Two-Stage Facility Location Games with Strategic Clients and Facilities

We consider non-cooperative facility location games where both facilities and clients act strategically and heavily influence each other. This contrasts established game-theoretic facility location models with non-strategic clients that simply select the closest opened facility. In our model, every facility location has a set of attracted clients and each client has a set of shopping locations and a weight that corresponds to its spending capacity. Facility agents selfishly select a location for opening their facility to maximize the attracted total spending capacity, whereas clients strategically decide how to distribute their spending capacity among the opened facilities in their shopping range. We focus on a natural client behavior similar to classical load balancing: our selfish clients aim for a distribution that minimizes their maximum waiting time for getting serviced, where a facility’s waiting time corresponds to its total attracted client weight. We show that subgame perfect equilibria exist and we give almost tight constant bounds on the Price of Anarchy and the Price of Stability, which even hold for a broader class of games with arbitrary client behavior. Since facilities and clients influence each other, it is crucial for the facilities to anticipate the selfish clients’ behavior when selecting their location. For this, we provide an efficient algorithm that also implies an efficient check for equilibrium. Finally, we show that computing a socially optimal facility placement is NP-hard and that this result holds for all feasible client weight distributions.

Simple Single and Multi-Facility Location Models using Great Circle Distance

Facility location problems (FLP) are widely studied in operations research and supply chain domains. The most common metric used in such problems is the distance between two points, generally Euclidean distance (ED). When points/ locations on the earth surface are considered, ED may not be the appropriate distance metric to analyse with. Hence, while modelling a facility location on the earth, great circle distance (GCD) is preferable for computing optimal location(s). The different demand points may be assigned with different weights based on the importance and requirements. Weiszfeld’s algorithm is employed to locate such an optimal point(s) iteratively. The point is generally termed as “Geometric Median”. This paper presents simple models combining GCD, weights and demand points. The algorithm is demonstrated with a single and multi-facility location problems.

Military Facility Location Problems

In the past decades, facility location problems have attracted much attention among researchers and practitioners from different disciplines. Among those problems, location models observed in military organizations have significant impact to the performance of the military organization since they require large amounts of money, resource, and people. Moreover, an efficient planning of military resources often leads to a good direction to victories. In this chapter, considering a number of selected papers, the authors give a brief survey of facility location models and solution techniques employed for military organizations. After providing the features of core location models, they analyze the military facility location models with respect to the context they are handled. After categorizing the articles with respect to the formulations and solution approaches employed, the authors highlight potential issues for further research.

From Recommendation Systems to Facility Location Games

Recommendation systems are extremely popular tools for matching users and contents. However, when content providers are strategic, the basic principle of matching users to the closest content, where both users and contents are modeled as points in some semantic space, may yield low social welfare. This is due to the fact that content providers are strategic and optimize their offered content to be recommended to as many users as possible. Motivated by modern applications, we propose the widely studied framework of facility location games to study recommendation systems with strategic content providers. Our conceptual contribution is the introduction of a mediator to facility location models, in the pursuit of better social welfare. We aim at designing mediators that a) induce a game with high social welfare in equilibrium, and b) intervene as little as possible. In service of the latter, we introduce the notion of intervention cost, which quantifies how much damage a mediator may cause to the social welfare when an off-equilibrium profile is adopted. As a case study in high-welfare low-intervention mediator design, we consider the one-dimensional segment as the user domain. We propose a mediator that implements the socially optimal strategy profile as the unique equilibrium profile, and show a tight bound on its intervention cost. Ultimately, we consider some extensions, and highlight open questions for the general agenda.

Military Facility Location Problems

In the past decades, facility location problems have attracted much attention among researchers and practitioners from different disciplines. Among those problems, location models observed in military organizations have significant impact to the performance of the military organization since they require large amounts of money, resource, and people. Moreover, an efficient planning of military resources often leads to a good direction to victories. In this chapter, considering a number of selected papers, the authors give a brief survey of facility location models and solution techniques employed for military organizations. After providing the features of core location models, they analyze the military facility location models with respect to the context they are handled. After categorizing the articles with respect to the formulations and solution approaches employed, the authors highlight potential issues for further research.