Upgrading edges in the maximal covering location problem

We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the length of the edges can be reduced at a cost, subject to a given budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions. This problem is NP-hard on general graphs. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some of the constraints. Moreover, we strengthen the proposed formulations including valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets. © 2022 The Author(s

Comparison of Emergency Medical Services Delivery Performance using Maximal Covering Location and Gradual Cover Location Problems

Ambulance location is one of the critical factors that determine the efficiency of emergency medical services delivery. Maximal Covering Location Problem is one of the widely used ambulance location models. However, its coverage function is considered unrealistic because of its ability to abruptly change from fully covered to uncovered. On the contrary, Gradual Cover Location Problem coverage is considered more realistic compared to Maximal Cover Location Problem because the coverage decreases over distance. This paper examines the delivery of Emergency Medical Services under the models of Maximal Covering Location Problem and Gradual Cover Location Problem. The results show that the latter model is superior, especially when the Maximal Covering Location Problem has been deemed fully covered

New Model of Maximal Covering Location Problem with Fuzzy Conditions

The objective of Maximal Covering Location Problem is locating facilities such that they cover the maximal number of locations in a given radius or travel time. MCLP is applied in many different real-world problems with several modifications. In this paper a new model of MCLP with fuzzy conditions is presented. It uses two types of fuzzy numbers for describing two main parameters of MCLP - coverage radius and distances between locations. First, the model is defined, then Particle Swarm Optimization method for solving the problem is described and tested

A Simulated Annealing method to solve a generalized maximal covering location problem

The maximal covering location problem (MCLP) seeks to locate a predefined number of facilities in order to maximize the number of covered demand points. In a classical sense, MCLP has three main implicit assumptions: all or nothing coverage, individual coverage, and fixed coverage radius. By relaxing these assumptions, three classes of modelling formulations are extended: the gradual cover models, the cooperative cover models, and the variable radius models. In this paper, we develop a special form of MCLP which combines the characteristics of gradual cover models, cooperative cover models, and variable radius models. The proposed problem has many applications such as locating cell phone towers. The model is formulated as a mixed integer non-linear programming (MINLP). In addition, a simulated annealing algorithm is used to solve the resulted problem and the performance of the proposed method is evaluated with a set of randomly generated problems

A Decomposition Heuristic for the Maximal Covering Location Problem

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, are identified and relaxed in the Lagrangean way, resulting in disconnected subgraphs representing smaller subproblems that are computationally easier to solve by exact methods. The proposed technique is compared to the classical approach, using real data and instances from the available literature

A Decomposition Heuristic for the Maximal Covering Location Problem

This paper proposes a cluster partitioning technique to calculate improved upper bounds to the optimal solution of maximal covering location problems. Given a covering distance, a graph is built considering as vertices the potential facility locations, and with an edge connecting each pair of facilities that attend a same client. Coupling constraints, corresponding to some edges of this graph, are identified and relaxed in the Lagrangean way, resulting in disconnected subgraphs representing smaller subproblems that are computationally easier to solve by exact methods. The proposed technique is compared to the classical approach, using real data and instances from the available literature

Developing dynamic maximal covering location problem considering capacitated facilities and solving it using hill climbing and genetic algorithm

The maximal covering location problem maximizes the total number of demands served within a maximal service distance given a fixed number of facilities or budget constraints. Most research papers have considered this maximal covering location problem in only one period of time. In a dynamic version of maximal covering location problems, finding an optimal location of P facilities in T periods is the main concern. In this paper, by considering the constraints on the minimum or maximum number of facilities in each period and imposing the capacity constraint, a dynamic maximal covering location problem is developed and two related models (A, B) are proposed. Thirty sample problems are generated randomly for testing each model. In addition, Lingo 8.0 is used to find exact solutions, and heuristic and meta-heuristic approaches, such as hill climbing and genetic algorithms, are employed to solve the proposed models. Lingo is able to determine the solution in a reasonable time only for small-size problems. In both models, hill climbing has a good ability to find the objective bound. In model A, the genetic algorithm is superior to hill climbing in terms of computational time. In model B, compared to the genetic algorithm, hill climbing achieves better results in a shorter time

Modular Capacitated Maximal Covering Location Problem for the Optimal Siting of Emergency Vehicles

To improve the application of the maximal covering location problem (MCLP), several capacitated MCLP models were proposed to consider the capacity limits of facilities. However, most of these models assume only one fixed capacity level for the facility at each potential site. This assumption may limit the application of the capacitated MCLP. In this article, a modular capacitated maximal covering location problem (MCMCLP) is proposed and formulated to allow several possible capacity levels for the facility at each potential site. To optimally site emergency vehicles, this new model also considers allocations of the demands beyond the service covering standard. Two situations of the model are discussed: the MCMCLP-facility-constraint (FC), which fixes the total number of facilities to be located, and the MCMCLP-non-facility-constraint (NFC), which does not. In addition to the model formulations, one important aspect of location modeling—spatial demand representation—is included in the analysis and discussion. As an example, the MCMCLP is applied with Geographic Information System (GIS) and optimization software packages to optimally site ambulances for the Emergency Medical Services (EMS) Region 10 in the State of Georgia. The limitations of the model are also discussed