total cost, explicitly considering regret. Regret is understood as a measure, for each scenario, of the loss incurred for not choosing that scenario's optimal solution if that scenario indeed occurred. We guarantee that the regret for each scenario is always upper bounded. We present a mixed integer programming model for the problem and we propose a solution approach based on Lagrangean relaxation integrating a local neighborhood search and a subgradient algorithm to update Lagrangean multipliers. The problem and the solutions obtained are first analyzed through the use of illustrative examples. Computational results over sets of randomly generated test problems are also provided.