A Bilevel formulation and Benders Decomposition for the Cooperative Maximum Capture Facility Location

C. Domínguez Sánchez, R. Gázquez, J. M. Morales, S. Pineda

In the Cooperative Maximum Capture Facility Location problem (CMCFL), we generalize the Maximum Capture Facility Location problem assuming that the facilities of the decision maker act cooperatively to increase the customers’ utility over the company. We propose a utility maximization rule between the captured utility of the decision maker and the opt-out utility of an existing competitor. Furthermore, we model the captured utility by means of an Ordered Median function (OMf) of the partial utilities of newly open facilities, i.e., as an aggregation of ordered partial utilities. We introduce a multiperiod non-linear bilevel formulation for the CMCFL with an embedded assignment problem characterizing the captured utilities. For this model, we present an effective approach based on Benders' decomposition. Extensive computational experiments show the effectiveness of our approach.

Keywords: Maximum Capture, Competitive Facility Location, Random Utility Maximization, Benders Decomposition, Mixed-Integer Linear Problem

GT12.GELOCA1 Invited Session
November 10, 2023  9:30 AM
CC1: Audience

C. Valverde, J. Puerto Albandoz

F. Temprano Garcia, D. Ponce López, J. Puerto Albandoz

G. González Domínguez, J. Puerto Albandoz, V. Blanco Izquierdo

B. Cobeña, I. Contreras, L. I. Martínez Merino, A. M. Rodríguez Chía