EFFECTIVE PLANNING AND ALLOCATION OF FIRE PREVENTION MANPOWER A THESIS ...

189 Pages·2008·3.81 MB·English

EFFECTIVE PLANNING AND ALLOCATION
OF FIRE PREVENTION MANPOWER
A THESIS
Presented to
The Faculty of the Division of Graduate
Studies and Research
by
David Michael Miller
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
in the School of Industrial and Systems Engineering
Georgia Institute of Technology
November, 1973
EFFECTIVE PLANNING AND ALLOCATION
OF FIRE PREVENTION MANPOWER
Approved:
Russell G. Heikes
j
P C
James C. SnyderU
Date approve! by Chairman:
ACKNOWLEDGMENTS
The successful completion of this research was aided by the con­
tribution and assistance of several people. I am especially indebted to
my advisor, Dr. David E. Fyffe, for his encouragement and guidance
throughout my graduate program. He has made a significant contribution to
the "learning experience" in my graduate education.
I am also indebted to Drs. Paul S. Jones, Russell G. Heikes, and
James C. Snyder for their critique of the research and their helpful
comments.
This research could never have been conducted without the coopera­
tion and participation of the Atlanta Fire Department. Every member of
the department contributed to the research effort. However, I am par­
ticularly grateful to Chief P.O. Williams and Chief J. B. Gossett for
their continuous support and assistance. Also, special thanks must go to
all members of the Fire Prevention Bureau for their efforts in data
gathering and education of this author.
Finally, I would like to acknowledge the contribution to the
research of my wife, Jennie. Her patience and support throughout my
graduate program were essential, and for this I am extremely grateful.
iii
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS . ii
LIST OF TABLES vi
LIST OF ILLUSTRATIONS vii
SUMMARY viii
Chapter
I. INTRODUCTION 1
Purpose
Problem
Approach
Scope
Presentation
II. BACKGROUND
The Atlanta Fire Service System
Fire Extinguishment
Operations
Planning Problems
Fire Prevention
Operations
Planning Problems
Relevant Literature
The Research Project
Purpose
Scope
Activities
Modelling
Data Collection
Data Analysis
III. PLANNING PROBLEMS
Determination of Inspection Rates
Criteria
Constraints
iv
Chapter Page
III. PLANNING PROBLEMS (Continued)
Determination of Inspection Districts
Criteria
Constraints
Determination of a Schedule for Inspections
Criteria
Constraints
Interelationship of Problems
IV. DETERMINATION OF INSPECTION EFFECTIVENESS 47
Effectiveness Measure
Estimation of Effectiveness
Model of Fire Incidence
Estimation of Model Parameters
Objective Estimate
Subjective Estimate
Combining Objective and Subjective Estimates
Effectiveness Function
V. DETERMINATION OF INSPECTION RATES
AND INSPECTION DISTRICTS . . .. 81
Model
Modelling Approach
Notation
Mathematical Model
Solution Procedure
Approach
Algorithm
VI. DETERMINATION OF A SCHEDULE FOR ROUTINE INSPECTIONS. . . .
Model
Notation
Mathematical Model
Solution Approach
Weekly Updating
VII. APPLICATION OF RATE-DISTRICT MODEL TO ATLANTA 127
Parameterization of Model
Approach
Interrelationship of Data Sources
Solution Results
Use of Model and Results
V
Chapter Page
VIII. RESULTS AND CONCLUSIONS 146
Summary
Conclusions and Recommendations
Extensions
APPENDIX I 154
APPENDIX II 165
APPENDIX III 169
BIBLIOGRAPHY . 175
VITA 178
vi
LIST OF TABLES
Table Page
1. Solution Inspection Frequencies 14-2
2. Fire Count from Historical Data 166
3. Fire Count from Experimental Data 166
4. Effectiveness Function Slopes 168
5. Model Parameters . 171
6. Current District Assignments 172
7. Proposed District Assignments 173
8. Census Tract Numbering System • 174
vii
LIST OF ILLUSTRATIONS
Figure Page
1. Organization Chart for the Atlanta Fire Department. . . .. 8
2. Current Inspection Districts in the City of Atlanta . . .. 32
3. Examples of Piece-Wise Linear Approximation
of Effectiveness Function 76
4. Determination of Effectiveness Function 80
5. Flow Diagram of Districting Procedure 112
6. Allocation Matrix for Scheduling Problem 121
7. Parameter Estimation Routines and Data Sources 139
8. Solution Inspection Districts 143
9. Current Inspection Districts 144
10. Coding Form for Inspections 156
11. Coding Form for Fires 157
12. Format for Coding Form for Fires 158
13. Supplemental Fire Report 163
viii
SUMMARY
The purpose of this research was to structure several important
decision problems concerning allocation and management of municipal fire
prevention manpower, and to develop the necessary models and solution
procedures to analyze these problems. The operations of the Atlanta
Fire Department were used as the basis for structuring these problems
and for formulating their mathematical models. The methodology devel­
oped in the research was applied to obtain solutions for these problems
for the Atlanta Fire Department.
Three problems were considered in the research. These are (1)
how often to conduct scheduled, routine inspections each year in each
type of building occupancy in each area of the city, (2) how to divide
the city into districts for inspectors, and (3) when to schedule each
routine building inspection. These three problems are interrelated, but
the approach taken in this research was to model the first two problems
together and treat the third separately. The mathematical models
formulated for these problems are mixed integer programming problems.
A piece-wise linear approximation is used in the objective function of
the problem of determining inspection rates and districts.
A heuristic procedure was developed to obtain a solution to this
first "Rate-District" problem. The procedure utilizes "knapsack" prob­
lem logic and an extension of the political redistricting scheme of Hess
and Weaver in obtaining a set of inspection rates and districts. A
solution procedure was not developed for the scheduling problem.
Extensive data-gathering activities were undertaken by the
Atlanta Fire Department to obtain the parameter estimates necessary to
apply the model and solution procedure to obtain inspection rates and
districts for Atlanta. This effort included a controlled experiment
designed to provide an objective estimate of the effectiveness of rou­
tine building inspections. The measure of effectiveness used is the
annual expected number of fires in each type of building occupancy in
each area of the city, which is a function of the annual frequency of
inspection. The experimental estimates were combined with subjective
estimates provided by management to obtain a composite estimate of the
"effectiveness function" for inspection frequency.
The results of the experiment do not indicate an increase in
effectiveness of higher inspection frequencies over lower frequencies.
However, the experiment is to be continued for an additional six months
to provide more conclusive data.
A set of inspection frequencies and inspection districts were
obtained from the Atlanta data and presented to department management
for consideration. The districts found were significantly better than
the current districts used by the department in terms of the balance of
the assigned annual workload among the districts. However, the average
compactness of the proposed districts is slightly greater than the cur­
rent districts (primarily due to two "single area" districts currently
in use). It was recommended that the department continue data gathering