Models for Public Systems Analysis

Models for Public Systems Analysis

1st Edition - January 28, 1977

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  • Author: Edward J. Beltrami
  • eBook ISBN: 9781483267104

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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


    Introduction Some Thoughts on Mathematics and Public Policy


    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


    Appendix A Linear Programming

    Linear Programs

    Feasible Sets and Optimization

    The Simplex Method

    Artificial Variables


    Transportation Problems


    Appendix B Integer Programming

    Set Covering



    Appendix C Random Processes

    Poisson Arrivals


    Some Special Cases

    Notes and Remarks

    Appendix D Nonlinear Optimization

    The Penalty Argument

    An Important Special Case



    Appendix E Graphs, Minimal Trees, and Shortest Paths



Product details

  • No. of pages: 234
  • Language: English
  • Copyright: © Academic Press 1977
  • Published: January 28, 1977
  • Imprint: Academic Press
  • eBook ISBN: 9781483267104

About the Author

Edward J. Beltrami

About the Editor

J. William Schmidt

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