Randomized Dimensionality Reduction for Facility Location and Single-Linkage Clustering

Random dimensionality reduction is a versatile tool for speeding up algorithms for high-dimensional problems. We study its application to two clustering problems: the facility location problem, and the single-linkage hierarchical clustering problem, which is equivalent to computing the minimum spanning tree. We show that if we project the input pointset $X$ onto a random $d = O(d_X)$-dimensional subspace (where $d_X$ is the doubling dimension of $X$), then the optimum facility location cost in the projected space approximates the original cost up to a constant factor. We show an analogous statement for minimum spanning tree, but with the dimension $d$ having an extra $\log \log n$ term and the approximation factor being arbitrarily close to $1$. Furthermore, we extend these results to approximating solutions instead of just their costs. Lastly, we provide experimental results to validate the quality of solutions and the speedup due to the dimensionality reduction. Unlike several previous papers studying this approach in the context of $k$-means and $k$-medians, our dimension bound does not depend on the number of clusters but only on the intrinsic dimensionality of $X$.Comment: 25 pages. Published as a conference paper in ICML 202

A joint replenishment competitive location problem

Competitive Location Models seek the positions which maximize the market captured by an entrant firm from previously positioned competitors. Nevertheless, strategic location decisions may have a significant impact on inventory and shipment costs in the future affecting the firm’s competitive advantages. In this work we describe a model for the joint replenishment competitive location problem which considers both market capture and replenishment costs in order to choose the firm’s locations. We also present an metaherusitic method to solve it based on the Viswanathan’s (1996) algorithm to solve the Replenishment Problem and an Iterative Local Search Procedure to solve the Location Problem.N/

An Iterative Cyclic Algorithm for Designing Vaccine Distribution Networks in Low and Middle-Income Countries

The World Health Organization's Expanded Programme on Immunization (WHO-EPI) was developed to ensure that all children have access to common childhood vaccinations. Unfortunately, because of inefficient distribution networks and cost constraints, millions of children in many low and middle-income countries still go without being vaccinated. In this paper, we formulate a mathematical programming model for the design of a typical WHO-EPI network with the goal of minimizing costs while providing the opportunity for universal coverage. Since it is only possible to solve small versions of the model optimally, we describe an iterative heuristic that cycles between solving restrictions of the original problem and show that it can find very good solutions in reasonable time for larger problems that are not directly solvable.Comment: International Joint Conference on Industrial Engineering and Operations Management- ABEPRO-ADINGOR-IISE-AIM-ASEM (IJCIEOM 2019). Novi Sad, Serbia, July 15-17t

Megaregional Passenger Transportation Hub Location Problem Considering Congestion Effects

The need to make effective plans for locating transportation hubs is of increasing importance in the megaregional area, as recent research suggests that the growing intercity travel demand affects the efficiency of a megaregional transportation system. This paper investigates a hierarchical facility location problem in a megaregional passenger transportation network. The aim of the study is to determine the locations of hub facilities at different hierarchical levels and distribute the demands to these facilities with minimum total cost, including investment, transportation, and congestion costs. The problem is formulated as a mixed-integer nonlinear programming model considering the service availability structure and hub congestion effects. A case study is designed to demonstrate the effectiveness of the proposed model in the Wuhan metropolitan area. The results show that the congestion effects can be addressed by reallocating the demand to balance the hub utilisation or constructing new hubs to increase the network capacity. The methods of appropriately locating hubs and distributing traffic flows are proposed to optimise the megaregional passenger transportation networks, which has important implications for decision makers

Location models in the public sector

The past four decades have witnessed an explosive growth in the field of networkbased facility location modeling. This is not at all surprising since location policy is one of the most profitable areas of applied systems analysis in regional science and ample theoretical and applied challenges are offered. Location-allocation models seek the location of facilities and/or services (e.g., schools, hospitals, and warehouses) so as to optimize one or several objectives generally related to the efficiency of the system or to the allocation of resources. This paper concerns the location of facilities or services in discrete space or networks, that are related to the public sector, such as emergency services (ambulances, fire stations, and police units), school systems and postal facilities. The paper is structured as follows: first, we will focus on public facility location models that use some type of coverage criterion, with special emphasis in emergency services. The second section will examine models based on the P-Median problem and some of the issues faced by planners when implementing this formulation in real world locational decisions. Finally, the last section will examine new trends in public sector facility location modeling.Location analysis, public facilities, covering models

Taxonomic classification of planning decisions in health care: a review of the state of the art in OR/MS

We provide a structured overview of the typical decisions to be made in resource capacity planning and control in health care, and a review of relevant OR/MS articles for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making

Locating a bioenergy facility using a hybrid optimization method

In this paper, the optimum location of a bioenergy generation facility for district energy applications is sought. A bioenergy facility usually belongs to a wider system, therefore a holistic approach is adopted to define the location that optimizes the system-wide operational and investment costs. A hybrid optimization method is employed to overcome the limitations posed by the complexity of the optimization problem. The efficiency of the hybrid method is compared to a stochastic (genetic algorithms) and an exact optimization method (Sequential Quadratic Programming). The results confirm that the hybrid optimization method proposed is the most efficient for the specific problem. (C) 2009 Elsevier B.V. All rights reserved

Median problems in networks

The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.P-median, location modelling

A new approximation algorithm for the multilevel facility location problem

In this paper we propose a new integer programming formulation for the multi-level facility location problem and a novel 3-approximation algorithm based on LP rounding. The linear program we are using has a polynomial number of variables and constraints, being thus more efficient than the one commonly used in the approximation algorithms for this type of problems

Cost-effective aperture arrays for SKA Phase 1: single or dual-band?

An important design decision for the first phase of the Square Kilometre Array is whether the low frequency component (SKA1-low) should be implemented as a single or dual-band aperture array; that is, using one or two antenna element designs to observe the 70-450 MHz frequency band. This memo uses an elementary parametric analysis to make a quantitative, first-order cost comparison of representative implementations of a single and dual-band system, chosen for comparable performance characteristics. A direct comparison of the SKA1-low station costs reveals that those costs are similar, although the uncertainties are high. The cost impact on the broader telescope system varies: the deployment and site preparation costs are higher for the dual-band array, but the digital signal processing costs are higher for the single-band array. This parametric analysis also shows that a first stage of analogue tile beamforming, as opposed to only station-level, all-digital beamforming, has the potential to significantly reduce the cost of the SKA1-low stations. However, tile beamforming can limit flexibility and performance, principally in terms of reducing accessible field of view. We examine the cost impacts in the context of scientific performance, for which the spacing and intra-station layout of the antenna elements are important derived parameters. We discuss the implications of the many possible intra-station signal transport and processing architectures and consider areas where future work could improve the accuracy of SKA1-low costing.Comment: 64 pages, 23 figures, submitted to the SKA Memo serie