连续设施选址:模型、方法与应用

给定度量空间和该空间中的若干顾客,设施选址为在该度量空间中确定新设施的位置使得某种目标达到最优。连续设施选址是设施选址中的一类重要问题,其中的设施可在度量空间的某连续区域上进行选址。本文对连续设施选址的模型、算法和应用方面的工作进行了综述。文章首先讨论了连续设施选址中几个重要元素,包括新设施个数、距离度量函数、目标函数;然后介绍了连续选址中的几种经典模型和拓展模型;接着概述了求解连续选址问题的常用优化方法和技术,包括共轭对偶、全局优化、不确定优化、变分不等式方法、维诺图;最后介绍了连续设施选址的重要应用并给出了研究展望。     

Heuristic Solution Methods for Two Location Problems with Unreliable Facilities

In this paper, the p-median and p-centre problems are generalized by considering the possibility that one or more of the facilities may become inactive. The unreliable p-median problem is defined by introducing the probability that a facility becomes inactive. The (p, q)-centre problem is defined when p facilities need to be located but up to q of them may become unavailable at the same time. An heuristic procedure is presented for each problem. A rigorous procedure is discussed for the (p, q)-centre problem. Computational results are presented.     

The Multi-Commodity Facilities Location Problem

The Multi-commodity Location Problem was one of the ‘multi-level’ location problems introduced by Warszawski and Peer in their paper on building sites. Methods of solution are developed for this problem via a dual-based approach and via a Lagrangean dual-based approach with hill-climbing. Numerical results are presented.     

Location of Facilities Producing Airborne Pollution

The location of a facility producing an airborne pollutant is considered and the 4-wind model introduced by Karkazis and Papadimitriou is described briefly. Ways in which the model may be enhanced are discussed; in particular, it is shown how the restriction to four wind directions may be removed. The applicability of the approach is tested on data relating to the Salonica district of Greece.     

Location of Preventive Health Care Facilities

This paper is focused on the problem of locating preventive health care facilities. The aim is to maximize participation to prevention programs. We assume that distance is a major determinant of participation and people would go to the closest facility for preventive health care. Each facility is required to have more than a predetermined number of clients because of the direct relationship between volume and quality of preventive services. We provide a mathematical formulation and present alternative solution approaches for this new location problem. We report on computational performance of the proposed methods in locating public health centers in Fulton County, Georgia and mammography screening centers in Montreal, Quebec.     

半讨厌型设施选址问题的模型与算法

研究了结合网络和平面模型的半讨厌型设施的选址问题.半讨厌型设施结合了讨厌型设施与喜爱型设施的性质,一方面由于这些设施对人们带来很多副作用,人们想要远离他们以避免遭到污染,但同时人们又希望距离设施不要过远,因此建立0-1整数模型,在保证所有人使用该设施的距离不超过既定距离的基础上,使污染范围最小.由于该问题是NP困难问题,本为给出了启发式算法,通过算例进行了比较分析,证明了算法的有效性.     

Location of Two Facilities with Minimal Separation

In this technical note it is shown how a problem of location of two facilities may be formulated as a non-convex optimization problem, and an algorithm is provided to determine an ?-optimal solution.     

停车设施选址的双层规划模型

为了解决城市停车难问题,针对目前日益紧张的土地资源和快速增长的交通流量,考虑停车设施对路网上交通流的影响,提出一种在土地利用规划基础上的,对路网影响最小,停车场使用者步行时间最省的停车设施选址的双层规划模型,借助现有的交通规划软件(Emme)进行求解,并应用于上海市江湾-五角场副中心地区停车设施规划研究中.     

Location of Service Facilities for the Elderly

Senior centers provide a variety of supportive services for independent elderly adults. In many metropolitan areas, the elderly population is growing and redistributing from central cities to suburbs, where accessibility to senior centers is limited. Policy analysts need to locate senior centers to best meet changing demands for service. We present alternative hierarchical facility location models for senior centers applied to Allegheny County, Pennsylvania. We find that a model that minimizes consumer disutility and unserved demands is preferred to one that maximizes utility alone, and that the former model is well-behaved in response to changes in structural parameters.     

Multi-Service Facility Location Models

The multi-service facility (MSF) concept proposes the co-location of a range of human services under a single roof. Thus, for example, services for preschoolers, teens, and seniors might be co-located within a joint facility. MSFs are a response to economies of scale; co-location reduces the monetary costs of providing a variety of services. Yet, the spatial distributions of different societal groups are different within a city – an MSF system will not provide optimum geographical accessibility to individual groups. We introduce two p-median based location–allocation models that trade off the fixed costs of providing services and opening facilities with the travel costs of three societal groups. We observe that some mixes of single- and multi-service facilities can provide efficient service systems without unduly compromising the accessibility needs of individual groups.     

Equity Models in Planar Location

In this paper we investigate planar location models with equity objectives. Two objectives are analyzed: (1) Minimizing the variance of the distances to the facility, and (2) minimizing the range of the distances. The problems are solved using the global optimization technique “Big Triangle Small Triangle”. Computational experiments provided excellent results. Solving a problem with 10,000 demand points required less than 5 s of computer time for finding the minimum variance, and less than half that time for finding the minimum range.     

离散设施选址问题研究综述

本文首先回顾了设施选址问题百年发展历史,认为其研究经历了零散研究、系统研究、不确定性研究三个阶段.离散选址问题包括中值问题、覆盖问题、中心问题、多产品问题、动态问题、多目标问题、路径选址问题、网络中心选址问题8个子问题.最后作者讨论了选址问题研究中存在的问题以及今后发展的趋势.     

Minimax Location of Two Facilities with Minimum Separation: Interactive Graphical Solutions

We consider the problem of locating two facilities so as to minimize the maximum of combined Euclidean distances to unweighted existing points when the facilities must be separated by at least a specified distance. Interpreting the problem as the minimum covering ellipse problem, we employ an interactive graphical method which easily produces near-optimal solutions. We describe the method, implemented on a microcomputer, because it exemplifies the more general technique of interactive optimization.     

Single-Period Location Models for Subsidized Housing: Tenant-Based Subsidies

Previous research has established a need for operations research models to help urban public housing authorities (PHAs) in the U.S. better manage the transition from the traditional model of high-rise public housing developments to tenant-based housing subsidies for market-rate rental units and project-based housing subsidies for scattered-site, low-density public housing. This paper presents the tenant-based subsidized housing location model (TSHLP) that is simplified and applied to a larger and more representative data set than has been done previously. Base-case and sensitivity analyses indicate that model solutions, which are approximations to a Pareto frontier of nondominated potential family allocations, give planners considerable flexibility in choosing alternative housing configurations that can satisfy the needs of various interest groups.     

Locating Multiple Competitive Facilities: Spatial Interaction Models with Variable Expenditures

We develop a new framework for location of competitive facilities by introducing non-constant expenditure functions into spatial interaction location models. This framework allows us to capture two key effects – market expansion and cannibalization – within the same model.We develop algorithmic approaches for finding optimal or near-optimal solutions for several models that arise from choosing a specific form of the expenditure functions.     

Optimizing the Location of Facilities on a Building Site

A mathematical model for optimized location on a building site is presented which is partitioned into several special cases, with solution techniques described for each case. Two applications are also given.