Models for Public Systems Analysis

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.

Contenu

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