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

Sophie N. Parragh (), Fabien Tricoire () and Walter J. Gutjahr ()
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Sophie N. Parragh: Johannes Kepler University Linz
Fabien Tricoire: Vienna University of Economics and Business
Walter J. Gutjahr: University of Vienna

OR Spectrum: Quantitative Approaches in Management, 2022, vol. 44, issue 2, No 5, 419-459

Abstract: 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-Benders-cut approach to a straight-forward branch-and-bound implementation based on the deterministic equivalent formulation.

Keywords: Bi-objective optimization; Stochastic optimization; Branch and bound; Benders decomposition; L-shaped method; Pareto efficiency (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00291-020-00616-7

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