A discrete competitive facility location model with proportional and binary rules sequentially applied

The paper is focused on discrete competitive facility location problem for an entering firm considering different customer behavior models: for essential goods, customers generally spread their buying power among all facilities within an attraction area, but if there are no facilities nearby, then customers choose a single highly attractive facility outside the attraction area to satisfy their demand. The new facility location model has been proposed considering the proportional customer choice rule for customers with facilities within the attraction area and the binary rule—for customers which facilities are located outside the attraction area. The model has been formulated as a non-linear binary programming problem and a heuristic optimization algorithm has been applied to find the optimal solutions for different instances of the problem using real geographical coordinates and population data of thousands of municipalities in Spain.