Stochastic facility location problem in a competitive situation: A game theory model for emergency financial services

Abstract

Facility location problems under conditions of uncertainty involve various situations, such as industrial plants, warehouses, distribution centers, and emergency services (ambulances, police cars). Because of this relevant matter, researchers have developed many mathematical optimization models that aim to establish a balance between costs and the quality of the services provided over recent decades. By and large, these proposals consider stochastic characteristics associated with demand uncertainty and the facilities’ availability. Since there is a lack of studies examining emergency financial services, we think of managing this kind of service in a competitive situation combining Game Theory and computer simulation. In addition to the usual stochastic conditions, this study introduces the use of a Nash equilibrium model that also incorporates uncertainties related to the actions of competitors applied to a dispute between two insurers as to where to locate their home insurance assistance bases. The focal point concept combined the results of a non-zero-sum game with those of the stochastic location model to define an unconventional strategy for the analyzed situation. The developed mathematical model provided more realistic location strategies compared to those obtained using traditional location models.