Models for Public Systems Analysis - 1st Edition - ISBN: 9780120855650, 9781483267104

Models for Public Systems Analysis

1st Edition

Authors: Edward J. Beltrami
Editors: J. William Schmidt
eBook ISBN: 9781483267104
Imprint: Academic Press
Published Date: 28th January 1977
Page Count: 234
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Description

Models for Public Systems Analysis considers the mathematical model formulation to improve the delivery of urban service systems, such as sanitation, fire, police, and ambulances. This book is composed of five chapters that demonstrate the translation of significant societal problems into a mathematical framework, as well as the advantages and limitations of these models.

Chapter 1 deals with the issue of plant location and siting questions, with a brief overview of water resource modeling, while Chapter 2 provides set-covering models for manpower scheduling as a direct outgrowth of the author's experience with the Sanitation Department in New York City. Chapters 3 and 4 describe the delivery of emergency services, particularly with models of congestion and delay and of optimal deployment. These chapters also present probabilistic analysis in nature since both the spatial and the temporal patterns of demand are intrinsically uncertain. The tools used are queueing theory and geometric probability. Chapter 5 examines network optimization methods, mainly to explore questions of vehicle routing and scheduling. This chapter also provides a few comments on large-scale models of urban growth, these being generally more familiar to the regional planner then to the operations analyst.

This book will prove useful to applied mathematics and policy science students.

Table of Contents


Preface

Acknowledgments

Introduction Some Thoughts on Mathematics and Public Policy

References

Chapter 1 Plant Location and Optimal Distribution

1.1 A Waste Disposal Problem

1.2 Optimal Location of Facilities

1.3 More on Optimal Plant Siting

1.4 Sewage Treatment Is Also a Plant Location Problem

1.5 Energy Models

1.6 Exercises

1.7 Notes and Remarks

Chapter 2 Manpower Scheduling

2.1 A Nonlinear Allocation Model

2.2 Who Is to Pick Up All the Garbage?

2.3 A Model for Manpower Scheduling

2.4 Exercises

2.5 Notes and Remarks

Chapter 3 Models for Deploying Emergency Services I: Response Delays

3.1 Models of Congestion

3.2 Cost Versus Service

3.3 A Spatial “Hypercube” Model

3.4 Priorities

3.5 Exercises

3.6 Notes and Remarks

Chapter 4 Models for Deploying Emergency Services II : Allocation of Units

4.1 Deployment of Firefighters

4.2 Some Geometric Models

4.3 The Inverse Square Root Law

4.4 Random Patrols

4.5 Exercises

4.6 Notes and Remarks

Chapter 5 Network Optimization

5.1 Where Do We Put the Fire Station?

5.2 Heuristic Techniques for Vehicle Routing

5.3 Some Questions of Scheduling

5.4 Cleaner Streets

5.5 Exercises

5.6 Notes and Remarks

Postscript Urban Growth Models

References

Appendix A Linear Programming

Linear Programs

Feasible Sets and Optimization

The Simplex Method

Artificial Variables

Duality

Transportation Problems

Notes

Appendix B Integer Programming

Set Covering

Unimodularity

Notes

Appendix C Random Processes

Poisson Arrivals

Queueing

Some Special Cases

Notes and Remarks

Appendix D Nonlinear Optimization

The Penalty Argument

An Important Special Case

Duality

Notes

Appendix E Graphs, Minimal Trees, and Shortest Paths

Notes

Index

Details

No. of pages:
234
Language:
English
Copyright:
© Academic Press 1977
Published:
Imprint:
Academic Press
eBook ISBN:
9781483267104

About the Author

Edward J. Beltrami

About the Editor

J. William Schmidt