A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem

Parragh, Sophie N. and Tricoire, Fabien ORCID: https://orcid.org/0000-0002-3700-5134 and Gutjahr, Walter J. (2021) A branch-and-Benders-cut algorithm for a bi-objective stochastic facility location problem. OR Spectrum. ISSN 0171-6468

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Abstract

In many real-world optimization problems, more than one objective plays a role and input parameters are subject to uncertainty. In this paper, motivated by applications in disaster relief and public facility location, we model and solve a bi-objective stochastic facility location problem. The considered objectives are cost and covered demand, where the demand at the different population centers is uncertain but its probability distribution is known. The latter information is used to produce a set of scenarios. In order to solve the underlying optimization problem, we apply a Benders’ type decomposition approach which is known as the L-shaped method for stochastic programming and we embed it into a recently developed branch-and-bound framework for bi-objective integer optimization. We analyze and compare different cut generation schemes and we show how they affect lower bound set computations, so as to identify the best performing approach. Finally, we compare the branch-and-Benderscut approach to a straight-forward branch-and-bound implementation based on the deterministic equivalent formulation.

Item Type:	Article
Additional Information:	Open Access funding provided by Vienna University of Economics and Business (WU).
Keywords:	Bi-objective optimization, Stochastic optimization, Branch and bound, Benders decomposition, L-shaped method, Pareto efficiency
Version of the Document:	Published
Depositing User:	Gertraud Novotny
Date Deposited:	11 Mar 2021 12:27
Last Modified:	25 May 2021 11:03
Related URLs:	Publisher
FIDES Link:	https://bach.wu.ac.at/d/research/results/99916/
URI:	https://epub.wu.ac.at/id/eprint/8039

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