operations Research and Economics Division

0

SENSITIVITY ANALYSIS OF

CIVIL DEFENSE SYSTEMS AND COMPONENTS

FINAL REPORT VOLUME I

R-OU-157

A COST-EFFECTIVENESS COMPUTER PROCEDURE FOR

OPTIMUM ALLOCATION OF FALLOUT SHELTER SYSTEM FUNDS

UNDER UNIFORM OR VARIABLE RISK ASSUMPTIONS

CLEARING G1H0 11.FOR FEDERAL SCI1'i:'

TE(O"NIrA.L INF,Hardeop ;

•,.. c( c' • • : L

"L ' .... ¾" ' a:. "" u

Prepared for

Office of Civil DefenseUnited States Department of the Army

under

Office of Civil Defense Contract No. OCD-PS-64-56OCD Subtask 4113ERTI Project OU-157

R RESEAR-CH TRIANGýLE INSTITUTE DURHAM, NORTH -CAROLINA

THE RESEARCH TRIANGLE INSTITUTE

Operations Research and Economics Division

OCD Review Notice

This report has been reviewed in theOffice of Civil Defense and approvedfor publication. Approval does notsignify that the contents necessarilyreflect the views and policies of theOffice of Civil Defense.

Distribution of this document isunlimited.

RESEARCH TRIANGLE INSTITUTEDurham, North Carolina

FInaL REPORT VOLUME

R-OU-157

A Cost/Effectiveness Computer Procedure forOptimum Allocation of Fallout Shelter System Funds

Un..er Uniform or Variable Risk Assumptions

by

Floyd M. Guess

October 1, 1965

Prepared for

Office of Civil DefenseUnited States Department of the Army

underOffice of Civil Defense Contract No. OCD-PS-64-56

OCD Subtask 4113ERTI Project OU-157

FINAL RLPORT VOLLUMU I

R -CW'-157

A Cost/Effe-c;i%.:..ss Co.nputor PrfcodrrOptimum Allocation of Fallout Shelter Svsten Funds

Ende i L'ni for: or Var i a -!)I Ris k As's',Ip t i on

Prepared for

Office of Civil Def:-.LtcUnited States Depa!Lrient of the Army

underOffice of Civil Defense Contract No. OCD-PS-64-56

OCD Subtask 4113ERTI Project 0U-157

by

Floyd M. Guess

RESEARCH TRIANGLE INSTITUTEOperations Research and Economics Division

Post Office Box 490Durham, North Carolina

Approved by:

Edgar[A. Parsons, Director

I October 1965 R. S. Titchen, Deputy Director

I ----- - - .,---s - -a.. ,- , -.. M- ..r

FOREWORD

This is Volume I of three separately bound volumes in which are reported the

research completed under the general terms of the Office of Civil Defense Subtask

Number 4113E, "Sensitivity Analysis of Civil Defense Systems and Components."

The research of the authors was very ably supported by Mrs. Helen Anderson and

Miss Mary B. Woodside. Mrs. Anderson is credited with the programming reported in

Appendix D, "The Risk-Oriented Allocation Program." Miss Woodside performed the

calculations reported in several of the Appendixes. Philip McMullan and Robert

Brooks are acknowledged for their valuable assistance in the preparation of the final

report.

iii

ABSTRACT

The dynamics of civil defense planning and systems evaluation require a pro-

cedure that yields approximate answers to questions concerning effective fallout

shelter improvement programs. To accomplish thýs, a computerized model for the

CDC 3600 is developed and demonstrated for OCD Region 6. The model permits an

evaluation of shelter improvement programs against any fallout environment, but it

is particularly valuable when RISK-type expressions of the probable fallout environ-

meuL are used as inputs. Using detailed data from the National Fallout Shelter

Survey and equally detailed estimates of the probable fallout hazard in a small area

(counties, in the demonstration), the extent to which an area's population is in-

adequately protected is determined. Fallout shelter system funds are then allocated

to areas of need in an optimal manner. The allocation employs shelter cost data

obtained from Ph;se 2 of the National Fallout Shelter Survey on ventilation and

shielding impr.•vements. E.stimated costs for package ventilation (PKV) and shelter

in new constructio- a:z. also employed in the demonstration in OCD Region 6. In all,

14 cost studies are run, using selected combinations of the budget level, the fall-

out risk 'evel, etc. The demonstration shows the practicability of carrying out

such largiý-scale cost/effectiveness analyses. It demonstrates a great need for

reliable input data--particularly for the unit costs and available numbers and

improvement options. The model and associated computer program not only provide

tools of great value to the decision-maker, but they also r-nphasize the criticality

of his assessment of factors within and outside the model (e.g., planning horizon,

impact of future changes in the expected attack environment, legacy value of existing

shelter programs, etc.). Future work includes extending the model to include direct

effects and performing more extensive demonstrations of the model.

v

ABS T ACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . .

TA~L,. Ut~ (AC;NTL.,NT:¢ . . . . . . . . . . . . . . .

LIST OF ABLES . ...

LIST OF FIGLRES . . . . . . . . . . . . . . . . . . . . . . . . . . ..

I. INTRODUCTIO0', . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

II. GENERAL DESCRIPTION OF MODEL .................... 2

III. APPLICATION OF T1!E MODEL TO A CIVIL DEFENSE REGION ........ ......... 3

A. General . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

B. Allocation of Shelter Spaces .............. ... .................. 3

C. Selection of Level of Risk .................. ................... 4

D. Determination of Effective Shelter Spaces ........... 4

E. Determination of Cost for Shelter Improvement ......... 5

F. Cost foi New Shelter ..................... ...................... 6

G. Allocation of Funs ...................... ...................... 6

11. Variations in Input Data ................... .................... 7

IV. RESULTS .............................. ............................... 8

V. ANALYSIS OF RESULTS .................. ......................... ..

A. Relationship of Costs and Level of Risk ..... ............ ....

B. Limitations of Phase 2 Data ........... ................. .. 13

C. Effect of Inclusion of Residential Basements in Shelter Data . . 4

D. Effect of Revised Protection Factors ...... .............. .. 14

vii

TABLE OF CONTENTS (CONTINUED)

E. Effect of Reduced Cost for Ventilation ...... ............ .. 16

F. Effect of Overcrowding of Shelters .......... .............. .. 17

VI. CONCLUSIONS AND RECOMMENDATIONS .............. ..................... 17

A. Introduction ...................... .... 17

B. The Introduction of Prompt Effects into the Model ........... .. 18

C. Application'Of the Methodology to Shelter System Programming , 22

D. Critical Decisions in Risk-Oriented Programming ... ......... ... 23

REFERENCES TO VOLUME I .............. ................................. 25

Appendix A - The Algorithm for Allocating CD Fallout Shelter Funds . . .. A-1

Appendix B - Relationship Between Population Inadequately Shelteredand Casualties ................. ....................... ... B-l

Appendix C - State Summaries of Case Studies Using the Risk-OrientedAllocation Program ............... ...................... ... C-I

Appendix D - The Risk-Oriented Allocation Program ............. D-1

viii

Ltoý OF iAiýL,E,ý

,isti' i i o ..• S ,-' r a s , d n- c i-' :prc- bi-- a-v

if -S ,1 l".p ,, - •,c) r a- ".' tr t . L-0 , , a .

RT T u: c I A! Ia . . .~ . .P.'-)[i, kuý;i w al .'I ; .:" r- ,f Casv t ;- t]its I-vin m P, Ri.• -'r rt ,"•d

All cation Progra. .. . . . . . . . . .. . .. . .

V Eifecý ot PossibLe Bias tn Existing Struct~urt PF Eati:. at

TWO MaX•ia '. Al. . I. CP1t .ev.ls . . . .. . .

VI Comparionr, of Effect of 25 Percent Overcrowding (95 percentrisk lc.el, Max ERD 100r) ................... 17

VII Categorization of Shelters by Vulnerability Index (VI) andProtection Factor (P F) . . . . . . . . . . . . . . . . . . . . .

C-I State Su,--rarv of Caset Studies Lsing ýie Risk-Oriented Allocation

Programý (State 1)l. .................. ........................ C-2

C-TI State Surunary of Case Studies Using the Risk-Oriented AllocationProgram (State 2) ...................... ........................ C-3

C-Ill State Sutainary of Case Studies Using the Risk-Oriented Allocation

Program (State 3) ................ ........................ C-4

C-TV Ftate- Summary of Case Studies Using the Risk-Oriented Allocation

Program (State 4). ................. ........................ C-5

C-V State Sumrary of Case Studies Usinf, the Risk-Oriented Allocation

Progra Satea .. 5) ............. ........................ C-6

C-Vl State Sunwmary of Case Studies Using the Risk-Oriented Allocation

Program (State 6) ................. ........................ ... C-7

C-WVI State Sunrar-y of Case Studies Using the Risk-Oriented AllocationProgram (State 7)...... . ...... ........................ ... C-8

C-Viii State Sunrwarv of Case Studies Using the Risk-Oriented AllocationProgram (State 8) .................. ........................ ... C-9

D-1 Illustration of Inut Data ............ .................. ... D-2

D-If Illustrative Risk-Oriented Shelter Budget Allocation .... .... D-S

ix

LIST OF FIGURES

Figure

1 Cumulative Probability Distribution of Unshielded ERD in a

Geographic Area ........... ................

2 Cost-Effectiveness Curves for Expenditures for Fallout Protectionin Region 6 at the 50 and 95 Percent Levels of Risk .......

3 Budget Level vs. Population Ineffectively Sheltered at TwoLevels of Risk . .......................

4 The Percentage Reduction in Population Ineffectively ShelteredThrough the Use of Residential Basements at the 50 Percent and95 Percent Levels or Risk ................. ...

5 Budget Level vs. Population Ineffectively Sheltered Under StazedLevels of Allowable ERD-Max and Protection Factors ........... ..

A-i Cost/Effectiveness Curves by Area ................ A-

xi

A Cost/Effectiveness Computer Procedure for Optimum Allocation of FalloutShelter System Funds Under Uniform or Variable Risk Assumptions

I. INTRODUCTION

The dynamics of civil defense planning and systems evaluation require a

procedure that will readily yield approximate answers to such questions as:

(1) How many lives could be saved with an expenditure of $1 billion, $5 billion,

$15 billion, or any other arbitrary budget level?

(2) Where should such budgets be expended--by regions, states, metropolitan

areas, counties, and detailed locations--for each assumed budget level?

(3) How and where would the expenditure pattern vary if one assumed that all

parts of the United States were subject to a uniform attack hazard--to a

different attack hazard?

(4) What is the dollar-costing relationship oetween attack hazard, casualties,

and standards of acceptable shelter?

Our approach has been to develop and demonstrate a computerized procedure that

will answer these and related questions under the following constraints:

(1) Use available data, such as the NFSS and National Location Code, wherever

feasible.

(2) Use existing computers, programs, and planning techniques used by OCD,

such as RISK or NAHICUS, wherever feasible.

(3) Provide means for readily accepting new or improved data, and for using

interim estimates where critical data deficiencies exist.

(4) Concentrate initially on cost and effectiveness of a fallout shelter

system, but include provision for extending the system to blast and other

prompt effects considerations.

(5) Provide means for accepting data on all civil defense subsystens of measur ,le

significance.

-1-

In the event of a nuclear attack upon the United States, some areaE may be

assumed to have a higher probabiliLy than others of experiencing hazardous levels of

fallout; such an assumption may provide a priority basis for the allocation of funds

for improving the fallout shelters system. Allocation of funds on this basis can

be said to be "risk-oriented". No presumption is made of OCD acceptance of a "risk-

oriented" policy for allocating funds. However, it is suggested that such an approach

will be useful in determining optimal fund allocations against which existing and

future plans may be (.:valuated.

In this volume, a risk-oriented procedure for evaluating the effectiveness of a

spectrum of alternative budgets for fallout shelter system improvement is described

and applied to a specific region of the United States. The effects of variations

in the options Chat are available to decision-makers, and other inputs to the alloca-

tion procedure, are analyzed. Extension of the allocation procedure from fallout

shelter syster costs to blast protection and other CD system costs is also discussed.

II. GENERAL DESCRIPTION OF MODEL

The general procedure for cost/effectiveness evaluation of fallout shelter

system budgets advanced here is as follows:

(1) The populations of given geographic areas are assigned to existing shelter

spaces within their respective areas (standard location, county, or other

area), always utilizing all of the higher PF (Protection Factor) shelters

first.

(2) On the basis of one or more fallout environments, determinsd by probabi-

listic programs such as RISK II [Reference 1], the estimated Equivalent

Residual Dose (ERD) for the occupants of each type of shelter is calculated.

('7 Spaces are considered effective in which the resultant Maximum ERD is be-

low a predetermined level (e.g., 200r). Areas in which some or all of

the population are not effectively sheltered become eligible, for compu-

tation purposes, for funds for improved or new shelters. (In this report

"improved" shelter spaces are those indicated in the Phase 2 NFSS data

to be improvable by ventilation or shielding.)

(4) The specific costs for possible ways of converting ineffective shelter

spaces into effective shelter spaces are determined for each of the areas

under consideration. Data from Phase 2 of the National Fallout Shelter

Survey provide such information. Estimated costs for creating new

-2-

effective sheIlter spaces are utilized also.

(5) Funds for improved and/or new shelters are allocated to areas having inef-

fective spaces; funds are provided first for the least costly alternative,

for adding effective shelter spaces, regardless of the area in which the

alternative exists. The process of moving to the next least costly

alternative continues until all of the assumed budget is expended, or ut.-

til all possible alternatives for improving existing shelters are exhausted.

(6) The computer program and model are flexible and versatile. At the option

of the decision-maker, the following inputs may be varied: (a) budget

level, (b) degree of risk or hazard, (c) definition of acceptable shelter,

and (d) new shelter construction costs.

This procedure maximizes the number of shelter spaces that can be made effect:'e

for a given amount of money and for an established level of fallout radiation. Th,

effects of changing the level of fallout radiation on the optimal allocation of

funds will be considered in Section V of this volume. The possibility of adapting

this fallout shelter system cost allocation procedure to include planning for

direct weapons effects will be described in Section VI.

III. APPLICATION OF THE 11ODEL TO A CIVIL DEFENSE REGION

A. General

For demonstration purposes, a risk-oriented method of allocating fu:nds was

applied to OCD Region 6, using the National Fallout Shelter Survey data. A CDC

3600 computer was used to perform the various allocation calculations. The mat!.

matical forniulation is given in Appendix A. A description of the computer prog.

is given in Appendix D.

B. Allocation of Shelter Spaces

The fallout shelter status in the eight states of Region 6 was determined m

Phase 2 data oL the NFSS. The basis for allocation of shelter :-ace was the cc •y.

That is, the population of a county had to be assigned to shelters within the c.-- -ty,

even though mrre effective shelters were not being used in an a>:acent county.: It

was assumed also tha: there would be no travel in fallout.

i/ Although a county basis was used in thc reported study, the -ogram a--d cor:; -

tion procedure ca:. be used for any geographical-political a--- for which da:are available.

vhe constraint against population niovemeiLt outside thc county may bt, unreal is tic

and ýie number of persons sheleered, therefore, may be underestimated. On the other

hand , if the counties are lar:-e and/or the time between warnirng and the arrival of

fallout is short, the nu1mber of persons .heltered can be overestimated.

C. S-lectcon of Level of Risl-

The fallout environment that would occii: in an- given locality is not predicta-

ble with certainty, and conceptions of ere-,-y-preferred target systems change as de-

fensive and offensive capabilities change. For analysis purposes it is assumed that

areas of the United States differ in probability of contamination by fallout and

that they can be expected to retain these differences for significant periods of

time. Information about fallout environments based on possible attacks, weapons

characteristics as determined from intelligence reports, and probable wind condi-

tions are available from many sources. Information about series of fallout environ-

ments has been compiled from an OCD source for use in the present demonstration. It

is relatively easy to determine from this compilation the proportion of the possible

attacks which result in a given level of radioactivity within a spt ific area.-'

This radioactivity can be expressed in terms of the ERD of an unsheltered population

within a given area. Thus, a probability curve for occurrence of given ERD's can be

prepared; such a curve is shown in Ffigure 1, Cumulative Probability Distribution of

Un:hielded ERD in a Geographical Area.

In Figure 1, an unsheltered EF.D equal to or less than IQOOr has occurred in

0.5 of the hypothetical attack conditions, and an unsheltered ERD equal to or less

than 3000r has occurred in 0.95 of the hypothetical situations. Conversely, in only

0.05 of the hypothetical situations would an unsheltered ERD be greater than 3000r.

In the present illustration, the 0.5 and 0.95 levels from RISK-type calculations

were used as the fallout environment in each county. These levels are referred to

as the 50 percent and 95 percent levels.

D. Determination of Effective Shelter Spaces

An effective shelter space is defined as one in which the ERD (as defined by

RISK) for a person in this space is below a given maximum. The ERD experienced is

determined by dividing the ERD for an unsheltered person, based on the probabilistic

fallout environment discussed above, by the protection factor (PF) of the shelters

to which population is assigned.

Other sources of fallout probabilities could also be used,

-4-

UP ERD C 3. 5

SUI- I

No"%

U

S0. 5-- - P -ERD 1000 C .50

, -IIOOr 20 0Or 30 0 nr

ERD Factor (G) in Roentgens

(The unshielded ERD values in the application of the model toRegion 6 were computed as explained in Reference '1 , in whichan approximation of ERD from a total dose equation is employed.)

Fig. 1. Cunu~laLivt ProbabiliLy DiLtribution of Unshielded ERDin a Geographical Area

This maximum allowable, ERD can be set arbitrarily. However, there arc2 at least

two reasonable values, lOOr and 200r, which might be chosen as criteria for deter-

mining the effectiveness of a shelter space. An ERD of lO0r is given by the linear

approximation of the dose response curve for casualties fReferences 2 & 3 as the

threshold below which casualties willAoccur. An ERD of 200r represents the threshold

below which fatalities will not occur .Refcrences 2 & 3 . (See also Appendix B.)

Both the 1OOr and 200r levels were used in the allocation program described here.

E. Determination of Cost for Shelter Improvement

Phase 2 data of the National Fallout Shelter Survey were used as the basis of

the costs for this application of risk-oriented allocations. Table I, Existing

Fallout Shelter Spaces and Spaces Improvable byv Shielding and Ventilation, is an

illustration of the type of cost data provided for a typical county.

"Improvable by Shielding" are existing PF Category 2 and 3 spaces t.lat can be

upgraded to PF Category 4 or better by shielding. "Spaces Improvable by Ventilation"

are those that can be added (by increasing the capacity of existing shelters) by

ventilation. The average costs of either of these improvements range from $1.00 to

$31.00 per space. These costs are representative for most of the counties in Region 6.

-5

TABLE I

Existing Fallout SheLter Spaces andSpaces Iripro..ahtc ny Shieding and Ventilation

Protection Factor All Ex isting Spaces Improvable Spaces Improvable

__ __ _ Spa ces S1, i lding by VmnrttiIation

Categorv PF N- T'.her Ttal S Number Ttal $

8 1000- 6339 9 C 14167 46558S 5(10-1000 1 164 3, 0 0 21693 21693

6 250- 499 98 0 0 22 6825 150- 249 88 0 0 303 24244 100- 149 85 0 0 333 19983 70- 99 301 301 4214 0 02 40- 69 2013 849 20451 0 01 20- 39 0 0 0 0 0

The minimu,:, value of the PF range was used in the example application of thepiocedure.

There appears to be no statisticaily significant correlation between cost and

level of protection of either new or improved shelter spaces. Most of the spending

alternatives involved creatinL new shelter spaces by ventilating existing shelters,

and ventilation costs are independent of the protection factor of the shelter. 3 -

The effect of this will be shown in Section V.

F. Cost for New Shelter

In addition to the possibility of improving existing shelters, an alternative

was included for providing shelter spaces under an incentive or other new construc-

tion program. These spaces would have a Pl Category 4. protection factor or better

(PF > 100). To facilitate computation in the absence of reliable data, it was

assumed that the numbeir of spaces available under this option amounted to a maximum

of ten percent of each county's population. For computation and demonstration pur-

poses, these spaces were arbitrarily estimated to cost $25.00 per space. Any costs

ray be used in the computation procedure.

G. Allocation of Funds

Using the CDC 3600 computer, the allocation of funds was progranmmed in such a

manner that the least costly means available for making an ineffective space into

/ It should be noted that Phase 2 data 4ixnclude some shelter spaces which can beadded only by first shielding and then ventilating the shelter. These spaces arenot included in the improvement alternatives in the input data used in this study.

"-6-

an effective one was always us:ed first. No funds were allocated where there would

be no shelter that neeled improvement, or where shelter improvements would still rt-

sult in an ineffective shelter at the assumed fallout level. As shown in the math,-

matical description of the model (Appendix A), this procedure leads to an optimal

allocation of funds--that is, the maximum number of effective spaces added for a

given budget.

'he allocation was constrained by a fixed budget in some cases and in other

cases the funds were unrestricted.

It should be noted that the cost of stocking the shelLers has been excluded in

this application of allocation of iunds. This would add $2.42 to the cost of each

added shelter space FReference 41, but would not affect the computation procedure

or relative results.

H. Variations in Input Data

Variations in the risk level (95 and 50 percent), in the maximum allowable ERD

(100r and 200r), and in budget constraints have already been noted. For sensitivity

analysis purposes, 14 case studies or calculations were made using the CDC 3600 com-

puter. Among the factors varied for analysis purposes are the following:

1. Residential Basements and Category I Shelter

In most of Lhe 14 computations, residential basements and PF Category

shelters were incruded. The number of residential basements was estimated cn

the ba is of selected SMSA's [Reference 5] and extrapolated over the entire

state for most of the states in Region 6. Where SMSA residential basement d6-a

were not available for a given state, estimates were made based upon neighbo ri

states. The residential basements were assumed to be available at no cost

to have a PF of 10.

In order to measure the effect of the residential basements and PF Cati- :)rv

1 shelter on the allocation model, residential basements and PF Category 1 v :0

excluded in another case.

2. Possible Underestimations in PF in the NFSS Data

Protection factors from the National Fallout Shelter Survey data were .

creased arbitrarily in order to measure the effect of a possible conservativ.

bias in the calculation of those data. Table II, Shelter Type, Protection

Factor, and Revised Protection Factor shows these protection factor increase

Possible underestimation in PF in the NFSS data was examined in Refercince (61

vised PF in Table II employed the estimates of conservative bias repo: ted in

reference.

-7-

[ABL F 11

Shelter Type, Protection Factor, and kc.isved P1ot ,..tion Factor

Protection Factor Re ised PF

H~omes 2

Res ident B ase 1Bas , ts 10PF CaLtgory 1 20PF Category 2 40 60PF Category 3 70 125PF Category 4 i+Oo 18PF Category 5 150 250PF Category 6 250 350PP Category 7 500 600PF Category 8 1000 1200

Lower limit of the PF Category for NFSS shelter categories.

3. Overcrowding of Shelters

To determine the effect of possible overcrowding of sheltt -s, a case stuUy

was designed whereby the .'oDacities of both existing and potential shelters

were increased by 25 percent.

4. Variations in Cost of Ventilation

In one case study, the impact of low cost ventilation devices was examined

by assigning a uniform cost of $3.00 to each space that could be made effective

bv ventilation.

IV. RESULTS

The progra- produced for each county and each combination of input data (RISK-

level, maximum allowable ERD, residential basements included or excluded, etc.) the

following data: (1) the total effective spaces added, (2) the average cost per space

added, and (3) the total cost of both new and improved shelters. Table III, Illus-

trative Risk-Oriented Shelter Budget Allocation, is an example of the output data.

(rhis output format is explained in detail in Appendix D, Section A-4.) In this

example, the funds available were limited to a $20 million budget.

Table IV, Regional Summary of Case Studies Using the Risk-Oriented Allocation

Pro.A..M, summarizes all fourteen cases in which the allocation model was utilized

(see also Appendix C). It should be noted that even in the cases where the budget

was not limited, some of the population would still be ineffectively sheltered.

This is because an insufficient number of new or improvable spaces was identified.

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41C 0.) QJ Ul 0 ~ -~to A(j. W U'0 (12 00' ýt c~ " O -4-4 ).Cý 0) (Q 0 w w 0s 34 u W0 r.

caU> z 4 a4C FAA V Q -4 ziCl) zW 0 0U : U AJ -4 U)(M

.. 4 ~*~4 * 4 L) 4 k W A4 *0J-C r.

4). U)U w ) 4 ýurz 6 8 Q 0(1 0

P4.

41-

u) U-i i- CI if Lf) (n) 00 r-- 0 0 0 N -4

C -4 - 0 1 1; c; 0 4 If) CO 0 C4! '0 -t ') 0; i a)w) C.: C'4 M' -4 M 4 M~ "' -4 NJ ,-4 M ~ .- d V) CN4 -4

ci 0

CA)

QU L. 4-- rn Cn Cn V (n -A -4 ) to En Co' En V3 (n cu Cd) U. 4. Lu >.. *.. C. U) 4. U). U) 4. f) U

Ca

I., V) -~4

4 ~0 0000 00 0 00 0 0 0r0.0(U~0 0000 00 0 00 0 0 0 0 C;

C '' UX 1 - -4 ' C-i .4 "I - -4 " 4 -4 d -4 ý4 -4 C X.')

jU)

CIO

.0.-r4 F-4.n C) It L0 I 0 IA) IA IA IA 0 UA 0 W%) It) I

C14 m% I) a, I) a% (7% o% 0s LA m' Un ON 0'A 17S C

cýj -4- .0

-~4 U)

- ,4 C-4 fn) 'n 'o-. r-- 00 O 0, a - VNC . ~ )

-10-

Figure 2, Cost/Effectiveness Curves for Expenditures for Fallout Protection

in Region 6 at the 50 and 95 Percent Levels of Risk, illustrates the increasing rate

of expenditure as the allocation proceeds from the least to the more costly improve-

ment alternatives. Limits are established by the maximum number of spaces available

for improvement as determined in the Phase 2 data.

Computations were also made of the cost of shelter for all of the population in

Region 6 under the 50 and 95 percent levels of risk. Since the numbers of alterna-

tives for improved and r•w shelters included in the allocation model were much

smaller than the numbers of the population with ineffective shelter, it was necessary

to estimate costs of additional means for providing shelter space. An arbitrary cost

of $50.00 was assumed for each additional effective space added. Figure 3, Budget

Level vs. Population Ineffectively Sheltered at Two Levels of Risk, illustrates the

increase in budget with decreasing numbers of population ineffectively sheltered

when this assumption is used.

V. ANALYSIS OF RESULTS

A. Relationship of Costs and Level of Risk

It is seen in Figures 2 and 3 that under the 95 percent risk level with its

higher average levels of radiation, more spaces will be ineffective than under the

50 percent risk level. Consequently, more spaces are eligible for improvement funds

in the allocation model, and the total cost will be greater. However, even after

all available improvable spaces are used, the number of persons ineffectively

sheltered under the 95 percent risk level is still much greater than under the 50

percent risk level. Thus it is apparent that budget requirements are extremely

dependent upon the level of risk that is assumed.

The influence of the level of risk that is assumed on costs can be clearly

seen in Figure 3, in which the estimated budgets for providing for all of the popu-

lation in Region 6 are shown. Under the 95 percent level of risk, a budget of

approximately $375 million would be necessary; under the 50 percent level of risk,

the budget would be less than $100 million.

It is important to note that when the budget is unrestricted there is no great

difference in average cost per space added regardless o-' which risk level is assumed.

This is due to the fact, as pointed out earlier, that there is no correlation be-

tween the cost and the PF of an improvable shelter space. Thus, while fewer spaces

need to be improved under the 50 percent risk level, their range of cost approximates

that for the greater number of spaces needing improvement under the 95 percent risk

level.

- 11 -

Maximum N,'umber of AvailableEffective Shelter Spaces

,4)

• J P !ERD, 0.50

P jERD -_ c 0.95

1.0 2.0 3.0Effective Spaces Added

(Millions)

Fig. 2. Cost/Effectiveness Curves for Expenditures fur Fallout Prutection

in Region 6 at the 50 Percent and 95 Percent Levels of Risk(Allowable ERDMa = 100r)

- 12 -

'.FSS Pr~t-t is'ý "Allo.iablc ERD = -ir

7 3rOO

00(

o 995 Level e f Risk

20t)

100

"@\\ %50' Level ot Risk

Populatior. Ineffectivel, Sheltered in Millions

.

Points at which a fixed $50 per space was used for eachfurther reduction of population ineffectively sheltered.

Fig. 3. Budget Level vs. Population Ineffectively Shelteredat Two Levels of Risk

When the budget is limited so that all spaces cannot be improved, the averagc

cost per space is higher for the 50 percent risk level than for the 95 percent risk

level. For example, the average cost is $9.69 for the 50 percent risk level (Case 9)

and $5.10 for the 95 percent risk level (Case 7); see Table IV. At the 95 percent

risk level, the budget is exhausted on the wmre numerous low cost. opportunities be-

fore allocation can be made to higher cost improvements.

B. Limitations of Phase 2 Data

In Case 4 of Table IV, the most optimistic case from the perspective of popula-

tion effectively sheltered, there were still more than one million persons in

Region 6 who could not be assigned to effective shelters. This, however, does not

mean that there are not unidentified spaces in Region 6 that could be made effective.

For a variety of reasons, many buildings or areas were excluded from the NFSS.

- 13-

Vhe rough estimate figure of $50.00 each for additional spaces is used to

illustrate differences of ultimate costs (costs of 100% effective sheltering) under

the two risk levels. The identification of more potential spaces and their associated

costs would be necessary to make a more complete risk-oriented analysis of Region 6

budget requirements.

C. Effect of Inclusion of Residential Basements in Shelter Data

Figure 4, The Percentage Reduction in Population Ineffectively Sheltered

Through the Use of Residential Basements at the 50 Percent and 95 Percent Levels of

Risk, shows that with a 50 percent risk level, inclusion of residential basement

spaces decreases the unsheltered population by about five percent in one state and

by nearly seventy percent in another. At the 95 percent risk level, lesser changes

are affected by including residential basements in calculations of shelter effective-

ness. This indicates that residential basements can be extremely important in

survival planning in some states, particularly when lower risk and fallout levels

are considered.-5 5

D. Effect of Revised Protection Factors

The effect of using protection factors less conservative than those of the

NFSS on numbers of people considered ineffectively sheltered is shown in Table V.

Fven before expenditures, approximately 1.5 million more persons in Region 6 would

be considered effectively sheltered under the 95 percent level of risk if the less

conservative factors were used.

TABLE V

Effect of Possible Bias in Existing Structure PF Estimatesat Two Maximum Allowable ERD Levels

Population Ineffectively Sheltered (millions)

Max. Allowable Max. AllowableERD = lOOr ERD - 200r

NFSS Data Revised PF NFSS Data Revised PF(Case I) (Case 5) (Case 3) (Case 6)

Before Expanditure 9.897 8.485 8.090 6.546After Expenditure 6.881 5.178 4.869 4.179

Se'i Table II.

In Figure 4 the apparent contradiction in the bar graph for state 2 resulted fromthe fact that in most counties of that state, homes with a prztection factor of2 were effective.

- 14 -

44,

qJ

wA

44J.

0 (

ý40 %

"0~~ r..~c

PaI~~~~~~Ia4S~~~0 A1A 3JU oIeno Ouj~na U~~-I a r.

- 15 -

400 Assuming:9511, Level of Risk

Sb

C 300INTSS Protectio. FdL•Lus & uts : LkD = IOu roentgunsc • (Case 1)

C ,

S230

-NFSS Pocion Factors & Naxit~um ERD =200 roent~uno

(Case 3)

.4 Re 'sed Prote ion Factors & Maximum ERD 200 roentgens

(Case 6)1l00

Population Ineffectively Sheltered(in Millions)

Fig. 5. Budget Level vs. Population Ineffectively Sheltered Under

Stated Levels of Allowable Maximum ERD and Protection Factors

lhe effect on cost can be seen most clearly when the budget for providing for

all of the population in Region 6 is considered. Under the 95 percent level of

risk, and with a maximum allowable ERD of 200r. the budget based on NFSS protection

factors would be approximately $280 million; based on revised protection factors,

it would be approximately $24•0 million. This is shown in Figure 5, and is based on

the same assumed cost used earlier of $50 per effective shelter space added beyond

those that were included in the allocation model.

E. Effect of Reduced Cost for Ventilation

In Case 14 the cost per space added by ventilation was estimated, for calcula-

tion purposes at $3.00. For Region 6 the averrge cost per shelter space added then

dropped from $10.01 for the comparable case (Case 1) to $3.35. From this it can be

conclhdsd that it would be extremely profitable to find less costly means of pro-

viding ventilation in potential shelters with a high PF. If Region 6 is typical of

the entire country, it seems that no other single step would be more important in

increasing the effectiveness of the present national shelter system.

- 16 -

F. Effect of Cve rc rowd injý of SI i l t--r s

A comparison of the ros,,Its of (asps I and I' i ndi cats - tht&e ,ffs'cts of over-

c:rowding shelters by 25 p~rcunt. Tri.s', effects ar - ,w:! in TalI VI.

TABLE VI

Co'-!parisor of Effect of 2) P( rccu t - \'A(CrcLowding

(9ý) purceuit risk level, fax ERD = 100 roe, jens)

Normal U%,ercrowding(Case 1) (Case 13)

Population Ineffectively Sheltered:

Before Improvement (millions) 9.897 9.184After Improvement (millions) 6.881 5.995

Spaces Added (millions) 3.016 3.189

Total Cost ($ millions) $ 30.2 $ 26.9Average Cost per Space ($) $ 10.01 $ 8.44

It should be noted that the effect of overcrowding shelters by 25 percent does

not increase the number of persons effectively sheltered by 25 percent. This is due

to the fact that in some counties there are fewer than that proportion of the popula-

tion who do not have effective shelter for the fallout environment comparable to the

95 percent risk level. In fact, in some counties, under normal shelter allocation,

there are no persons who are ineffectively sheltered, and crowding the higher PF

sheiters adds no effective spaces.

VI. CONCLUSIONS AND RECONMENDATIONS

A. Introduction

The preceding sections of this volume have described a rational, well-defined

methodology for engaging in risk-oriented programming. Further, by applying the

methodology to Region 6, the practicability of carrying out large scale analyses has

been demonstrated. From the results obtained, it is believed that if risk-oriented

programming were undertaken, the budget allocation model could be used in its present

state to provide guidance in allocating funds and for evaluating the cost/effective-

ness of various policies and proposed CD shelter programs. Examples of current

interest are:

1. The evaluation of government incentive programs for the inilusion of fall-

out shelters in new construction.

- 17 -

2. The evaluation of noLW 'entilation equipment.

3. 1he evaluation of policies regarding the inclusion of various catugories

of shelters (e.g., residential basements and PF Category 1 shelters) as

components in the CD shelter system.

It should he emphaqizcd that the rec.rmended applications of the budgcL allo~a-

tion model in. its present state are directed toward providing guidance to the policy-

r7akers !t the national cr perhaps regional level. Also, the applicatiosti are lirmiLCd

to the "falloitt only" case.

In order to make more detailed and comprehensive analyses at the operating

(local) level, further refinements to the model must be made. Also, additional data

requirements 1.ave been identified which, if met, could enhance the utility of th,

model. These model refinements, and additional data requirements as well as some

special problem areas are discussed at length below.

B. The Introduction of Prompt Effects into the Model

1. General

The allocation model described above has been used exclusively for fallout

shelter development, and prompt effects have been temporarily ignored. Funds

were allocated for the improvement of the fallout shelter posture in some areas

with a high probability of suffering serious direct effects. As a result, the

fallout shelter spaces near the blast area would tend to be ineffective.

Conceptually, the inclusion of prompt effects in the model can be handled

in much the same manner as fallout. The extension of the model to blast effects

is described briefly below to illustrate the concept. Other prompt effects

could be incorporated similarly, if warranted.

The measure of effectiveness to this point has been population effectively

sheltered. Adapting this same measure of effectiveness to the analysis of a

total shelter system (including blast effects) requires only that a new risk

parameter defining the attack environment, principally the blast overpressure,

and a new shelter parameter, vulnerability index, be introduced. In practice

however, other difficulties arise, particularly in data requirements as dis-

cussed below.

2. Shelter Classification fQr Resistance to Radiation and Blast

For the following Jiscussion, it will be useful to define the protection

afforded by a shelter with a blast and fallout classification system as shown

- 18 -

In

I-S

00

e-4

V C14

14'

,4 u

-4J CL

41

~-4 >U

Ci) -

E -4 4. IA

-,-4

4.,4

~0en

41AA

0W0

-4 c

- 2

4. �Modification ol Lxist irg .odcl

As an -xample. assume that ar a viverl livcl of rf' 4 the rPT) factor i -

1O,O00r and tte hiast uverpr,-ssiri is S psi. 'This reprts-res t,'t attack e( -

vironment against which the population in the area mu ,t he protected. If the

allowable Maximum ERD is lOOr, PF Category 4 or better shtltLrs will be elas-

sified as etfecti'.v: Spaces wttu rr-puLct L o fallout. Also, a vulnerabilit'

index of 3 or better riy be classified as effective spaces with respect to

blast. hutS, Lu b= contid'Dd eieLtUive, a shelter space must nme. both re-

quirements. Note that this procedtire allows for the inclutsions of blast shel-

ters a& p-tential i-proveerent alternativtes (given appropriate cost and protec-

tion data).

The fact that there are two criteria for evaluating a shelter space raises

the problem of how to allocate population to shelters within any given area.

In the "fallout only" cases where only one criterion (PF) was used, the problem

was easily resolved by assigning population to shelter giving the highest PF

first priority in assignments. However, when two classifications are used

(PF & Vulnerability Index), the above procedure does not hold and a nuw pro-

cedure must be developed.

The only other change from the existing allocation model is the manner in

which the shelter spaces are determined to be effective or ineffective. Except

for the need to reexamine the location of people relative to shelter in a

prompt effects situation, other procedures remain the same, including the

measure of effectiveness (population effectively sheltered) of the shelter

system. Therefore, the procedure described in Sectior I1 for allocating

shelter development funds remains unchanged, and the optimality of the procedure

is still valid.

5. Prompt Effects Data Requirement

Although the concept has remained unchanged from the "fallout only" model,

several new data requirements have been imposed. Perhaps, the major change

relates to the accumulation unit, or geographical area, whose dimensions equal

the allowable uncertainty in shelter location (or equivalently, the area within

which the attack environment is homogeneous) and over which funds are to be

allocated. In .he case of fallout, it is convenient and plausible to consider

the county as the accumulation unit because the level of downwind fallout could

be considered constant over the entire county. However, when considering blast

overpressure as one of the risk parameters, a much smaller geographic unit must

be chosen for those areas which are potential targets.

- 21 -

Another data req. irement is thke classitijat ion of shelter spaces witih

respect to the vulnerabil ity indices. These data arv available from the, NFSS

Phase 2 data, nr nor in a form which is readily adaptable to the purpose rc-

quired by the model described above.

C. Application of the McthodoluiSy to Stiulter S-stem Prograviniing

T-Ph data used In tn1e cdemonstratLon of risk-oriented progranming described above

were the best readil, available. Most of these data. however, were compiled during

or before 19b2. Therenore, no attempt was made in the discussion of results to

draw Lonclusions applicabl& Lo detailed planning at LhL local level.

Further, the model as developed is static, or time independent. However, tim:e

is a factor which must be considered. For example, suppose that a five-year plan

for fallout shelter development was being devised and that the existing data were

used in developing spending strategies. At the end of the five-year period, the

population data would have changed, the risk m.ay have changed, new spending alterna-

tives may have been discovered, etc. Thus, the strategies developed would have been

less than optimal.

Although there are no provisions in the model for including the time factor,

the analyst may include it in the preparation of the data. The first step is to

select a time-planning horizon, e.g., 1970. Then the input data (population,

shelter, and threat estimate) would be forecast to that point in time.

One major problem which has been emphasized by the studies described above is

the shortage of spending alternatives for improving the shelter status of the popu-

lation. For example, even at the 50 percent level of risk, approximately 150 of

the 619 counties in Region 6 had a significant percentage of the population inef-

fectively sheltered after completely exhausting the spending alternatives. At the

95 peicent level of risk, approximately 500 of the 619 counties had a significant

percenLage of the population ineffectively sheltered. Of these counties, 275 had

over 75 pLrcent of the population ineffectively sheltered. These results indicate

that a major effort should be exerted to identify new methods of creating acceptable

low cost shelter spaces at the local level. This is obviously a major undertaking,

but one which is essential if fallout shelters are to be made available to the total

populatioi in an efficient and well-planned manner.

It follows further that shelter expenditures are most likely to be effective

in areas where population is ineffectively sheltered at low levels of risk.

- 22 -

Another factor requiring more caref;:l analysis, befcre attempting risk-oriented

programrming, pertains to population location. The residential population, as taken

from the NFSS Phase 2 data, was used in the demonstration described above. However,

in certain areas where the day and night population data differ significantly from

the residential population or from one another, further study is required to determine

which set of or combination of population data should be used.

D. Critical Decisions in Risk-Oriented Progranmming

The model and allocation procedure described still leaves scope for the

decision-maker. A decision-maker must resort to judgment in many matters. Among

the decisions on which judgment must be exercised in utilizing the results of the

current model directly are:

1. The planning horizon to be used and the resulting posture over time--five

$1 billion annual budgets spent sequentially as contrasted with a single

$5 billion budget planned and spent over a period of five years.

2. The impact of future changes in expected attack environments (for better

or for worse)--attack environments determine the shelter posture purchased.

(How sorry might we be in 1975 to have planned with 1965 estimates of the

probable attack environment?)

3. How best to hedge our decisions when the optimum improvement programs in

an area are very different for day and night population.

These are but examples; it is felt that the impact of wrong decisions (due

primarily to the inherent uncertainty of forecasting the future) can probably be

clarified best by numerous systematic case studies on a small scale (so that the

mind can clearly grasp the relations among the parameters). These seem to be the

best vehicles for giving maximum insight to guide decisions of this nature.

It should be noted that the acceptability per se of risk-oriented programming

is not subject to analysis in the context of this study. However, through case

studies in which the attack environment is varied in a manner to reflect confidence

(or lack thereof) in attack environment estimates, insight can be gained into the

possible errors in allocation of shelter improvements, due to fallible estimates of

the attack environment.

To illuminate further the plausibility (or implausibility) of risk-oriented

progrartming, comparisons in terms of cost, effectiveness, and "robustness" of

allocation, rules should be made between risk-oriented programming and simpler

decision rules for shelter i:,iprovement programming, such as:

- 23 -

1. In all SMSA's, plan towards equal fallout and blast shelter coverage; time

phasing may also be varied (improve poorest coverage areas first, spend

first in the largest SMSA's, etc.)

2. Improve all areas' fallout shelter systems not already at x percent

(say 110%) of population coverage to x percent, and then incorporate blast

shelter protection according to simple rules (largest SMSA's first, for

example).

3. Incorporate blast shelter only in the largest 100 (or 50, or 200) cities

without adding fallout protection in these areas. Later, earlier, or

simultaneously, add fallout shelter in the remaining SMSA's having a

shelter deficit.

These are but examples of simple decision rules which are easier to explain

and apply, but which have a lesser cost/effectiveness, for most objective functions

at least. The discrepancy in effectiveness between the risk-oriented allocation

and the simpler allocations is to be weighed against our confidence in the estimates

of the probable attack environments. Only by comparing the effectiveness of these

alternative decision rules over a range of attack environments suitably chosen to

reflect confiderce in them, can we gain insight into the desirability of the more

complex risk-oriented decision rules.

- 24 -

. L-rRL,,(.i!;S i.'O)i •.';)L: :11 1

Linnea G. Laurtý and Irving E. Gaskill. Risk Ii: ,.A( Vuln:rabili.ty- AnalysibProLraiA Mod1i 1. 2-CCD Tutiii ical Manual "U. T. .ational Damage- Asss.ss:-:.t

,,s .p=. U. T% CI., r, Nuclar Attacb !lnzard and Resource E-,al-iatia. Mn&U sWainw ~ N atio; -a 1 Ri So-'',irC F v a -, ion- Gen t er, 18 Octuber 1 9L1 .

;3 1.,- L.. arnes and Denis Taylor. Radiation Hazards and Protection. (;eorgvNewness Limited: London, 1958. pp. 23-27.

U. S. llo,.e of Reprcesentatives. Hearings Before Subcorzrittee No. 3, Cor'Mittkr

on Armed Services. Eighty-Eighth Congress, First Session, Washington: IL. S

Government Printing Office, May 28, 29 and June 3, 1963. Page 3099.

5 Philip 'McMullan and Philip McGill, et al. Improvement of Protection Data .iasefor Damage Assessment and Data Base on Shelter Needs. Final Report,R-OU-82/83, Volume II, Appendix A, OCD Subtasks 4521A and ,613A, Durham, Nrt!nCarolina: Research Trianglel Institute, Operations Research Division, 13January 1964.

6-' E. L. Hill. Analysis of Survey Data. Final Report, Part II, R-OU-81, Subtask115A, Durham, North Carolina: Research Triangle Institute, Operations Re-

search Division, 15 February 1964.

- 25 -

I

Appcndix A

:he Algorithm for Allocating CD Fallout Sheultcr Funds

I. ASSESSMENT OF SHELTER ADEQUACY

A. Input Data

Phe input data can be described as a group of matrices, and row and column

vectors. The algorithm for allocating funds involves simple operations upon the

elements of these matrices and vectors.

The existing shelter spaces are classified according to the degree of protection

they afford against fallout. Further, they are accumulated by area (e.g., county,

S"ISA, or standard locations). Therefore, the existing shelter spaccs- (S) can be

recprvsente by a .atrix and uCeoted by

S Sj i 1, 2, ... m (A-)

j = 1, 2, n

where s = the number of identified shelter spaces of the j protectionF i.th

category in the i area.

Two other matrices are used to represent the addition of shelter spaces that

can be cceated by additional expenditures and the corresponding cost per space for

these additions. These matrices are denoted by

A ak i = 1, 2, . m. , m (A-2)

11 cik k = 1, 2, r

where a ik = the number additional spaces of category k in area i that can be

created at a cost of Cik per space. Note that the protection categories in S are

not necessarily the same as in A .

The additional input is denoted as follows: Let

Pi = total population in area i

-A-I

Pij = population in area i assigned to shelters of category j in

area ith

E. = tile fallout environment for the i area stated in terms of un-I

shielded equivalent residual dose.

M = maximum allowable equivalent residual dose.

f. = protection factor of protection category j for the existing3

shelter spaces for the matrix S .

fk = protection factor of protection category k for the potential

spaces-in matrix A

B = total funds available for fallout shelter development.

B. E::isting Shelter Allocation

Using cost-effectiveness as the decision criterion for allocating CD funds

requires, first, that the existing shelter status of the population be known. This

requires an assignment of population to existing shelters. To accomplish this,

assume that the protection categories are ordered such that

f -1 --f fj f j+l . fn (A-3)

Then the assignment of population to existing shelters is made in the following

order. (The technique described below is equivalent to assigning population to

shelters by protection category, assigning highest priority to shelter spaces with

the highest protection factors.)

nP - s s., forq <n)i j=q+l sn

Pin = 'in (A-4)

Pi,n-I .s.il~n-I

.. . .. . . for i 1 , 2, .... m

.... .

"- A-2 -

whery the subscript q denotes the lowest order shelter space required to shelter

(though perhaps inadequately) the total population for the i th area. Vherefore, a

population-to-shelter ,;signment natrix (P) has been formed. This matrix will be

an nA x n rmatrix with the elements pij = 0 for all j - q.

Since residential dwellings represent the lowest grade of shelter, the number

of spaces in this category can be assumed to be equal to the population (i.e.,

s il = Pi). Therefore, when the population exceeds the number of shelter spaces

(excluding homes), q = 1; and for area i ,

n

P =pi - _s (A-5)"SI J=2 sij

From Equation A-4, it should be noted that assignments of population in thehth ri

i area are made only to shelter spaces in the i area. This implies the assump-

tion that population is allowed complete freedom of movement within their own area,

but no movement outside the area. A model allowing movement both within and among

areas was developed and is described in Volume II, A Sensitivity Analysis of Selected

Parameters Based on 8 SMSA's.

C. Shelter Adequacy

Given a distribution of population to shelter, the adequacy of the existing

shelter status can be determined quantitatively. This is accomplished by subjecting

the sheltered population to a fallout environment, Ei. The shielded equivalent

residual dose (e ij) for population in each protection category (j) and each area

(i) is given by

e Ek/f fot i w 1, 2, ... , m (A-6)eij

j = q, q+l, ... , n

For the shelter spaces to be considered adequate, the shelter spaces must meet the

, .. *:.. ij) be less than sone ;:iximuri allowable ERD (M), se that

M - eij > 0 . (A-7)

When this condition is not met, the population is considered to be unsheltered, or

to be in inadequate shelter spaces.

D. Shelter Posture Improvement

Since the primary interest from this point forward is to improve the shelter

status of the population, only the population inadequately sheltered need be con-

sidered. Therefore, we introduce a Kronecker delta such that the number of persons

- A-3 -

rllish 'l t ur d in thVe I i ar a is ,ien by tht, uxp ussion

1, for N - 0

'_.iPp.. whtr, Ž.. = (A-r)j=l

0, for M - r

For the i area, let (j u ii) be the "!inilnum protection category which meets the

condition in Equation A-7. 1,Ln, the number of persons in . th area consideredu-1

to be inadequately sheltered is given by P.ij. (Note that where q = u, the total

j~lpopulation in area i is adequately sheltered.)

This completes the risk-oriented assessment of the existing shelter status of

the population and defines tht shelter needs of each arua. Thus the ground work tias

been laid for determining how and where shelter development funds should be spent.

II. ALLOCATION OF FUNDS

A. Allocation Objective

The a ik matrix (alternatives for improving the shelter status of the popula-

,ion) and the associated cik matrix (costs of these alternatives) can now be used

in allocating a total budget among individual areas. The objective is to allocate

funds such that the cost/effect±',eness will be maximized. In thlis instance, the

effectiveness is measured in shelter spaces added per dollar. This will be discussed

further in Section D.

B. Improvement Alternatives Evaluation

Before considering the alternatives for improving the shelter status of the

population, a risk-oriented procedure similar to Equations A-6 and A-7 must be per-

formed on each of the protection categories in each area to determine their adequacy.

In this case, the shielded equivalent residual dose that a person would receive in

each cf the protection categories and all areas is given by

elk ' Ei/fk for i = 1, 2, ... m n (A-9)

k =, 2, ... ,r

For these potential shelter spaces to be considered eligible for shelter development

funds, they must meet the follr- "ng requirement:

- A-4 -

ik > 0 (A-10)

By introducing another Kronecker delta, the total number of shelter spaces in area

i that can be made available bN shelter development funds is given by

1, m - eik >r

- ik aik where bik (A-II)k=l

0, M -e ik 0 .

C. Allocation Constraints

Before proceeding to the next step of allocating the total budget (B) among

the n areas, two factors must be considered. First, if the total budget is greater

than the total cost of the improvement alternatives, or

m r

z Z 5ikij ik < B (A-12)i=1 k=l

then the constraint is not the financial resources, but is the number of identified

potential new shelter spaces. Further, if the number of persons inadequately

sheltered in existing spaces is greater than the total number of identified potential

new spaces; i.e.,

m rE E b ij Pij >l z~ 5 6ik a ik ,(A-13)

i j iml k-1

the input data is not sufficient and a shelter gap remains after the allocation is

made. Therefore, if the condition of Equation A-12 or both Equations A-12 and

A-13 exist, the amount of funds expended in each area is given by

rBi = E bik Cik aik for all i. (A-14)

k=l

For the fund allocation, it will be assumed that the available funds will be

limited. Then the direction of the inequality in Equation A-13 is of no consequence.

D. Fund Allocation

The allocation of available funds is to be performed in a manner which will

maximize the number of adequate spaces added. Since a "go/no-go" principle has

been adopted for evaluating shelter spaces, all potential spaces meeting the

-A-5-

rt-qi;1irerent given b\ Equation A-i0 are effective shelter spaces. For purposes of

allocating funds, the identity of the protection catopory mav be ignored since a

space is either adequat- or inadequate. Therefore the subscr ipt k of C

and a can be dropped. However, associated with each a improvable shelters1K • ik •

is a unique cost c ByJ replac ing subscript k with a subscript ; and

order jig :hu w get:

Sc j., C i c. . (A-15)

lte corresponding ai and Cik are ordered in like ::)nner. Thus, a table of potential

spaces has been developed in which spaces are listed in order of ascending costs.

Note that the area identity (subscript i) has been maintained.

A single allocation of funds thus becomes c.i c i ai i f 6 ý-0, no alloca-

tion results. This meets the requirement that no funds will be allocated to im-

proving or creating an adequate shelter space (as defined by E., the fallout environ-

ment for county i). Hence, the value c. becomes the cost per adequate space addedI'

(the measure of cost/effectiveness for adding the a. shelter spaces in the i

area).

With c i as the measure of cost/effectiveness, the optimal spending strategy

is to allocate funds to the lowest cost alternative first. The first allocation

would be bi = Eii cii a where b. is the amount of money allocated to the ith

area for the shelter spaces denoted by al.

The allocation of funds must satisfy at least one of the three following

conditions:

SPi = 0 (A-16)

i = 1, , .,., n6 a. i MO, (A-17)

or

E c a -B. (A18)

ij ij il A-8

This means that either all of the population must be effectively sheltered

(Equation A-16), all of the available improvement alternatives must be used

(Equation A-17), or the total budget must be allocated.

The Equation A-16 also implies that before an allocation is made to the ith

area, the inequality j 51J Pij > 0 must hold. If the inequality did not holdsJAl

- A-6 -

further addition of shiL ter spac4s woj, I b1 (I lCLiCL and the funds would be wasted.

The allocations of funds to the iti area (subject to the constraint

.. p.. > 0 is given byj=l i

b. = ,ii c. a. (A-19)

where the subscript denotes the order in which the allocations are made. The

value bi, however, does not necescarily represent the total funds allocated to that

area. The original notation for the available improvement alternatives before

ordering them by ascending cost was a aik, k = 1, 2, ... , r. Therefore, in the

resulting table of shelter spaces, there can be as many as r potential allocations

made to the area. Thus, the total funds allocated to the ith area is given by

bi= = Eb= 1. C.i a.i (A-20)

summed over all alternatives carrying the subscript for the i th area.

From the above description of the model, it can be seen that a series of cost/

effectiveness curves (one for each area) havy been developed similar to those shown

in Figure A-1.

Area #1

S~Area #2

Effective Spaces Added

Fig. A-1. Cost/Effectiveness Curves by Area

Note that each of the cost/effectiveness curves are, in practice, a series of line

segments, each of which represents a group of shelter spaces that can be added at

a constant cost per space.

The spending policy described by Equation A-19 states in effect that the

criterion for choosing the next spending is to purchase the shelter spaces described

-A-7 -

by tHe line segment with tOIL 1'ast sloptu. This policy insures that the alternative,

cho-tbn will be the one whicu will givu Lite maximum number of adequaLe spaueb added

for the, Lxpenditure. He'nCt', t'he funds arc allocated in an optimal manner.

° A-8 -

App•'!•1 ix<

Rtlationsý ip Bttwtkri-i Pop latiorlnadequately S•l•itlured and Casual tieb

. - :A i - .lA-1I CAL PRPO L

A. State:mcnt to bc Proven

If a Maximum ERD of 20Cr is 'hoseui, the popul ation inadequatelv si:cl1ereod will,

on the average, be equal to the expected number of casualties from fallout, provided

the distribution of population receiving ERD's in the range of 100r to 300r is

symnetric around 200r.

Let PD = Pr (an individual chosen at random ib made sick if he roceiv%-s dose- D).

Let P(D) = Pr (an individual chosen at random receives dose D or 1,.ss).

Let p(D) = density function corresponding to the distribution factor P(D).

Assume

0 D, - 100

2 D-00 100 < D <300 (B-I

D 1200 ,>0I D > 300

1. Theorem

If p(D) is continuoub and synmmetric about the vertical line (D = 200r) over

the range (lO0r-300r), then the expected number of casualties is equal to the

total number of people receiving dose > 20Gr.

2. Proof

Let N = total population

- B-I -

Expuctud Nurnbvr of Casualts Lc

F PD dP(D) (.-2)

00o 200}= pD P(D) + PD dP(D)

0 i 00

+ PD UP(D) + PD dP(D)20 0 30o

JP+ dP(D) + " i' dP (D)2000 / )b 200

+ dP(D)

300

In thc first integral, Ilc. D = 200 - C, and in the second integral, let

D = 200 + C.

Then

Expected Number of CasualtiesN

+ ( poo. to 100 p l 0+ce=0 - -dP(200p-C) + (- P(200+C)

+ (the proportion of people receiving dose > 300r)

.10 10000+C+0" IdP (200+c2)

- O & 2-• dp(2O0+C) + 0 200 /

+ (the proportion of people receiving dose > 300r)

100j dP(200+C) + (the proportion of people receiving dose > 300r)

0

300S0 dP(D) + (the proportion of people receiving dose >_ 300r)

200

- the proportion of people receiving dose > 200r.

So the expected number of casualties , the number of people receiving dose > 200r.

- B-2 -

Appendix C

State Summaries of Case StudiesUsing the Risk-Oriented Allocation Program

- C-I -

41 to $

to = al 0 o - Lf 00 a~ m 0 tQ ' Go Cm% ..

0 j 0 ('. %0. m- C40 (N ý fn cy % t'- m' .

0-41

4) u

GO wo ul

Ei > A4-40 4

0J

010 0 en Ue %- 1- I- U . 0j,-. 4 0' Q% -4 0D V n % E

u v ' - -? 0 ? n -4-,mto 1 4 . . . . . . . . . . . .i

to

0V

31 1 mC *

oe 0 .6 (411

.0 r, 00.-4 *

-- 0

W1 w a41iv M mi m cV co

> 41 go to 0 0 5 C! 4 ) :

.o 41 Go .Q c0

I~~~U D140 0 00 U

V%~E 4' 00 fn CJf7 4%

C) U) Co U U ..

s", 4 4 i( "

'0

0 0 En0 41

*0 40 ZP P-4 V) 4c t E w. w w 144cj '.00 (n 4 ,- U' .. 00% 0% w% 0, cc

41 u.- V) z ' 02 (N 0% w .. zr z (N V. -z .4 V0 V

U) ~ d)

414to4

o 0 02 04

-,41U cr. U,% cy. U.. E-ý (-' (a. m1 C. a,~ C.m C. ( .0% "4"

(12j

CC-

IVU TS .- 4 I '%00% -, D ' r-. kn IA .4 M ~ 0 .0% '-041 0 -4 %00 LO-1 MA C-4 - . f' 4 M 0% 0.-. 1CU.-4 . . . 41)

-00

0-4

-4 -dc) O 0 C4 -' O C C1 0 O -4 -4

In .' .A .' .4 .0 . .- .~ .% . .A .I) ~ -co 0 OD 0 .- % CJ.4- Cs0% Ln M 0

0

0 U)0 00) JC'4 '00 Cn ID C'4 IA LA Cn 0 0 %. ' 0 C4~ '0 .

r.U0 4 '0 .. 4 LM 0 '0 M M L) rA'4 I".- -. 4 C- '0 '00.'' U)

1-44-4 U

'0 CU n Cu 0

ý4- I I CU1 0 . W- (4 U) U U V3

Aj CA

o 4-40-.

60E4- 004-4a -r4 CU CU ' J

0-4 Q)'. 00 go CA CA4

41 tk0 uu LM 4 v4.) 4) W 041 &JC' =.

.4C a cc0 j r 0r-101

AJ~~~C 43 8.)ý w

U)~ ~ .4 Ur, 4CA rX -Cr4 0 % -

C) ~ ~ ~ ~ 4 -Ic -4 DInm C %D 0En tn C')-1 C') 0% C'4 0000

U) IA 144- O C<r' . -I f 41 % '0 C)C

4,41

0 0 0 Q

*.4 (A 00 01 $4 l 001 0c n (A c n nr

u 0 z O U) $.4) 1-4C) ) U W/ (n (n 0 En Wr444) 41Un;L -4 H .4U ) ) ) ) ) rx- r" w.. P4.

41 Cu4. c .1.F4 Cz 0 d 0

4') U)

CACto ti4

-4 -4 -4

0 0.0 -i

-4

w' CA LnI 0 I 0 Ib L^ IA LIA 0 LA 0 LA IA 4n 41 cIA4 C% L 0% UIA (% 0% m% M% IA 4, IA 0% 0% 0% .4 .4

-4 -4 -4 4 -4

-C-3-

0 4).4 4 J 0)ca :3 4) r. r, %m ON,..' -4 LM 1-4 C4 r 00 0% z ~

W -4 - % N 0 0 (44 l %I N -CL 0 0 -4 -'' 4 .. ' .. 4 -

0 (aU-C

'I'A

00 r- N' m% (, c% co 00 0 P- 00 Nm 4w%cc a 00 oo m % 0 u.1 r- Cl 0 f- c0 0 1-4 c N C14

i04)00 C ON000%C000% 00N c. 0> C -4 -4

0 <,I0

0 V 0

-,4 Q w-. -4 N 00 N* '0 0 en r- r'- -4 C% 0% 00 4v- 10 It en C n "f %n 4iI 0 m Nq 4 U'M Ce'Stv V- 0 -4 . .. . . . .I

U .,-4 06

0-4 v4U0- u

0z -,0 0 CsC C. al -4) QIj' 0 4J

V) POU C U ~. 0 4 4)

A- 4 4) 54 0I jto a4- IV.

w 0 > 0 0 0

r. 1.4 4c C-4 0 Cd414 0 0d 0 r- ON4 I 4 r 04

-4' 00 0D I 0>l ". CY 0 U n 4 P 4 e

(a *4j. 00 0 . 0

0 cn 09

4..0 v10 0 w4 V) -0% 00A%4.,4 Ai CO-,-................................. 00WF4

000 CI- Lu.W P ..W 44 4.1

1-4'4.4 A CO

0 0 0 00

a~0 00000 0 000000000 0 00 0 8I- ~ ~ 4 0. UO Z 0000-540000 0 0 00 0 0

4.00- -4 " Z Z -4 Z 4 -4-

00 ~ 00

(o001.J C)LN0 i n - n 0 L V MU) 4

4..4

N~4 ,.4 ,- .-d . 4 -4 J

C-4 -4

ai -4 WI " n k ) %OZJU. 4jS . .4

CL 10G 4v m - -4 4 C4 C4 .4 C4 C4

rid ccn4

4)U u-

*l Lo

0

0*

o; 4).4 t m4D 0 #elr oc-4 U)4 00 -4 0% 0 -&M .- 17%

LI~ ~ ~~1 -- u . 0 - 0 f '0%-0 4% 0U ~ ~ C. .,444...

0 En c

41 0

:1~~4 .4 P 4 )$44

J.J V4 44)

-A 1 O -,4 "9o4 - 40 500

c~~L 'I > 4 %a

.. c . 4j1 4)z r. Vh L54 4 4 )41 >

I xL4-Q4 4)- ZU - SL

0) C% UU1 -4 U

c0 0 En 0L 4))4U)U >

0 w- 44r n L ca .4

$4)

-4,- -4- 4 4 . 14

5 00

U)V

(a >IUL in 0 LM In LM IA 0 &M 0 IM IA IALI

-, 0 WI 0% VI a% 0% 0% 0% V' % O u & 0% 0% -,4

-.4

.4 ~ ~ ~ ý IA '0 r % 0 .4 N4 4 4

-44-5' -

'~~~0 "4. U0 0% 0 07%If ~ . 0 Xfc c . 1al 00 ' T 0 '0 0 0 - ' 1 0 0 .0

'" 0.0 M1 ON -4 -- 00 -4 0-; 0 0 n T

M o00 Aj

0 <A-

V01-4 0 P- %D~ 0 0 r'S CO- fn -4 OD0

.0 eq'-n4(n e 4 C4 - 1a.. < 0U. . . . . . .

411.d 0L .0 .S .~t 4 ~ C d 0 U.S 0wI U)U u cn14 0

'JO .61

on .Ag oM 0 w - 0L) bo u n

.0, 00 IAQ U) 1) "4 z

01 .0) a.4( '50 C9 r 0 ý05- UILJ4 li C4 t 01 00 4

ri.01

~0 40 u

YK w w 0 mW C c )W U n ( r.4 140"I ua z w . F4~ tn w1 00) c ) 6

Qj -i 0 -EnS w 0 w US, 2 % E ~ S-4 H0 P- P s 44 tu W .w0cc&JU( 0I"4. '0 4% z z '00 w '0 z- '0 z% '0 z0r

)) .0.

0 01 C

-4

0 0 ) 001rA >i.0 LA U) in) 0) U)C) Ln t) UI) a)1) Ce) Ln41r

rd' 4% UA a, C) M) 0% 0% -r kn aU Ln 0% a%1) (7% -A -4J

-5C-6

.- 4 C) C4 C

0.. V Qo m. x t

M 0% m - 0V % 0 0 rI-. m m .

00

00

u 00' C% - ~.!4 ' f 0% ' 00 = 0 0-

(a V . . . . . . . .'

m -i0 to

I- -< to

0V V t

0 W0

'- 00 *

.1 0.-. U

to 0 w04 A

-) 4W-Q U)

Q) Ea Z .j . .0 ..4 L4O C04 D0-0n L I D -

(3 -- U)

Ln0 tJO -. 0

o - .0 1044 Ai4 .3~

01 0

.- C 000- V)0 0 0)'-4' (C U) Wn V) >.

.0 $4 00 f0 n E Om 0 a r) C0. ZJO K) 00 0 0 Cn~ -40 1- -0 4

4. . X P. .0r.N xJ

(0 m.41 1- 0 0 0 4 00 U. F4 4

V)) P.3

0 U)U)

U) ' .- 0 -4 -4 A4- 0 -j.-

-00

Ln 0 ,% 0e % 0 , 0 m 0 n M

-4

0r 0 en 0ouj. U) ý4d'

C-7 -4

41 to . N4 4 (Cc (04) 0 0 NO 0 r 0% 11^ N4 0 N 0 0 .7 0

Or, CrA 1ý 0 v -40 C- NO fn 0-? - 4 .

adr.4 .

oo Cc D 01c f)U 1

9-4 (0

> U)

-4 4) -40 '0Ln0 '0 N ý 0 en 00C0 14n 0u -u - - -4 - -4 -

M -. .% .0 . . . ... .n 0 .- .0? . %(0 >c-i

hto

V 041 41or Y1441 A4- -

= (A

C4 O(0 .4Aj

bo ui 01 44) w4 -'-4 41 0r

1.4 Cd 01 A10 .0 1 C - 4 -?4.C ' % d 0 V-40

0 C0 -, (00 " C C l 0 M n*.

> n -0 80 Eýh 04 C44 C4

ccc

10

(0 1d 01(w4 4.00 4 ' C ' N O '0 cn 0 0 cn c .,l0 z1. Ln u ) 1414 N CL2 (A Cn Ca Wn ON4 0

'(n I" Cý2-44.............................................. . 1'- 41-. 94 .-4 -4 N N -4 4 V r

-%4

0 00 0 0 0 000

C-4 (.0 Z A 44 C%4 (4 (A (A 4 ý ý 4 .

0.

4-, (0

W0 >0 00C I 0 L L n i n n tQ- a, al % t C%(0O (1 L h n Ct a

-M0 n 0 ? 0 0 0 0ý 0 0 0

C-84

0~ a) - - -- -

S-4414

-4 4i 0a 1

tv TU~ W " Z 0(% 0 0 r-. i- 9^ %D0 .- r- 0%l c-

~.0 to10

co In

0 j .4 .- 4 14 -4 -40U -4

O0 0 e f

0

(U-4J

0 004.. 1 - -

-4 W

'0 00-Ai V0i A j o e

-,4 to4 (a 00.. 40~ . 4* rz$W V w ý

>. 'jc v$ LJO V 0cn0 0 $w V4V D

t .0 4J1 w'w4

- - U(U in U

C 0 0 0% t'' n 0 0, --A-4e 0.0. UU % v% 4~ 4 C4*

0 I 00, -4 . U )0

(U 01 041 0

U4-0 0 n00w

'0 J0i 000 w% .w. D w( 0 0%4J U' tn .- 4 z z. d o . 00

0 go L.E-

zt ca C0i-i to b

z z0(Uý4E-4

010% tU in un M% m% C% 0% LM' 0% LI 0% C7% 0% - ,

oI) 4 - C in 'D r-. w 0% 0 .4 N ( .caI

)

AppI .nd i:I I )

A. rrotra::, Description

Because of tih nragnitude of the problem involved in allocating fupds arz-ng aLarge n-:-ber of areas, a con7Puter progran has been deýveloped to perfor' me t:•;ction

described in Appendix A. The program was written in FORTRAN 63 for the CDC 3600.

Tle FORTRAN statements and the associated flow diagrams are shiwn in sections 5a and

5b ef this Appendix.

1. Input Data

'The basic input data (the existing shelter spaces, potential nTew sheltLr

spaces, csts, population, and a fallout environment) is put in by magnetic

tape. All these data are accumulated by some geographic area. The progran,

as well as the allocation techniquc itself, was tected by using the county asthe accumulation unit. Thus, the input data are stored internally as a series

of matrices, and row and column vectors. For example, Table D-I illustrates

the manner in which tho existing shelter spaces are stored internally. The

potential new shelter spaces and their associated costs per space a• stored in

similar matrix arrays. Associated with the protection categories of both the

existing and potential shelter spaces are data regarding the protection factor

of each of the protection categories. This information is supplied in the form

of control cards along with the computer program.

The computer program and selected control cards are put in by cards before

each run. Since control of the program is exercised by the control cards,

maintaining this information on cards facilitates making changes in the major

parameters between runs.

2. Set Modifications

The principal function of the computer program is to perform a risk-oriented

allocation of funds among the areas described in the input data, by the procedure

- D-l -

TABLE D- I

11 1ustratio orof Tnpl'l Data

Shel terClass i I icat ions

Area 1 2 3 4 5 6 7 8 9 10

(Coi, t k 1 10,000 '4000 (B)O 1000 10 f) S0 1)' 00 0 500

2 25,000 6200 3000 500 300 800 500 100 0 100

y, O.l) I JO 1000 1000 '200 ) 0 0 0

m 8,000 5000 5000 800 0 0 0 100 500 600

Possible Identification of protection categories:

Shelter Classifications Identification Protectio. Factor

1 Residential dwellings 2

2 Residential basements 10

3 PF Category 1 20

4 PF Category 2 40

5 PF Category 3 70

6 PF Category 4 1007 PF Category 5 250

8 PF Category 6 500

9 PF Category 7 750

10 PF Category 8 1000

described in Appendix A. However, the computer program contains other features

designed to facilitate a more comprehensive analysis of civil defense spending

for fallout shelter development. Most prominent among these is a feature called

set modification.

This set-modification feature allows for arithmetic operations to be per-

formed on a single number or certain sets of numbers in the input data by the

use of a single control card. For example, suppose it was desired to evaluate

the effects of overcrowding in the existing shelter spaces by say 25 percent

on the allocation of funds and the resulting shelter status. To accomplish

this, two computer runs would be required. In the first run, the existing

n •-2

shelter spaces could consist of those spaces identified it, thc :NFSS-Pilase 2

data. In th( second run, a control card would be introduced which would serve

to increase the number of shelter spaces in all counties and all protection

categories by 25 percent. If so desired, the same type of analysis could be

performed, after allowing overcrowding in only certain areas and/or for certain

categories of shelters.

As another example' O-the use of set modifications, suppose it was desired

to evaluate the effect of considering residential basements as potential shelter

spaces upon the shelter status of the nation and upon a risk-oriented allocation

of shelter funds. Here again, two runs would be needed. In the first run,

residential basertent data for each area would be included as existing shelter

spaces. In the second run, a control card would be used to eliminate all

shelter spaces in the protection category designated for residential basements.

(This is accomplished by multiplying the number of spaces in the column desig-

nated for residential basement data by zero.)

3. Computer Processing

As mentioned above, the primary objective of the computer program is to

perform a risk-oriented allocation of shelter-development funds among areas

(e.g., counties) of the nation, to assess the shelter posture both before and

after the allocation of funds, and to evaluate the overall cost/effectiveness

of the expenditures resulting from the allocation. Several case studies have

been run on the CDC 3600 computer at the county level for Region 6 using all

available data on existing shelter spaces and potential new shelter spaces.

The computer processing time required for these runs ranged from two to three

minutes per study. A similar analysis for all of the eight regions (over 3000

counties) would require an estimated twenty minutes of computer time.

4. Computer Output

Table D-I1 is an illustration of the computer output taken from one of the

case studies. The column headings are defined as follows:

STATE CODE - A numerical code of the state

AREA CODE - A numerical code of the areas to which fundsare to be distributed. For the applicationdiscussed below, this is a county code.

RESIDENTIAL POPULATION - Residential population in each area.

- D-3 -

. INEFFECTIVELY SHELTERED The number of persons considered inadequatelyPOPFTLATION• - sheltered as a function of the fallout en-

vironment and the existing shelter postureof the population in each county.

TOTAL POTENTIAL SPACES - The total number of new or improvable sf:elterspaces that have been identified as eligiblefor fallout shelter development funds.

TOTAL SPACES ADDED - The number of fallout shelter spaces addedin each area as a result of the risk-oriented distribution of funds for OCDRegion 6.

AVERAGE COST/SPACE ADDED - The average cost of all of the spaces addedin each area.

SINEFFECTIVELY SHELTERED The number of persons remaining inadequatelyAFTER EXPENDITURE - sheltered as a percentage of the total popu-

lation after the funds have been distributedand thp appropriate spaces have been added.

DISTRIBUTION OF FUNDS - The total dollar expenditures in each areaas a result of the risk-oriented allocationof funds. Note that this is ., function of(1) The fallout environment,(2) the availability spending alternatives

for improving the shelter status ofthe population,

(3) the cost of the new or improvableshelter spaces, and

(4) the adequacy of the existing shelterstatus of the population.

Also note from Table D-II that the above information is summarized for each

state.

-D-4-

c % 0t 0% 'C1 o A)~ 'C., 00 r, :.T en ' 3 ' .()0 C'J 0

Aj 4 '0 0 0n LAO Ln It w' 1% ('0'Q~ '0 u' c A 0 - '

>

Q) C.) -4 0 C-4 'D .' 0% m- 'I (n M0 co

44L.wl4 c - a, -4, -; C4 c. C 4 4 t . . . N

',4 o0 0'i L l 0 M0 C4 0A a-~ - '0 %D en %

u ) - M

P V)

OCJ -1 4) '0 'i %0-4 A- 0n0 ( I'T en0 C l, '-04 c 0' 0 0" IA .01 .01 0 0% C-

a-. :3 o 0 oý 4 G , L

0~- .- '4J' In -cc '0 -. A 4 ul %' 0

C)1

Q- 4 -4 w I - 0 z0 n - 0 0 r

-4J r.4 U2 '01 00 c00 .' 0 L -. M '001 " 04 C 0 )cJ r N n '0 '00 IA -4 -. 4en (7 ý CA 40%

a).~( 0) "0 M4 '00 %0 .1 0 . 0 W% 0

Ci 0

0-

0- -, ) -,

.,4 4W i'0 9)'-44a: 11 0' 1; C 0' 00 '0 1 A% C""J- "' %4 LA =A w .% on N, '0 (A 0D 'A *

.0-j 4 ~ I4) '0 ' 0 00. A L ' ''

4j .0 cU2 .4ta ,4 -

ALAor. uu

-,4 04J .4 &n '0 '0 4 -4 40' ON P A 'l00 N1 .a. 4 t0% N4 &A C% %n 0' '0 -4 0 IT 4

Q (A r 04 A C4 0A .A ' N 00' '0 en (R 44 . 4.)V.I 44 en .- 1% m' LA %A ,0 t % '0(nr IA LIO ,-4 'T 4 -.4 4ý 0% .-M .-4 ND 00 0 0r

40 N 4 -T-4

to

I4 -4 0 )

-4 -4

41 a 4) 04 * 0) 4.4 a '.4 4.446 -4 . 4 .- 94 . 4 C-i N- N* N4 . . 0o 0 '

-D-5 -

5. Flow Diagrams

a. Generalized Flow Diagram

Alternatives forImprovement fromPhase 2 Data

RISK Data as resultof RISK attack at a95% or 50% level ofrisk

Assignment ofPopulation toExisting Shelters

Calculate segment of Calculate protected Calculate AlternativesPopulation inade- ERD by area and PF for Improvement ade-quately sheltered category quately sheltered

{Calculate totalpotential spaces <that can be added

Arrange potentialspaces added and assoc-iated parameters inascending cost order

Allocate funds byleast cost criterion

output

-D-6 -

b. Detailed Flow Diagram

Program Go/No-Go

START

TFCV =

BUD = CONTROLDERM = CARDSLED =

Read 2_Crd()PFR(I) ,I=1, 14

(2) PFC(I), I=1,14

[Distribution of\BUD in L2 /

s sstates /

cad Input Tap•

KODE, J I

SJ4(L)=JIK4 (L)=KODE

N=INID=I15

cad Input Tape•

•ERSO (J) ,J=N,NID

-D-7-

> 0NID-ii

< 0

-IN+1 5ID-NID+15

NID-Jl

>04

NID-Jl

2 ontinueC Cont

N=lNID-15

73Read Input Tape

DER95(J),J-NNID

> 0ID-JI

< 071

=N+15ID=NID+15

<NID-Jl

1.0

NID=Jl

D-8

72

Continue

D020J=1,Jl

Read Input Tape

(1) POP(J),PFCA(J)(2) ES(IJ),I-1,10(3) AI(IJ),I=1,10(4) CA(IJ),I-1,10(5) AI(12,J),CA(12,j

AI(13,J),CA(13,J)

CA(11,J)-25.Al(llJ)-.10*POP(J)

6 20

-A

0LED-50

0

48

C

D049J=1,JlDER(J)=DER50(J)

Go To49

47

10)

D-9

01

206 1O

DC41 1,m3

-ýB OP Io-0P2

402

01

-D 1+

S4'

(A (j)

D021=1 10

S~~~~ 13-12 -lý9

U D ' / 7 l , UIý

0

I-11

0 -1

I NI0I

313

31-1 ~A LAS (J) =A LL.S (J) +A I(I, J)

31 D 14

At

(ID1 .1 T I

u NSIUMM=

1=0

41

ESIc,(J)- 0 RSIS=ESIS(J)

AIAS(J) TLA(J)=LSIS(J)

(J)

42 > 0

RSIS=AIAS(J)TTA(J)=AIAS(J)

33

K-1

< 0 N-1

> 0

6

D-15

33

9IT

CA SA )C (K)- SSA()RI

I(I,,J)=SA(K)PFCX(I ,J)=XTFC (K)Cl (K)=C1 (K)+lO0.FAT( i,J)=FATN(J)FAlf(lJ)=FATNl(J)-(SA (K) /POP (J) )

16-1

21

1T =N SLU4 (L)I

D07.J=IJlN2 = 12 (J)

I=I+l

< 0 C (1, L)=0N2 %rA T I T T '. - ,

LOC (I, L) =KODE+J

> 0 RFA','I, L)=ES IS (J) /FOP(J)

L 7 A

v

K=l

14

M-1

I=I+l

D028J-1,JlN2-I2 (J)

D-17

A(IL)%TT((K M)

01

M= D-8

(; EN FILE ~

JPICJAT(IL)LO(L)1= ITNSML

AREAD TAPE 2:

r'2 (L) =IL

>~ 0

-D-20

C-)

C(iM)- C(K, L)

053

52 RF-A (I J. M)- 0 I=KRFA (K, L) M=L

0

51

SUMC=.SUMC+(C(IM)*XAI(IM))

0BUD-SUMC

> 0

62

0

t

KTOZ-0

D-21

60

F 2 (Mr2 (M) +1 AI$M

DIFF=BUD- SLUMCI.A=DIFF/C(I,!4)

L2) SUMC=SUMC+SAX*

673

' TOT

D-22 -

1T=XSý U(L)

RREAD TAPE 2:

TLA(J),J=1,JlC(2) C (I, L) ,XAI(I,L) ,REA(T,L),

PFCA']. (1, L), LOG (1, L),[=1,*IT

DO65J=1 ,JlCl (j)=O.SA,%(J) =0.

FATN (J)=~O.KODE=K4 (L) +J

D06 1=1 F- 613

VGCA (J) =('I(J)!/SA (J) I'TlnTl-r)-Th7(>I (~J)j

TELýIý=TSIS+ESIS(J)

FATSý-((TV SI-'- Tc)TfSA),'rpf'tjpW 100.

TIIAz=TT.LA+TlA(J)

(1)~~ SLSE OTLS

4 63

HEA~~ DD2 I-S N

iLC-TCITOJTCIATS A 4-'101S

(tCRTTE OU1TPUT

3 LED

-D-25-

N 4 z j00/00/00

14~ TN~T 18 As( I I 1* S- A~ L 16~.E! 1 1~ 2 ( i I a #jjsANl~)AGAl 18 )1 PD iq 4( 1

r'- ( 14 . FR

2_, 100jr00u.

13 6OiU LtJ = 0,95.45RwI4wN U 2R wI Nu 1IwqITE Oul'UT TAPE 4o130, RLJD ,L2

1" 10 L:I..L 2vý-AD INPJUF TAPE: 10,102. l(orE-E ~ij 4(L )2J1

3 R;-A i I NPU I TAPE 10,107, (D)FR'4ji), in N.Nln)

N + N -.kNID a NID + 15ii (NIU-jI) 3,3.4

4 N I Sl2

2 r*3N I INUE

15 4tAD INP~f TAPE 10,107, (DFR95(J), Jo N,NII1)I -N Iri- J1 71.7 2. 12

7 1 to N 1)oN;jfn z N IL) * 1.5T' CN1D-JI.)7J.1.3.74

74 NJIT ' 2J Iq 0 TO0 73

12 erDNTINUEVID 2D J1jai iREAD INP.Jf TAPE 10,103, PopCj)s PFCA(J)RtAfl INPiJI TAPE: 1.0*104. (FS(lj.J). I a 1,101RIEAD INP'J[ TAPE l.0slO5. (AttIJhs T 8 1.t10R*FD INPLJI TAPE 10#106, (CACI.J)e 1 2 1,1(1)REAn INPUT TAPE iO-110, AC12,J).tA(12,J).AI(1,ijJ).CA(1.3.j)CA(11.J) 225.AI(11.j) x.10 v POP(J)

20 tCON1INUEPý (LED-5U)47.48.47

48 eriNTINUE-m,3 49 J 2 141lf¶jR(J) c L)FR5OCJ)

49 fINIINUtnj TO 75

-D-26 -

N 4. 00/00/00

47 fo'ýNIINUt

/$6 rDNTINU&/9 '-N T INU&

?J ~ ~ i~~j2,16 r~..ýN11NuE

nK) j04 I 1.1

PI- (EAb( I J) )209.20&1.08

2j9 Al (l#J 4 P

2 ý4 P7KiKNI INUE!; (Tý CV,1.0)402#400,402

40O R-AD) 450- L6

4-ýD rORMAI (14)MDi 401 M 1' L6REAb 451, IRA, IRS. JCA, jCB. OPI, 0P2. Xfln

4,-) rýJRMAT (414. 2F6.2# V3.0)n~j 411 J x JCA* .JC8!) 411 1 2 IRA* !-RP; (X ID-?. 0)412,413, 414

412 r-S(19J) x ES(1eJ) * OPI *0P2M 0 TO 411.

413 A](l'JJ 41(1,J) * OPI + OlPif,, i 10 411

414 f-A(I,J) *CA(I#J) *OPI * fiP2411 t"DNTINUE401 7j N f INU E402 r7DNTINUE

N S iM (L ) z

P;CC11) =PFCA(J)noC 31 M1610sjmbS=SUMEs#ES( I ~)IF(PFCA(J)-PFC(1fl31#J5,31.

35 P;R(Il) 2 PFR(I)31 CONJTINUE

1'; (PUP(J) - suMEs)45&38.3838 F.S( 10.J)sS( 10sj).POPtJ)aSUtES45 PSIS(J)z POP(J)

ODJ 32 191.11PDER( I )xuO:(J)/PFRI)(I1w (PUER(l)-DEPR4)36,32.32

,36 T; (AI(j.J))37937,4040 AIASCJ) 9 AjAS(j) *AltliJ)

-D-27 -

0010010Q

vwFC(N) a PFC(I)

17 ?; CI-lC)53V,39o3ZicQ PSlb(j.) a FýIstj) - FS(IIJ)

!; CE1Sj 68F32.3o2.ns

ul21; ( Tr5- I ,)30* bZM)o,,30ij

3.)M P )JNTI NUL-rJ 511 1 1;2- ,3

h4VEH DERM

411A 21SJ A1TAS(J) + l(11

N * N* 1

Cl(N) z i C (I J)

.1 t 1 P7N T INUET

1; 90406

P I- (N)5#!),19594ý, ( L () z SUMCL) + 1

rj ITU 23

1.9 1 .151.(ESiS(.Jf-AIASi(J))41,41a42

41 4S!S Z iSJ?IA(J) =tsis(i)

110 TO 3342 RSIS zAIAScJ)

TIA(J) =AIAS(J)S3 !ýNTINUE

Tý (C1(K) - Cl(MI)34,34,18

34 CONTJNUt

1;CSA(K) -RSIS)4S.43o4444 SACK) mRSIS

ARC 1.4) 3 SAMKa~rx(1,J) z XPFCIK)

!ACI(J) X ATNCJ)00

FA!N4(J) F ATN(J) -(SA(K)/PQP(J))

aSYS zRSIS 9 bA(K)

27 491TtA emýNTINUE

-D-28 -

e (I -1

S kiM(L)2KSUM(L)*12VJ)2?1 1 N T 1INuE

c 0

12( 1V(Nd)30,3O,/

XATC!.L) 0.

7 'Jý;NIINU

14 ! + I

12 (N2282S2

,?9 fONINUEn3 22 Na I#N2

22 r~JNTINUt28 17ONINMUF

!'( I,L):CA(K,M)XAI I DL )A1(K.M)

P-CAT(oiL) =PF"CX(KmM)

L~rAI#L):- tKOID + MQ;A(I'L) =FAT(K5 M) - (AI(K,M)/POP(M~)1; (I-IT)14,24o24

24 f",OJTINUEwRITE TAPE 2.(POP(J).AIAS(J).ESIS(J).TIA(JI,.J21aJI)WqTIF TARC ?.(C(h#L),XAIH,#L)DRFA(T,L)DPFCAT(hL),LOC(lL)eiu1. IT)

IA n ýNTlNUFFND FILE 2RiWIND 2sJmc 0,NIOT 30

no~ 12 Lz1.L2jlj~z4'L)

IT NSUJ4(L)READ IAPý 2#~ (POP(j)aAI AS(J)PESIS(j) ,TIA(J) 1 Ja*2J1)OEAD TAPE 2. (CCIL).XAI(TILJ.RFA( T.LhPFCATCI.L),iLOC(b*L)elu1.IT)

1? CONTINUE

1 .050 1 2 1.

*4OT NTUT * NSUM(L)126 is I I

-D-29

00/00/00

-4o4 I ,L)

~.(Ke(1() - Nsum(mH) 83,f83,01sp X M * 1fs ý ,C A 0

I n ) I INUJn3 51 L;2.L2

l;4(2tL) - NSUMC00~7,570,31,,) !rONTINUE

t. (CC IM)-C(K#.L) )51.,52,53

aLii ,DNTINUECJM C 2 SUMC (C(I.M) *XAI(I*Mfl1; (HLD * SUMC)54,62,62

62 P!ONT!NUE

n) 6U L 1,L260 t( ; K.rT * K2(L)

1: ('(lOT -NTUT -L2)96,67.o',7#ý 7 0"% r U 0

nO TO 59-54 f'S 8 *

SJMC SUM4C *(C(I-M) W XAI(I-,A))

N9t a M1

MIFF = BO-SUMCfAa [UIFF/C(LM)

SAX; IARJMC SUMC *SAX*C(IP¶)

TSA 9 0.REWINU 2mO 63 LsI.L2TýTC 0.TOTSA 0.T L51S a0.TTIA 0s

TPOP a.W~3 x 9(2(L) 1tr (L-MX) 97*9L1.91

97 C0NtINUEjluJ4(L)tT- NSUJM(i)

READ TAPE 2, (POP(J) #AIAS(,J).ESIS(J). TJA(Jb.Jal.J1)OEAD TAPE P. C(t.(L),XAIII*L).RFA(v.L),PFCAT(!.L).LUC(!.L).lx.~.IT)WAI(Ix.mK) aSAXINO 65 Juloji

-D-30-

% 4UOIe

r A T(N)(:)

,1 64 1=1,K3Tý (LUC( I L)tKODE)64*61#64

~A (J ):sl( J) #X I (I *L*XI,)

rATN(.I)) 10A( I.L) * 100."14 MCNTINUF-

AwGiCA(J) ZCl(j)/SA(J)

TjTC-,J ioTOr-CICi)

T3TSAzTofjh.SA(J)T*!z~i

* SSJ

WAS ((IFsls - TCTSA)/TP1P) 10tn.TIIA3-ITIA#TIA(.J)

1)9 FATN(J)=(t~lS(J)/PoP(J) )*100.

4-,ITE OuTPUT TAPE 4,131W~i rE OjTtlt)T TAPE 4.132,4IT oUTfLIT TAPE 4#134"-i 66 Jr1.j1

,TTE OuTfLIT TAPE 4,19 j, POP(.J),SA(J),AVCCA(.J)aES1Si(J).!IA(,j)-

o) -ý'TINUEW;ý!!F OUTPU1T TAPE 4#133wRI'E 0UftltT TAPE 4.120. K4(L),TPOP.TOTSA.AVCSATtSIS.TTIAFATS,

Tr' i- * TUTCTSA =f:ýA +TOTSA

t63 ý )NT I N, UJ.F4TTE OGi!PUT TAPE 4#121*VSAITCwRHTE 03rQiT TAPE 4,123, CNSMWRTF OUrPULT TAPE 4,140. LFD~.1.41TT0! OTtrUj TAPE 4.,141# TFlRM

ijlj roRmAl (1.4F4.0)1U2 rORMAl (16.13)103 rORMAi ( FA.O. F4.0)104 rORMAI (10F6,0)105 PORMAI (1lJ F6.0)106A rORMAl (IUF6.2)

J19 rORMAT (16,2F10.1. F10.2s2F1O.1.Flfi.3. F14.2#/)12n FORMAT (16p2V10.1. FIO.2s2r1O.1,Fjn.3, Fi4.2.1///)121 FORMAT (2!i TOTAL SURVIVORS ADIVED x F10o.6.15H TUTAL COST : F1690)123 FORMAT (31Hd~ COST OF NEXT SURVIVOR ADDED a F6*2)13fl FORMA, (3ubi O!STRIpUTION OF 5.710.O.3H I114.147W STATES

1, i/I)131 FOJRMAT (82W AREA POPUJLATION TOTAL AVG.COSTi INADEOUATE TOTAL

1 PERCENT DISrRIBUTION )132 FORMAi (82N CODE SPACES SPACE SHELTFREE PCTFTI

IAL REMAINING OF)110 rORMAI (2(f6-Q*F6.2)134 FORMAT (821, AODDD ADnED POPULATIC% SPACE

- D-31-

'IN4.deu OO/0&/Do

1% uNS>HEL.IUREf FUNDS 11 53 rjMh ý)PmAI 1;i STATS TUTA.S//)14n rC)PMAI (15i- CONTROL I r 14)

-D-32 -

PC" t I I C rContract -tOCD-?PS-6- - 5,

Fr -, ! I , I I 'i

Rupor t trit it I eA "S, 1 S i Li v i Lv% Ania I N's i o, C ix Li D*' fnse :v .ci id C' o u t

N.f Cop i eAdd( r c t

50 cttfcc o: Civil DcttrcscOffice;~ ~~ (,. Lh. • r; :: ot t!:', t::.

Washington, D. C. 20 310

A t1, : As-' . Dir , - tt•.. of Cli.;i [ mf•,rs (R - t-

3 Offic, of LwLt Adjutant Generat

Departmrent of the Army

Washington, D. C. 20310

Attn: AGAL-CD

1 Chief of Naval Research (Code 104)

Department of the NavyWashington, D. C. 20360

Assistant Secretary of the Army (R&D)

Washington, D. C. 20310

Attn: Assistant for Research

1 Chief, Bureau of Nitval Weapons

(Code RRRE-5)

Department of the Navy

Washington, D. C. 20360

1 Chief, Bureau of Medicine & Surgery

Department of the Navy

Washington, D. C. 20390

1 Chief, Bureau of Supplies & Accounts

(Code L12)Department of the Navy

Washington, D. C. 20360

Chief, Bureau of Yards & Docks

Office of Research (Code 74)

Department of the Navy

Washington, D. C. 20390

U. S. Naval Civil Engineering Laboratory

Attn: LibraryPort Hueneme, California 93041

Advisory Committee on Civil Defense

National Academy of Sciences

2101 Constitution Avenue, N. W.Washington, D. C. 20418

Attn: Mr. Ricnard Park

"N'C.A S 3 I F IEDSfcuntv Classification

DOCUMENT CONTROL DATA- R&D

1 19I-IPNA I I-, IsAC ýi Y, V C'q,f.O.f *.Ih"F 2. N P S CA Z

Research Triangle Institute - N A. 1FI E _Post Office Box 490 2 b - RouI

Durham, North CarolinaI F;D TI TL E

A COST/EFFECTIVENESS COMYflPTER PROCEDUýRE FOR OPTIMUM ALLOCATION OF FALLOUTSAiLTER SYSTEM FUNDS UNDER UNIFORM OR VARIABLE RISK ASSUMPTIONS

4 0 ESC RIP IV E NO'ES , Type ,( rp-,~F A-1 n,,-1-,e d* to m

Volume I of a Final Report in 3 volumes plus Suw-aryS AU THOR() vLavt ýwn* fi,crt* -te fýOa

Guess, Floyd M.

6 REPORT DATE a TOTAL NO Or PAGF- 7h NO Or RFFS

October 1, 1965 90 6so CO)NTRACT OR GRANT No OCD-PS-64-56 9A ORIGINATObR'ScýPORT NU%4BER(S!

S PROJECT No Subtask 4113E R-OU-i57

S Systems Evaluation Division o •OTHER REPORT NOS) (Any other numihr. the(maybe assigedIt~his report)

d OCD Research Directorate10 A V A IL A131LITY LIMITATION NOTICES

Qualified requestors may obtain copies of this report from DDCo

II SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

Office of Civil Defense (OCD)Department of Lhe ArmyWashington, D. C. 20310

13 ABSTRACT The dynamics of civil defense planning and systems evaluation require aprocedure that yields approximate answers to questions concerning effective falloutshelter improvement programs. To accomplish this, a computerized model for the CDC3600 is developed and demonstrated for OCD Region 6. The model permits an evalua-tion of shelter improvement programs against any fallout environment, but it is par-ticularly valuable when RISK-type expressions of the probable fallout environment areused as inputs. Using detailed data from the National Fallout Shelter Survey andequally detailed estimates of the probable fallout hazard in a small area (counties,in the demonstration), the extent to which an area's population is inadequately pro-tected is determined. Fallout shelter system funds are then allocated to areas ofneed in an optimal manner. The allocation employs shelter cost data obtained fromPhase 2 of the National Fallout Shelter Survey on ventilation and shielding improve-ments. Estimated costs for package ventilation (PKV) and shelter in new constructioare also employed in the demonstration in OCD Region 6. In all, 14 cost studies werrun, using selected combinations of the budget level, the fallout risk level, etc.The demonstration shows the practicability of carrying out such large-scale cost/ef-fecriveness analyses. It demonstrates a great need for reliable input data--particu-larly for the unit costs and available numbers and improvement options. The modeland associated computer program not only provide toolE of great value to the decisomaker, but they also emphasize the criticality of his assessment of factors withinand outside the model (e.g., planning horizon, impact of future changes in the ex-pected attack environment, legacy value of existing shelter programs, etc.). Futureork includes extending the model to include direct effects and performing more

extensive demonstrations of the model. (U)

DD IJN a$1473 UNCLASSIFIEDSecurity Classification

UNCLASSIFIED

L. LI N' A C!4 Se

Civil Defense Systems 9 4

Sensitivity Analysis 8 1

Shelter Allocation 8 4

Radioactive Fallout 5 3 5 3

Cost/Effectiveness 10 4

Models 10 3

Prograrmning (Computers) 10 2 10 2

Protection Factor 1. 1

Radiological Dosage 2 1

INSTRU CTIONS

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such as:2a. REPORT SECURITY CLASSIFICATION: Ene h vrI2a EOTSC~YCASFCTO:Enter the over. P 1 "Qualified requesters may obtain copies of thif

all security clasnification of the report. Indicate whether Sreport from DDC.""Restricted Data" is included. Marking is to be in accord- rance with appropriate security regulations. (2) "Foreign announcement and dissemination of this

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tory notes.6. REPORT DATE: Enter the date of the report as day,month, year; or month, year. If more than one date appears - 12. SPONSORING MILITARY ACTIVITY: Enter the name ofon the report, use date of publication. the departmental project office or laboratory sponsoring (pay-

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cial report number by which the document will be identified 14. KEY WORDS: Key words are technically meaningful termsand controlled bv the originating activity. This number must i or short phrases that characterize a report and may be used asbe unique to this report. index entries for cataloging the report. Key words must be9b. OTtHER REPORT NUMBER(S): If the report has been selectee' so that no security classification is required. Iden-assigned any other report numbers (either hy the originator tier,;, such as equipment model designation, trade name. mlilt-or hai the sponsor), also enter this number(s). o tare- project code name. geomraphic location. may be used as

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UNCLASSIFIEDSecurity CTY~ '{c -•