A two-level facility location and sizing problem for maximal coverage

This paper presents a two-stage hierarchical location problem for systems where the lower level facilities act as the first points contact for the customers while the upper level facilities act as suppliers of the lower level facilities that either serve them or provide advanced services to customers. Furthermore, more recent and realistic coverage constructs such as gradual and cooperative covering are included in our setting. Although our problem can be applicable in various settings, the most fitting application is in wireless telecommunication networks to determine the location of base stations and mobile switching centers. We have developed two competing formulations for the problem, each of which involve nonlinear components that are difficult to deal with. We then develop their respective linearizations and tested their performances. These formulations are solved by commercial optimizers for a set of reasonably large problem instances and it is found that majority of the problems can be solved within a maximum of 10% optimality gap within a short time

Hybrid Set Covering and Dynamic Modular Covering Location Problem: Application to an Emergency Humanitarian Logistics Problem

This paper presents an extension of the covering location problem as a hybrid covering model that utilizes the set covering and maximal covering location problems. The developed model is a multi-period model that considers strategic and tactical planning decisions. Hybrid covering location problem (HCLP) determines the location of the capacitated facilities by using dynamic set covering location problem as strategic decisions and assigns the constructive units of facilities and allocates the demand points by using dynamic modular capacitated maximal covering location problem as tactical decisions. One of the applications of the proposed model is locating first aid centers in humanitarian logistic services that have been addressed by studying a threat case study in Japan. In addition to validating the developed model, it has been compared to other possible combined problems, and several randomly generated examples have been solved. The results of the case study and model validation tests approve that the main hybrid developed model (HCLP) is capable of providing better coverage percentage compared to conventional covering models and other hybrid variants

Directional approach to gradual cover: the continuous case

The objective of the cover location models is covering demand by facilities within a given distance. The gradual (or partial) cover replaces abrupt drop from full cover to no cover by defining gradual decline in cover. In this paper we use a recently proposed rule for calculating the joint cover of a demand point by several facilities termed "directional gradual cover". Contrary to all gradual cover models, the joint cover depends on the facilities' directions. In order to calculate the joint cover, existing models apply the partial cover by each facility disregarding their direction. We develop a genetic algorithm to solve the facilities location problem and also solve the problem for facilities that can be located anywhere in the plane. The proposed modifications were extensively tested on a case study of covering Orange County, California

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

Spatial organization of public services: models and applications

Location decisions are crucial in the spatial organization in both public and private sectors as they can have a long term impact on operational performances and on service levels. Social cost minimization, universality of services and equity, expressed in terms of users' accessibility, are the main objectives in public services contexts. Nevertheless, the enduring trend of public expenditures revision poses, also in the public sectors, the need to pursue objectives of economic efficiency. In the literature, two families of optimization problems are typically used to address these problems, namely Facility Location Problems (FLPs) and Districting Problems (DPs). The aim of this thesis is to show how FLPs and DPs can be used to underpin spatial organization processes of public services, providing analytical models able to assist the decision making. To this end, novel mathematical models are developed with application to the healthcare and postal service sectors. In particular, a hierarchical facility location model is formulated to reorganize an existing regional Blood Management System (BMS) while an integrated location-districting model is proposed for the organization of postal collection operations in urban areas. A constructive heuristic procedure is also devised to solve the latter problem. Extensive computational experiments are realized to validate the proposed models and to show their capability to provide insightful managerial implications. Finally, the thesis aims at filling another existing gap in the literature due to the absence of stochastic models for DPs. Hence, a two-stage stochastic program for districting is introduced and tested on real georgaphic data. Several extensions of the proposed modeling framework are also discussed

Estudio de problemas de clasificación supervisada y de localización en redes mediante optimización matemática

This PhD dissertation addresses several problems in the fields of Supervised Classification and Location Theory using tools and techniques coming from Mathematical Optimization. A brief description of these problems and the methodologies proposed for their analysis and resolution is given below. In the first chapter, the principles of Supervised Classification and Location Theory are discussed in detail, emphasizing the topics studied in this thesis. The following two chapters discuss Supervised Classification problems. In particular, Chapter 2 proposes exact solution approaches for various models of Support Vector Machines (SVM) with ramp loss, a well-known classification method that limits the influence of outliers. The resulting models are analyzed to obtain initial bounds of the big M parameters included in the formulation. Then, solution approaches based on three strategies for obtaining tighter values of the big M parameters are proposed. Two of them require solving a sequence of continuous optimization problems, while the third uses the Lagrangian relaxation. The derived resolution methods are valid for the l1-norm and l2-norm ramp loss formulations. They are tested and compared with existing solution methods in simulated and real-life datasets, showing the efficiency of the developed methodology. Chapter 3 presents a new SVM-based classifier that simultaneously deals with the limitation of the influence of outliers and feature selection. The influence of outliers is taken under control using the ramp loss margin error criterion, while the feature selection process is carried out including a new family of binary variables and several constraints. The resulting model is formulated as a mixed-integer program with big M parameters. The characteristics of the model are analyzed and two different solution approaches (exact and heuristic) are proposed. The performance of the obtained classifier is compared with several classical ones in different datasets. The next two chapters deal with location problems, in particular, two variants of the Maximal Covering Location Problem (MCLP) in networks. These variants respond to the modeling of two different scenarios, with and without uncertainty in the input data. First, Chapter 4 presents the upgrading version of MCLP with edge length modifications on networks. This problem aims at locating p facilities on the nodes (of the network) so as to maximize coverage, considering that the length of the edges can be reduced within a budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some constraints. Moreover, we analyze the characteristics of these formulations to strengthen them by proposing valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets. The following chapter, Chapter 5, also considers a MCLP, albeit from the perspective of uncertainty. In particular, this chapter addresses a version of the single-facility MCLP on a network where the demand is distributed along the edges and uncertain with only a known interval estimation. We propose a minmax regret model where the service facility can be located anywhere along the network. Furthermore, we present two polynomial algorithms for finding the location that minimizes the maximal regret assuming that the demand realization is an unknown constant or linear function on each edge. We also include two illustrative examples as well as a computational study to show the potential of the proposed methodology

Remote sensing in the coastal and marine environment. Proceedings of the US North Atlantic Regional Workshop

Presentations were grouped in the following categories: (1) a technical orientation of Earth resources remote sensing including data sources and processing; (2) a review of the present status of remote sensing technology applicable to the coastal and marine environment; (3) a description of data and information needs of selected coastal and marine activities; and (4) an outline of plans for marine monitoring systems for the east coast and a concept for an east coast remote sensing facility. Also discussed were user needs and remote sensing potentials in the areas of coastal processes and management, commercial and recreational fisheries, and marine physical processes