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

Abstract

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

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