Optimizing Locations and Qualities of Multiple Facilities With Competition via Intelligent Search

We study a new competitive multi-facility location and quality design problem in a continuous space. The facility location and quality design are considered together because of their interdependence. Especially, new entrant facilities compete for customer demands with existing ones and the latter's reactions are taken into account. The goal is to maximize the profit of all new entrant facilities by optimally determining their locations and qualities. For this problem, a probabilistic Huff-like gravity model is adopted to analyze the market share to be captured by new and existing facilities, and then a mathematical programming model is provided based on the market share analysis. Since it is shown to be strongly NP-hard, a new iterative solution framework is first proposed to solve it, where at each iteration, new configurations of facility locations are firstly generated, and then the quality decisions of all facilities are modelled as a competitive decision process by a non-cooperative game. The best qualities for new and existing facilities are determined by their Nash equilibrium. Finally, optimal or near-optimal solutions are calculated. Then based on the proposed solution framework, a particle swarm optimization-based approach is developed. Computational results for randomly generated instances indicate that the devised algorithm is able to find suitable locations and qualities of newly entering facilities in a competitive environment and outperforms favorably a genetic algorithm-based approach.