Robust Fault Tolerant uncapacitated facility location

In the uncapacitated facility location problem, given a graph, a set of demands and opening costs, it is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities. This paper concerns the robust fault-tolerant version of the uncapacitated facility location problem (RFTFL). In this problem, one or more facilities might fail, and each demand should be supplied by the closest open facility that did not fail. It is required to find a set of facilities R, so as to minimize the sum of the cost of opening the facilities in R and the cost of assigning all node demands to open facilities that did not fail, after the failure of up to \alpha facilities. We present a polynomial time algorithm that yields a 6.5-approximation for this problem with at most one failure and a 1.5 + 7.5\alpha-approximation for the problem with at most \alpha > 1 failures. We also show that the RFTFL problem is NP-hard even on trees, and even in the case of a single failure

Fault-Tolerant Hotelling Games

The $n$-player Hotelling game calls for each player to choose a point on the line segment, so as to maximize the size of his Voronoi cell. This paper studies fault-tolerant versions of the Hotelling game. Two fault models are studied: line faults and player faults. The first model assumes that the environment is prone to failure: with some probability, a disconnection occurs at a random point on the line, splitting it into two separate segments and modifying each player's Voronoi cell accordingly. A complete characterization of the Nash equilibria of this variant is provided for every $n$. Additionally, a one to one correspondence is shown between equilibria of this variant and of the Hotelling game with no faults. The second fault model assumes the players are prone to failure: each player is removed from the game with i.i.d. probability, changing the payoffs of the remaining players accordingly. It is shown that for $n \geq 3$ this variant of the game has no Nash equilibria

How to locate services optimizing redundancy: A comparative analysis of K-Covering Facility Location models

Redundancy aspects related to covering facility location problems are of extreme importance for many applications, in particular those regarding critical services. For example, in the healthcare sector, facilities such as ambulances or first-aid centers must be located robustly against unpredictable events causing disruption or congestion. In this paper, we propose different modeling tools that explicitly address coverage redundancy for the underlying service. We also evaluate, both theoretically and experimentally, the properties and behavior of the models, and compare them from a computational and managerial point of view. More precisely, by starting from three classical double-covering models from the literature (BACOP1, BACOP2, and DSM), we define three parametric families of models (namely, K-BACOP1, K-BACOP2, and K-DSM) which generalize the former to any possible Kth coverage level of interest. The study of such generalizations allows us to derive interesting managerial insights on location decisions at the strategic level. The CPU performance and the quality of the solutions returned are assessed through ad-hoc KPIs collected over many representative instances with different sizes and topological characteristics, and also by dynamically simulating scenarios involving possible disruption for the located facilities. Finally, a real case study concerning ambulance service in Morocco is analyzed. The results show that, in general, K-BACOP1 performs very well, even if intrinsic feasibility issues limit its broad applicability. Instead, K-DSM achieves the best coverage and equity performances for lower levels of redundancy, while K-BACOP2 seems the most robust choice when high redundancy is required, showing smoother and more predictable trends

How to locate services optimizing redundancy: A comparative analysis of K-Covering Facility Location models

Redundancy aspects related to covering facility location problems are of extreme importance for many applications, in particular those regarding critical services. For example, in the healthcare sector, facilities such as ambulances or first -aid centers must be located robustly against unpredictable events causing disruption or congestion. In this paper, we propose different modeling tools that explicitly address coverage redundancy for the underlying service. We also evaluate, both theoretically and experimentally, the properties and behavior of the models, and compare them from a computational and managerial point of view. More precisely, by starting from three classical double -covering models from the literature (BACOP1, BACOP2, and DSM), we define three parametric families of models (namely, K-BACOP1, K-BACOP2, and K-DSM) which generalize the former to any possible Kth coverage level of interest. The study of such generalizations allows us to derive interesting managerial insights on location decisions at the strategic level. The CPU performance and the quality of the solutions returned are assessed through ad -hoc KPIs collected over many representative instances with different sizes and topological characteristics, and also by dynamically simulating scenarios involving possible disruption for the located facilities. Finally, a real case study concerning ambulance service in Morocco is analyzed. The results show that, in general, K-BACOP1 performs very well, even if intrinsic feasibility issues limit its broad applicability. Instead, K-DSM achieves the best coverage and equity performances for lower levels of redundancy, while K-BACOP2 seems the most robust choice when high redundancy is required, showing smoother and more predictable trends