Richard L. Francis

EVACNET+: A computer program to determine optimal building evacuation plans

EVACNET+ is a user-friendly interactive computer program that allows the modeling of emergency building evacuations. An EVACNET+ model is a network consisting of a set of nodes connected by arcs. The nodes represent building components such as rooms, halls, landings, stairs and lobbies. The arcs represent the passageways between the building components. The program identifies optimal evacuation plans for user defined buildings.

Invited reviewLocational analysis

For our purposes, locational analysis is the formulation and solution of location problems. We consider locational analysis which is carried out by the construction and solution of locational models. Such models typically involve locating one or more new facilities, and may include transport costs, fixed costs, constraints on the number of new facilities, upper bounds on distances between new and existing facilities, as well as determining amounts to be shipped between new and existing facilities. We give a selective review of the locational analysis literature, concentrating on models which have been thoroughly tested, and which can be solved by ‘reliable algorithms’. For convenience, we consider four classes of locational models: planar models, warehousing models, network models, and discrete, or mixed-integer programming, models.

Convex Location Problems on Tree Networks

This paper studies problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths. We establish that a large class of such problems is convex, in a well defined sense, for all choices of the data if and only if the network is a tree. A number of useful properties of related convex functions end convex sets are identified.

Aggregation error for location models: survey and analysis

Location problems occurring in urban or regional settings may involve many tens of thousands of “demand points,” usually individual private residences. In modeling such problems it is common to aggregate demand points to obtain tractable models. We survey aggregation approaches to a large class of location models, consider and compare various aggregation error measures, identify some effective (and ineffective) aggregation error measures, and discuss some open research areas.

Aggregation Error Bounds for a Class of Location Models

Many location models involve distances and demand points in their objective function. In urban contexts, there can be millions of demand points. This leads to demand point aggregation, which produces error. We identify a general model structure that includes most such location models, and present a means of obtaining error bounds for all models with this structure. The error bounds suggest how to do the demand point aggregation so as to keep the error small.

Finding efficient solutions for rectilinear distance location problems efficiently

Abstract Given n planar existing facility locations, a planar new facility location X is called efficient if there is no other location Y for which the rectilinear distance between Y and each existing facility is at least as small as between X and each existing facility, and strictly less for at least one existing facility. Rectilinear distances are typically used to measure travel distances between points via rectilinear aisles or street networks. We first present a simple arrow algorithm, based entirely on geometrical analysis, that constructs all efficient locations. We then present a row algorithm which is of order n (log n ) that constructs all efficient locations, and establish that no alternative algorithm can be of a lower order.

Network models for building evacuation

How can a large building with many occupants be evacuated in minimum time, and where are the bottlenecks likely to occur in such an evacuation? In order to address this question, three network building evacuation models have been presented. It is believed that the models provide useful new tools for the analysis of building evacuability, and have the potential to facilitate the study of the interrelationships with building design, building redesign, and building evacuability.

On worst-case aggregation analysis for network location problems

Network location problems occur when new facilities must be located on a network, and the network distances between new and existing facilities are important. In urban, regional, or geographic contexts, there may be hundreds of thousands (or more) of existing facilities, in which case it is common to aggregate existing facilities, e.g. represent all the existing facility locations in a zip code area by a centroid. This aggregation makes the size of the problem more manageable for data collection and data processing purposes, as well as for purposes of analysis; at the same time, it introduces errors, and results in an approximating location problem being solved. There seems to be relatively little theory for doing aggregation, or evaluating the results of aggregation; most approaches are based on experimentation or computational studies. We propose a theory that has the potential to improve the means available for doing aggregation.

Row-Column Aggregation for Rectilinear Distance p-Median Problems

For large-scale p -median problems, it is common to aggregate the demand points. This size reduction via aggregation makes the problem easier to solve, but introduces error. Doing this aggregation well is provably difficult. We present a median-row-column aggregation algorithm, MRC, with provable properties including an error bound, an (attainable) upper bound on the maximum objective function error. MRC adjusts spacing of individual rows and columns to exploit problem structure. For e demand points, r rows, and c columns, the algorithm has computational order e ( c + r + log e ), and order e storage requirements. We report encouraging computational experience.

Letter to the Editor-Some Aspects of a Minimax Location Problem

Some aspects of a minimax version of the Steiner-Weber location problem are studied. A necessary condition is given for a minimax location, or solution; a lower bound on the value of a minimax solution is given that is attained for many problems; and an explicit minimax solution is given for the case where the lower bound is attained. Also, a geometric characterization of the minimax solution is discussed, and a closely related facility design problem is examined.