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We study the existence and determination of Nash equilibria (NE) in location games where firms compete for the market with the aim of profit maximization. Each competing firm locates one facility at one point on a network and customers, which are located at the nodes of the network, distribute their buying power between the firms from which they ge...
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We study a variant of the competitive facility location problem, in which a company is to locate new facilities in a market where competitor’s facilities already exist. We consider the scenario where only a limited number of possible attractiveness levels is available, and the company has to select exactly one level for each open facility. The goal...
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Citations
... This model determines the equilibria location of two competing firms in a Location of competitive facilities linear market. Since then, a large number of studies have been performed to address various CFL challenges such as new entrant firm location, expansion of the already existing firms (Drezner et al., 2018;Fern andez et al., 2019;Shan et al., 2019), location equilibria (Fern andez et al., 2014;Pelegr ın and Pelegr ın, 2017;Gur et al., 2018), cannibalisation and franchisor-franchisee problems (Redondo et al., 2015;Pelegr ın et al., 2016;Aboolian et al., 2021). Few recent articles have also studied competitiveness in the hub and supply chain location problems (Bilir et al., 2017;Lancinskas et al., 2017;Fern andez et al., 2018;Ljubic and Moreno, 2018). ...
Purpose- The research in competitive facility location (CFL) is quite dynamic, both from a
problem formulation and an algorithmic point of view. Research direction has changed
immensely over the years to address various competitive challenges. This study explores CFL
literature to highlight these research trends, important issues and future research opportunities.
Design/methodology/approach- This study utilises the Scopus database to search for related
CFL models and adopts a five-step systematic approach for the review process. The five steps
involve a) Article Identification and keyword selection, b) Selection criteria, c) Literature
review, d) Literature analysis, e) Research studies.
Findings-The paper presents a comprehensive review of CFL modelling efforts from 1981 to
2021 to provide a depth study of the research evolution in this area. The published articles are
classified based on multiple characteristics, including the type of problem, type of competition,
game-theoretical approaches, customer behaviour, decision space, type of demand, number of
facilities, capacity and budget limitations. The review also highlights the popular problem areas
and dedicated research in the respective domain. In addition, a second classification is also
provided based on solution methods adopted to solve various CFL models and real-world case
studies.
Originality/value- The paper covers 40 years of CFL literature from the perspective of the
problem area, CFL characteristics and the solution approach. Additionally, it introduces
characteristics such as capacity limit and budget constraint for the first time for classification
purposes.
... Depending on the situation modeled, the players are assumed to make decisions simultaneously, step-by-step, sequentially, or more complexly. The models of the first class are motivated by looking for Nash equilibrium and related concepts [27,28,34]. At the same time, decisions on locating commercial, producing or infrastructural facilities are long-term and are often unlikely to be revised. ...
... Under mill pricing, location Nash equilibria rarely exist. On a tree network, some conditions for existence are shown in Eiselt and Bhadury (1998) and Pelegrín and Pelegrín (2017). Under delivered pricing, a location Nash equilibrium exists if demand is fixed in each market (see Dorta-González et al. 2005;Pelegrín et al. 2011). ...
We deal with the location-quantity problem for competing firms when they locate multiple facilities and offer the same type of product. Competition is performed under delivered quantities that are sent from the facilities to the customers. This problem is reduced to a location game when the competing firms deliver the Cournot equilibrium quantities. While existence conditions for a Nash equilibrium of the location game have been discussed in many contributions in the literature, computing an equilibrium on a network when multiple facilities are to be located by each firm is a problem not previously addressed. We propose an integer linear programming formulation to fill this gap. The formulation solves the profit maximization problem for a firm, assuming that the other firms have fixed their facility locations. This allows us to compute location Nash equilibria by the best response procedure. A study with data of Spanish municipalities under different scenarios is presented and conclusions are drawn from a sensitivity analysis.
Organizations continuously endeavour to enhance their decision-making processes. With the advancement in information system, customers are becoming more attentive towards the market condition, competition and, the availability of substitute products. Therefore, instead of placing fixed demand, customers vary demand in response to market dynamics. To capture these factors, the model takes into account the dynamic nature of customer behaviour and incorporates the “law of demand” theory into the price-demand relationship, assuming demand to be a concave function of the price of goods. The study examines a location-price game to identify equilibrium location for firm operating in a foresight competitive market where firms first choose their respective locations and then establish delivered prices to maximize profits. To maximize profit while meeting customers demand satisfactorily, firms compete for providing the goods at a minimum price in minimum time. Due to the NP-hardness of the problem, even the small data set requires excessive computational time by the conventional method. Therefore, to addresses computational challenges associated with this complex CFL model the study employed a two-phase exploration and exploitation based heuristic. Comparative analysis against established algorithms across 33 datasets reveals that the proposed heuristic perform extremely well within negligible computational time across all cases. The study aims to provides insights for managers involved in foresight planning of facility location and pricing, offering a competitive advantage in today's rapidly evolving marketplace.
We address the facility location problem for firms that sell an homogeneous product and compete on delivered prices. If the firms set equilibrium prices at each market, the problem can be seen as a location game for which there exists a Nash equilibrium if demand is inelastic. However, this equilibrium may be Pareto-inefficient and the firms could decide to collude if they can guarantee themselves higher payoffs than those prescribed by the equilibrium. The aim of this paper is to study the joint profit maximization problem to obtain a collusive solution of the location game (Pareto-efficient) and determine if such a solution is also a Nash equilibrium. We develop Integer Linear Programming models to find Pareto-efficient solutions for multiple and single facility location. Nash equilibria are obtained by the best response procedure. An empirical investigation is performed to compare the joint profit of the firms and the profit of each one of the firms, got through the Pareto-efficient locations, with those got through the Nash equilibrium.
We investigate a bi-level optimization program that models a two parties’ competition in the form of a Stackelberg game. Each of the parties must decide where to open facilities and how to assign them to service customers in a way that maximizes a profit. A party can service a customer only by a facility which is preferable to all the competitor's ones for that customer. In the present work, we introduce an exponential family of inequalities satisfied by all the feasible solutions of the bi-level model and show some properties of these inequalities. Based on these results, we develop a cut generation scheme that finds an optimal solution of the model by iteratively supplementing the relaxation of the model, called a high-point problem, with additional constraints. Further, we implement a branch-and-bound algorithm where the introduced constraints improve the upper bound's quality. In the experimental part of the paper, we tune the parameters of the algorithms and investigate their performance on artificially generated input data.
