In this paper, there are two competitors in a planar market. The first competitor, called, the leader, opens p new facilities. After that, the second competitor, the follower, reacts to the leader's action and opens r new facilities. The leader and the follower have got some facilities in advance in this market. The optimal locations for leader and follower are chosen among predefined candidate locations. In this paper, it is assumed that the demand is inelastic. Considering the huff model, customers share their demand among all facilities, probabilistically. The leader's objective function is the maximization of its market share after the follower's new facilities entry. The leader and follower problems are solved via an exact solution method.

This paper presents a bi-objective Competitive facility location model for congested systems in which the entering facilities compete with the competitors’ facilities for capturing the market share. In the proposed model, customers can choose which facility to patronize based on the gravity function that depends on both the quality of service provider and the travel time to facilities. The proposed model attempts to simultaneously maximize the captured demand from each facility and minimize the total waiting time in the system. Two multi-objective evolutionary algorithms, involving a multi-objective harmony search algorithm (MOHS) and a non-dominated sorting genetic algorithm-II (NSGA-II), are designed to solve the proposed model. The performance of solution procedures are compared on the basis of different performance metrics including generational distance, spacing metric, diversification metric, and number of non-dominated solution. The computational results based on different test problems show that in general MOHS outperforms NSGA-II.

facility location problem is a branch of operations research and computational geometry. It covers the best allocation of facilities to minimize transportation costs by considering the factors involved (e. g., avoiding the placement of dangerous materials near the premises and the facilities of competitors). Given the unique customer characteristics and the fi, erce market competition of business-to-consumer e-commerce, the expected value model and chance-constrained model for uncertain facility location problems were constructed. Owing to the intricacies of the Competitive market, supply capacity, delivery cost, and customer demand were assumed as uncertain variables. The deterministic equivalent forms of the models were discussed using the inverse uncertainty distribution method. A hybrid algorithm was proposed to solve these models. Some numerical experiments were used to verify the effectiveness of the proposed models and method.

Network location models comprise one of the main categories of location models. These models have various applications in regional and urban planning as well as in transportation, distribution, and energy management. In a network location problem, nodes represent demand points and candidate locations to locate the facilities. If the links network is unchangeably determined, the problem will be an FLP (facility location problem). However, if links can be added to the network at a reasonable cost, the problem will then be a combination of facility location and NDP (Network Design problem). In previous studies, capacity of facilities was considered to be a constraint while capacity of links was not considered at all. The proposed MIP model considers capacity of facilities and links as decision variables. This approach increases the utilization of facilities and links, and prevents the construction of links and facility locations with low utilization. Furthermore, facility location cost (link construction cost) in the proposed model is supposed to be a function of the associated facility (link) capacity. Computational experiments as well as sensitivity analyses performed indicate the efficiency of the model.

In an uncapacitated facility location problem, the aim is to find the best locations for facilities on a specific network in order to service the existing clients at the maximum total profit or minimum cost. In this paper, we investigate the uncapacitated facility location problem where the profits of the demands and the opening costs of the facilities are uncertain values. We first present the belief degree-constrained, expected value and tail value at risk programming models of the problem under investigation. Then, we apply the concepts of the uncertainty theory to transform these uncertain programs into the corresponding deterministic optimization models. The efficient algorithms are provided for deriving the optimal solutions the problem under investigation.