Variable Neighborhood Descent for Finding the Threshold Stability Radius in the Facility Location and Discriminatory Pricing Problem

A new threshold stability problem in the context of facility location and discriminatorypricing is considered. In the statement of facility location and pricing problem, the companydecides to open facilities and assign prices to each customer at each facility. The implementationof discriminatory pricing leads to a scenario where each customer is compelled to expend themaximum amount of their available financial resources, thereby ensuring the maximum revenuefor the company. In the threshold stability problem, the available financial resources or budget ofeach consumer is a parameter with a known expected value. The objective is to maximize thedeviation of the parameters from the expected value, provided that the company’s income remainsabove a given threshold.

An algorithm based on variable neighborhood descent (VND) is proposed to solvethe threshold stability problem. Numerical investigation of the algorithm is carried out on knowninstances and randomly generated ones. Various ways of constructing the starting facility locationand different criteria for comparing the location vectors are analyzed.