Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network

Data-Collection for the Sloan Digital Sky Survey: a Network-Flow Heuristic

The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of the entire sky, determining the positions and absolute brightnesses of more than 100 million celestial objects''. The survey will be performed by taking ``snapshots'' through a large telescope. Each snapshot can capture up to 600 objects from a small circle of the sky. This paper describes the design and implementation of the algorithm that is being used to determine the snapshots so as to minimize their number. The problem is NP-hard in general; the algorithm described is a heuristic, based on Lagriangian-relaxation and min-cost network flow. It gets within 5-15% of a naive lower bound, whereas using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete Algorithms (1998

Multi-period maximal covering location problem with capacitated facilities and modules for natural disaster relief services

The paper aims to study a multi-period maximal covering location problem with the configuration of different types of facilities, as an extension of the classical maximal covering location problem (MCLP). The proposed model can have applications such as locating disaster relief facilities, hospitals, and chain supermarkets. The facilities are supposed to be comprised of various units, called the modules. The modules have different sizes and can transfer between facilities during the planning horizon according to demand variation. Both the facilities and modules are capacitated as a real-life fact. To solve the problem, two upper bounds-(LR1) and (LR2)-and Lagrangian decomposition (LD) are developed. Two lower bounds are computed from feasible solutions obtained from (LR1), (LR2), and (LD) and a novel heuristic algorithm. The results demonstrate that the LD method combined with the lower bound obtained from the developed heuristic method (LD-HLB) shows better performance and is preferred to solve both small- and large-scale problems in terms of bound tightness and efficiency especially for solving large-scale problems. The upper bounds and lower bounds generated by the solution procedures can be used as the profit approximation by the managerial executives in their decision-making process

An Improved Location Model for the Collection of Sorted Solid Waste in Densely Populated Urban Centres

This paper presents a facility location model for improving the collection of solid waste materials. The model is especially suitable for densely populated regions with several housing units as well as encourages initial sorting of wastes. Each individual house in the collection area is designated a customer, with randomly selected customers comprising the set of candidate hubs. The fundamental feature of the model is to group the customers into clusters by assigning each customer (house) to the nearest hub. Each cluster is then assigned to exactly one waste collection site drawn from the set of potential collection locations. The objective is to minimize the total number of activated waste collection sites such that all the customers’ requests are satisfied without violating the capacity limit of each site. A simple Lagrangian relaxation heuristic is developed for the problem and solved with the CPLEX solver on the AMPL platform to find a feasible solution. Results from the numerical implementation of model show the model is efficient and competitive with existing solid waste collection facility location model

A Local Search Algorithm for Clustering in Software as a Service Networks

In this paper we present and analyze a model for clustering in networks that offer Software as a Service (SaaS). In this problem, organizations requesting a set of applications have to be assigned to clusters such that the costs of opening clusters and installing the necessary applications in clusters are minimized. We prove that this problem is NP-hard, and model it as an Integer Program with symmetry breaking constraints. We then propose a Tabu search heuristic for situations where good solutions are desired in a short computation time. Extensive computational experiments are conducted for evaluating the quality of the solutions obtained by the IP model and the Tabu Search heuristic. Experimental results indicate that the proposed Tabu Search is promising.integer programming;complexity theory;Tabu Search;software as a service

Algoritmos de aproximação para problemas de localização e alocação de terminais

Orientador: Lehilton Lelis Chaves PedrosaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: No Problema de Localização e Alocação de Terminais, a entrada é um espaço métrico composto por clientes, localidades e um conjunto de pares de clientes; uma solução é um subconjunto das localidades, onde serão abertos terminais, e uma atribuição de cada par de clientes a uma rota, que começa no primeiro cliente, passando em um ou dois terminais, e terminando no segundo cliente. O objetivo é encontrar uma solução que minimize o tamanho de todas as rotas somado com o custo de abertura de terminais. Os algoritmos de aproximação da literatura consideram apenas o caso em que o conjunto de terminais abertos é dado como parte da entrada, e o problema se torna atribuir clientes aos terminais; ou então quando o espaço é definido em classes especiais de grafos. Neste trabalho, apresentamos o primeiro algoritmo de aproximação com fator constante para o problema de, simultaneamente, escolher localidades para abrir terminais e atribuir clientes a estes. A primeira parte desta dissertação cria algoritmos de aproximação para diversas variantes do problema. A estratégia principal é reduzir os problemas de localização e alocação de terminais aos problemas clássicos de localidades, como o problema de localização de instalações e o problema das k-medianas. A redução transforma uma instância de localização e alocação de terminais em uma instância de um destes problemas, que então é resolvida usando algoritmos de aproximação já existentes na literatura. A saída do algoritmo induz uma solução para o problema original, com uma perda constante no fator de aproximação. Na segunda parte, o foco é o Problema de Localização e Alocação Única de Terminais (SAHLP), que é uma variação em que cada cliente deve estar conectado a apenas um terminal, além de não haver limite na quantidade de terminais abertos. A principal contribuição é um algoritmo 2.48-aproximado para o SAHLP, baseado em arredondamento de uma nova formulação de programa linear para o problema. O algoritmo é composto por duas fases: na primeira, a solução fracionária é escalada e um subconjunto de terminais é aberto, e na segunda, atribuímos clientes aos terminais abertos. A primeira fase segue o formato padrão de filtering para problemas de localidades. A segunda, no entanto, exigiu o desenvolvimento de novas ideias e é baseada em múltiplos critérios para realizar a atribuição. A principal técnica atribui cada cliente ao terminal aberto mais próximo, se este estiver em sua vizinhança; caso contrário, o cliente se conecta ao terminal que melhor balanceia múltiplos custos, relacionados à distância entre elesAbstract: In the Hub Location Problem (HLP), the input is a metric space composed of clients, locations and a set of pairs of clients; a solution is a subset of locations to open hubs and an assignment for each pair of clients to a route starting in the first client, passing through one or two hubs and ending in the second client. The objective is to find a solution that minimizes the length of all routes plus the cost of opening hubs. The currently known approximation algorithms consider only the case in which the set of hubs is given as part of the input and the problem is assigning clients to hubs; or when the space is defined on special classes of graphs. In this work, we present the first constant-factor approximation algorithms for the problem of, simultaneously, selecting hubs and allocating clients. The first part of the thesis derives approximation algorithms for several variants of the problem. The main strategy is to reduce the hub location problems to classical location problems, such as Facility Location and k-Median. The reduction transforms an instance of hub location into an instance of a corresponding location problem, which is then solved by known approximation algorithm. The algorithm¿s output induces a solution of the original problem within a constant loss in the approximation ratio. In the second part, we focus on the Single Allocation Hub Location Problem (SAHLP), that is the variant in which a client must be connected to only one hub and there is no limit on the number of open hubs. Our main contribution is a 2.48-approximation algorithm for the SAHLP, based on the rounding of a new linear programming formulation. The algorithm is composed of two phases: in the first one, we scale the fractional solution and open a subset of hub locations, and in the second one, we assign clients to open hubs. The first phase follows the standard filtering framework for location problems. The latter, however, demanded the development of new ideas and is based on a multiple criteria assignment. The main technique is assigning a client to a closest open hub only if there are near open hubs, and otherwise selecting the hub which balances multiple costsMestradoCiência da ComputaçãoMestre em Ciência da Computação2016/12006-1CAPESFAPES

Cluster Before You Hallucinate: Approximating Node-Capacitated Network Design and Energy Efficient Routing

We consider circuit routing with an objective of minimizing energy, in a network of routers that are speed scalable and that may be shutdown when idle. We consider both multicast routing and unicast routing. It is known that this energy minimization problem can be reduced to a capacitated flow network design problem, where vertices have a common capacity but arbitrary costs, and the goal is to choose a minimum cost collection of vertices whose induced subgraph will support the specified flow requirements. For the multicast (single-sink) capacitated design problem we give a polynomial-time algorithm that is O(log^3n)-approximate with O(log^4 n) congestion. This translates back to a O(log ^(4{\alpha}+3) n)-approximation for the multicast energy-minimization routing problem, where {\alpha} is the polynomial exponent in the dynamic power used by a router. For the unicast (multicommodity) capacitated design problem we give a polynomial-time algorithm that is O(log^5 n)-approximate with O(log^12 n) congestion, which translates back to a O(log^(12{\alpha}+5) n)-approximation for the unicast energy-minimization routing problem.Comment: 22 pages (full version of STOC 2014 paper

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LOCATION-ALLOCATION-ROUTING APPROACH TO SOLID WASTE COLLECTION AND DISPOSAL

Various studies have indicated that the collection phase of solid wastes, which comprises of the initial col- lection at the source of generation and the transportation to the disposal sites, is by far the most expensive. Two fundamental issues of concern in solid waste collection are the locations of initial collection and the period of collection by the dedicated vehicles. However, considering the prevailing conditions of adhoc lo- cation of waste containers and the faulty roads in many developing countries, this research was conducted to develop two e�ective models for solid waste collection and disposal such that new parameters measuring the capacity of waste ow from each source unit and road accessibility were introduced and incorporated in the mathematical formulations of the models. To formulate the problems, two classes of integer pro- gramming problems namely, Facility Location Problem (FLP) and the Vehicle Routing Problem (VRP), were used for the collection and disposal respectively. The clustering process involved in the model for the collection phase was based on the Euclidean distance relationship among the various entities within the study area. In this model, the study area was considered as a universal set and simply partitioned with each element representing a cluster. At this stage, a threshold distance was de�ned as the maximum allowable distance between a cluster and the potential collection sites. In the VRP formulation of the disposal model, two new parameters, called the accessibility ratio and road attribute, were introduced and included in the formulation. The inclusion of these parameters ensure that a waste collection vehicle uses only roads with high attributes. The solution to the model on the collection phase was based on the Lagrangian re- laxation of the set of constraints where decision variables are linked, while in the model on waste vehicle routing, the assignment constraints were relaxed. Both resulting Lagrangian dual problems were solved using sub-gradient optimization algorithm. It was shown that the resulting Lagrangian dual functions were non-di�erentiable concave functions and thus the application of the sub-gradient optimization method was justi�ed. By applying these techniques, strong lower bounds on the optimal values of the decision variables were obtained. All model implementations were based on randomly generated data that mimic real-life experience of the study area (Eti-Osa Local Government Area of Lagos State, Nigeria), as well as large-scale standard benchmark data instances in literature. These computational experiments were carried out using the CPLEX and MINOS optimization solvers on AIMMS and AMPL modeling environments. Results from the computational experiments revealed that the models are capable of addressing the challenge of solid waste collection and disposal. For instance, more than 60% reductions were obtained for the number of collection points to be activated and the container allocations for the different wastes considered. Numerical results from the disposal model showed that there is a general reduction in the total distance covered by a vehicle and a slight improvement in the number of customers visited. Result comparison with those found in literature suggested that our models are very efficient

Facility Location Problems: Models, Techniques, and Applications in Waste Management

This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for e�ective and e�cient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP