The 1-Center and 1-Highway Problem

In this paper we extend the Rectilinear 1-center as follows: Given a set S of n points in the plane, we are interested in locating a facility point f and a rapid transit line (highway) H that together minimize the expression max p ∈ S d H (p,f), where d H (p,f) is the travel time between p and f. A point p ∈ S uses H to reach f if H saves time for p. We solve the problem in O(n 2) or O(nlogn) time, depending on whether or not the highway’s length is fixed.Peer ReviewedPostprint (published version

Locating a service facility and a rapid transit line

In this paper we study a facility location problem in the plane in which a single point (facility) and a rapid transit line (highway) are simultaneously located in order to minimize the total travel time of the clients to the facility, using the L 1 or Manhattan metric. The rapid transit line is represented by a line segment with fixed length and arbitrary orientation. The highway is an alternative transportation system that can be used by the clients to reduce their travel time to the facility. This problem was introduced by Espejo and Rodríguez-Chía in [8]. They gave both a characterization of the optimal solutions and an algorithm running in O(n 3logn) time, where n represents the number of clients. In this paper we show that the Espejo and Rodríguez-Chía’s algorithm does not always work correctly. At the same time, we provide a proper characterization of the solutions with a simpler proof and give an algorithm solving the problem in O(n 3) time.Peer ReviewedPostprint (published version

On the multisource hyperplanes location problem to fitting set of points

In this paper we study the problem of locating a given number of hyperplanes minimizing an objective function of the closest distances from a set of points. We propose a general framework for the problem in which norm-based distances between points and hyperplanes are aggregated by means of ordered median functions. A compact Mixed Integer Linear (or Non Linear) programming formulation is presented for the problem and also an extended set partitioning formulation with an exponential number of variables is derived. We develop a column generation procedure embedded within a branch-and-price algorithm for solving the problem by adequately performing its preprocessing, pricing and branching. We also analyze geometrically the optimal solutions of the problem, deriving properties which are exploited to generate initial solutions for the proposed algorithms. Finally, the results of an extensive computational experience are reported. The issue of scalability is also addressed showing theoretical upper bounds on the errors assumed by replacing the original datasets by aggregated versions.Comment: 30 pages, 5 Tables, 3 Figure

FATORES DE DECISÃO QUANTO À LOCALIZAÇÃO DE FORNECEDORES NO SETOR AUTOMOTIVO NACIONAL

Esse artigo apresentou através de levantamento bibliográfico os principais fatores que influenciam na decisão quanto à localização de fornecedores no setor automotivo nacional. Atualmente o setor automotivo é estratégico para o país, com significativa participação nas exportações nacionais. As decisões quanto à localização de organizações industriais envolve basicamente três áreas de conhecimento: teoria da localização, logística e pesquisa operacional. Um campo de estudos interdisciplinar com possibilidade de diversas interações com outras áreas do saber

Mixed planar and network single-facility location problems

We consider the problem of optimally locating a single facility anywhere in a network to serve both on-network and off-network demands. Off-network demands occur in a Euclidean plane, while on-network demands are restricted to a network embedded in the plane. On-network demand points are serviced using shortest-path distances through links of the network (e.g., on-road travel), whereas demand points located in the plane are serviced using more expensive Euclidean distances. Our base objective minimizes the total weighted distance to all demand points. We develop several extensions to our base model, including: (i) a threshold distance model where if network distance exceeds a given threshold, then service is always provided using Euclidean distance, and (ii) a minimax model that minimizes worst-case distance. We solve our formulations using the “Big Segment Small Segment” global optimization method, in conjunction with bounds tailored for each problem class. Computational experiments demonstrate the effectiveness of our solution procedures. Solution times are very fast (often under one second), making our approach a good candidate for embedding within existing heuristics that solve multi-facility problems by solving a sequence of single-facility problems. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 68(4), 271–282 2016