cost and utility: where does the balance lie for governments?

Cost and Utility: Where Does the Balance Lie for Governments?Author(s): D. W. Daniel and D. P. DareSource: The Journal of the Operational Research Society, Vol. 34, No. 3 (Mar., 1983), pp. 193-200Published by: Palgrave Macmillan Journals on behalf of the Operational Research SocietyStable URL: http://www.jstor.org/stable/2581320 .

Accessed: 28/06/2014 16:10

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Palgrave Macmillan Journals and Operational Research Society are collaborating with JSTOR to digitize,preserve and extend access to The Journal of the Operational Research Society.

http://www.jstor.org

This content downloaded from 193.142.30.77 on Sat, 28 Jun 2014 16:10:56 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=pal

http://www.jstor.org/action/showPublisher?publisherCode=ors

http://www.jstor.org/stable/2581320?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


J. Opl Res. Soc. Vol. 34, No.3, pp. 193-200, 1983 0160-5682/83/030193-08S03.00/0 Printed in Great Britain. Operational Research Society Ltd Crown Copyright

Cost and Utility:

Where Does the Balance Lie for

Governments?

D. W. DANIEL and D. P. DARE

Operational Research Branch, RAF Strike Command and Scientific Advisory Group, Army Department, Ministry of Defence

An hypothetical, but typical, example of defence procurement is used to illustrate the problems in Government of balancing costs with the services they provide. Difficulties arise because most Government activities cannot be measured in money terms and balanced in a profit and loss account. Commercial techniques for policy appraisal, such as discounting, seem to have limited relevance to the problems of managing departmental budgets where there is no recourse to a banker. A mathematical programme is used to solve the hypothetical problem and demonstrate that simplistic comparisons of the costs and utilities for various policy options yield little information. Good choices can be found, but are not always obvious ones. They are heavily dependent upon the richness of the problem context. Finally, the authors wonder to what extent the problems they ascribe to Government are also faced from time to time by Industry.

INTRODUCTION

Government departments, other than those connected with the Treasury or revenue

collection, are concerned with the business of providing some service to the community. The essential difference between these activities and those of Industry and Commerce is

that they cannot usually be balanced in a profit and loss account; there is, in general, no

market price for the end product. Because of this, cost and the service provided, often

called utility, cannot be measured in the same units (money) as they might be in a free

market, and the questions arise: where does the balance lie, how much is the service worth?

It may be argued that these are issues to be resolved by Ministers in Cabinet. This is

certainly true for broad policy directives, but how should the Minister be advised on the

details of which road to build; what size of hospital to choose; which weapon system to

buy? In this paper an hypothetical, but typical, example taken from defence procurement is

used to illustrate the issues and to demonstrate that there are no abstract or general solutions to the. problem, only pragmatic ones heavily dependent upon context. Defence

procurement has been chosen because of the considerable effort devoted in most European nations through trials, modelling and simulation to place quantitative measures on the

relative contributions various weapon systems make to national defence. Defence pro? curement is, therefore, an area of Government business in which some quantitative measures can be placed on the utility provided by expenditure. Though these measures are

by no means perfect, there are other areas of Government activity in which the measures

are considerably worse. The purpose of this paper is to illustrate the difficulty of

establishing what is meant by cost effectiveness, or value for money, even when adequate measures of cost and effectiveness are assumed to exist.

PROCUREMENT EXAMPLE

The example concerns the partial re-equipment of an air force. It is an apparently simple

problem in which all the data are to hand and yet it has the richness and complexity found

The original version of this paper was presented at the Fourth European Congress on Operations Research, Cambridge, July 1980.

? Controller, Her Majesty's Stationery Office, London, 1982.

193



Journal of the Operational Research Society Vol. 34, No. 3

Table 1. Relative effectiveness

Mk 1 (existing aircraft) 1.0 Mk2 1.1 Mk 3 1.4

in typical real-world problems. In particular the dimension of time has been included. Not all the re-equipment options for consideration are available for introduction into service

at the same time, and the flow of expenditure required by each is different. A scenario is set in which an air force possesses 60 aircraft at the beginning of a 10 year

planning period. These aircraft are formed into four operational squadrons of 12

operational aircraft in each, with 12 in-service reserves. There is a strict manpower limit, and no additional squadrons can be formed during the planning period. Advances in

technology since this aircraft entered service allow two levels of improvement to be

considered to engine, airframe and avionics. These can be either incorporated into new aircraft or retro-fitted to existing aircraft. For all practical purposes, new or retro-fitted

aircraft to the same standard would have identical performance. Relative effectiveness

assessments are given in Table 1. For simplicity it is assumed that overall effectiveness is

proportional to the number of aircraft times their relative effectiveness.

R&D costs

The R&D cost for modification of Mk 1 aircraft to Mk 2, either as a retro-fit or as a new purchase, is ?9M spread over a two-year period that must be complete at least one

year before the aircraft enters service. The cost is spread unevenly over the two years, with ?7M in the first and ?2M in the second. The R&D effort needed to produce the Mk 3

version would cost an additional ?34M on top of the Mk 2 R & D. Again it must be

complete at least one year before entering service and is spread over three years in two

instalments of ?16M, followed by ?2M in the third. It is assumed that new aircraft could be purchased to Mk 1 standards for no R & D expenditure.

Unit costs

Unit purchase cost of new aircraft is assumed to be spread evenly over the two years before it enters service. Unit purchase cost and earliest in-service dates are given in

Table 2. It is assumed in all cases that once a production order is placed, a minimum

rate of production of seven aircraft a year must be maintained, but the production line has a maximum capacity of only 10 aircraft. Once a production line has been closed, it cannot be re-opened. R&D and production can commence part-way through a year, with

costs apportioned accordingly.

Modification costs

Costs of modifying aircraft to Mk 2 or Mk 3 standard, once the R & D are complete, are assumed to be incurred in the year in which retro-fitting takes place. Unit retro-fit costs

assumed are given in Table 3. It is assumed that up to 18 aircraft a year can be modified to Mk 2 standard but that floor loading limits modifications to Mk 3 to only six aircraft a year. There is no minimum modification rate.

Annual running costs

For every aircraft held on inventory there is an annual charge of ?0.1M, and for every operational aircraft there is an additional running cost of ?0.2M.

Table 2. Unit costs and earliest in-service dates

194



D. W. Daniel and D. P. Dare?Cost and Utility

Depletion

Finally, it is assumed that aircraft are 'written-ofF owing to accidents, irrepairable damage and expiry of fatigue life at a rate of 5% of operational aircraft each year. This means that a minimum of 12 new aircraft have to be purchased in the 10 year planning period, just to maintain the four operational squadrons.

SIMPLE ANALYSIS

A few simple sums should serve to illustrate that there is no simple answer. Superficially the Mk 3 aircraft looks an attractive option. Its unit production cost is 25% more than standard aircraft, yet it achieves a 40% improvement in effectiveness. In contrast the Mk 2 version provides only a 10% improvement in effectiveness for an increase in

production cost of 16%. This seems to imply that Mk 2 can be dismissed as not cost effective.

So far this simplified analysis has ignored the overhead R&D costs, which amount to ?43M for the Mk 3 aircraft. Taking account of these, plus five or 10 years' running costs, leaves the standard Mk 1 aircraft better value for money compared with the Mk 3 for investments up to a break-even figure of ?200-250M, depending upon running cost

assumptions. But this level of expenditure is sufficient for a purchase of 40-60 new aircraft, yet only 12 are needed to replace losses, and the maximum number of aircraft that can be operated is 48. So the simple analysis needs to be extended to incorporate organisational and manning constraints.

Assuming that the funds needed to run the existing inventory are committed, a series of feasible options can be drawn up and a comparison made of their costs and effectiveness. An example (not exhaustive) of such a comparison is shown in Fig. 1. For simplicity it has been assumed that new purchases, or modificationst enter service mid-way through the

planning decade and incur five years' running costs. A more sophisticated approach might involve the use of discounted cash flow techniques, though the value of discounting techniques is discussed later. The measure of effectiveness given is the percentage increase in fleet effectiveness at the end of the decade compared with the starting conditions of 48 standard aircraft. On the figure are annotated a few of the options. The precise basis for these calculations is certainly open to argument, but the general point the authors wish to illustrate is that no option can be singled-out as the most 'cost effective'. A few options

Additional cost over committed cost ( ? M ) Fig. 1. Cost and effectiveness of some feasible options.

195




can be rejected on the grounds that, at similar cost, there are alternatives which provide considerably better effectiveness. But the general conclusion that can be drawn is merely that increasing expenditure provides increasing effectiveness. The final selection of option is, therefore, determined either by setting an effectiveness goal or a budgetary limit. Of these two the thesis is that, in defence at any rate, the budget limit is more likely. Certainly within the U.K., overall defence expenditure remains tightly controlled.

MATHEMATICAL PROGRAMMING

A little more complexity can be added to the problem by supposing that there is a strict

budget limit of only ?30M set aside each year in the hypothetical planning decade for the

re-equipment programme. A constant budget such as this, which is not unrealistic,

obviously imposes severe constraints on anticipated peak expenditure demands for R & D

and for aircraft production. With this constraint added, devising a feasible programme becomes difficult, let alone devising one that optimises operational effectiveness. One

solution is to use a multi-time period mathematical programming model to find an optimal allocation of resources. This might be seen as taking a sledge hammer to crack a nut but

the reader is reminded that a simplified illustrative example is being discussed. It is quite

possible that, as a result of the applications of such exact methods, heuristics could be

devised which would be more suitable for day-to-day application. However, mathematical

programming does have the attraction, during the 'research' phase of a study, of offering low model development overheads at the expense, possibly, of high running costs. In this

particular example, of course, it is necessary to use an integer programme to model the

discrete nature of the options. The model the authors have used takes as input a

specification of the various aircraft purchase and modification options, with all their

attendant cost profiles, production limits and earliest in-service dates, and an assessment

of their relative effectiveness. The model then seeks a year-by-year aircraft modification

and production programme over a period of 10 years that fulfils all the constraints

(operational, budgetary and production) and provides the maximum overall capability. It

is assumed that, as defenders, the western nations have to be prepared to fight a war at

any time. The authors have, therefore, chosen to maximise the sum of the capabilities in

each year, subject to a minimum in any one year equivalent to 40 standard aircraft. Other

objective functions such as minimax could be chosen, but debating alternative objectives is not the subject of this paper. A description of the model can be provided on request.

Average +9.6%

Year

Fig. 2. Changes in effectiveness of optimal solution compared to starting mix.

196




2

28

24

20

26

12

Squadron running costs and aircraft maintenance

_i_ J_I_I_I_L I 2 3 4 5

Year

6 7 8 9 10

Fig. 3a. Budget breakdown for optimal solution.

60 h

50

40 -

30 -

20

I 0 -

Retro fit -\

Original Mkl

3 4 5 Year

6 7 8 9 10

Fig. 3b. Aircraft inventory.

The details of the solution include profiles of:

a. numbers of each type of aircraft held in each year; b. an indication of the year-by-year level of in-use reserves; c. the budget breakdown between various forms of expenditure.

These measures show that a 10% overall improvement in effectiveness, averaged over the

decade, can be achieved by a series of purchases and modifications that finally leaves the

four squadrons 30% more effective than at the start. This is illustrated in Fig. 2. Because

of the mismatch between the budgetary availability of funds and the peak demand of

R&D and capital expenditure, only 95% of funds can be utilized, with the slack occurring in years 1, 9 and 10. By starting R&D immediately it is possible, by the end ofthe decade, to have converted two squadrons of Mk 1 to Mk 3 standard, one squadron to Mk 2

standard and, in addition, to have bought a squadron of new Mk 3 aircraft. But in-service

reserves are tight throughout the decade, dropping to zero in years 4, 5 and 10. The budget

ors 34/3?b 197




breakdown and aircraft inventory are illustrated in Figs 3a and b. Money is such a restraint that a 'penny-pinching exercise' in year 3 is needed in which a flight of four aircraft are withdrawn from squadron operational service in order to save ?0.8M in running costs. Modification of Mk 1 to Mk 2 is split into two phases, the first in year 4 and the second

spread over years 7, 8 and 9. In the simple analysis the Mk 2 modification appeared to be rejected. This was because the simple analysis had ignored two contextual factors

favouring Mk 2 modification:

d. it can be introduced into service earlier than Mk 3; e. it is the lowest-cost way of improving, albeit by only 10%, the effectiveness of the

existing fleet.

DISCUSSION

The solution to the aircraft replacement problem has been obtained by maximising the

average effectiveness of the operational squadrons while keeping within annual budgetary limits. This approach was chosen because it reflects the real procurement process in which funds are allocated over a 10 year period to a particular capability (in this case an element of the Air Force) and the appropriate Service Department (Army, Navy or Air Force) conducts studies to determine how to spend the funds to best effect. In a sense this is a

sub-optimal approach. In theory it would be more efficient to recognise only one constraint in each year, the total defence budget, and to include in the model all the defence

programmes. Such an approach would be less restrictive since it would allow the spending on individual programmes to vary greatly from year to year if necessary. In practice, however, there are a number of severe difficulties which prevent this theoretically ideal course from being followed. Firstly, the sheer size and complexity of the defence

programme would make the model too unwieldy for solutions to be obtained easily and

quickly with current computers. Secondly, for the model to be constructed, common measures of effectiveness relating disparate defence capabilities would be needed, and these do not exist. For instance, it is not possible at present to compare analytically the effectiveness of a general purpose frigate for the Navy with that of a close support aircraft for the Air Force. Thirdly, even if the first two essentially technical problems could be

overcome, there remains a practical obstacle. If a set of programmes had been decided

upon which neatly dove-tailed together so that the peak spending on some projects coincided with troughs in others, difficulties would arise as soon as any one programme began to run into problems and was delayed. The schedule for all the other programmes would need to be re-worked.

The need to simplify the management of defence programmes and to reduce the impact of changes in one programme on others has led, in the U.K., to the de-centralisation of

defence management. The 'Central Staffs' assess the priorities to be attached to various

categories of capability and allocate funds for them in what are called the long term

costings. Thereafter programme managers of the appropriate Single Service Department

attempt to maximise capability within their budgets. Their situation can be contrasted with that of a commercial investment manager who can obtain (almost) unlimited funds in the

market so long as the expected return is good enough to attract investors. The spend can

be varied from year to year at will since money can be borrowed when needed and any

surpluses can be invested.

It is often suggested that Government Departments should follow the commercial

practice of discounting using a discount rate set by the Treasury for public sector use to

assist in the appraisal of projects with differing expenditure flows, but in the public sector

the return on investment is rarely measurable in cash terms, and Government Departments do not raise funds in financial markets. The investment is designed to lead to some social

benefit upon which policy makers have placed a value or utility. In the context of defence, the benefits are likely to be measured in terms of increased effectiveness of some branch

of the armed forces. Funds are not raised directly in the market but are voted annually

198




by Parliament. Because of these divergencies from the commercial scene, considerable care

needs to be exercised in carrying over techniques of commercial investment appraisal when

public sector investments are being analysed. The most compelling argument for discounting future costs is that, when the national

economy is growing through increased productivity, it will be easier for the Government

to raise ?1M (say) next year than it is this year. (The converse argument that, during

periods of economic recession a negative discount rate should be used, does not appear to have found favour with economic advisers!)

In the case of defence, if, instead of spending money on an equipment programme, the

money is left in the private sector, then it can be assumed that it will be invested in some

project which will give a real rate of return equivalent to the discount rate. In these

circumstances it seems entirely logical to compare the costs of alternative defence

programmes of equal effectiveness by using a discounting approach to determine which

is preferable. The case for discounting holds so long as defence managers are required to minimise

costs while achieving a certain minimum or required level of defence effectiveness. In the

experience of the authors, this is rarely the case. The more usual requirement is for defence

managers to maximise effectiveness while staying within financial limits. This applies to

the defence budget as a whole and to individual defence capabilities through the planning mechanism of the long term costings. In the illustrative example quoted, the budget available for the aircraft re-equipment project was held constant over a 10 year period. It could equally well have been set to grow in line with the expected growth of the defence

budget, of G.D.P., or at any other rate. Once the problem has been constrained by a fixed

budget, the use of discounting becomes irrelevant. Economic factors, such as the expected rate of real growth of the private sector, which determines discount rates, have already been taken into account when setting the fiscal limits for the programme in future years. Once the limits have been set, the problem reduces to^one of mathematical programming and can be tackled in the manner illustrated by the example. If programme costs are

discounted, then the budgetary limits should be discounted at the same rate, but this

procedure will have no effect on the solution to the mathematical programme. Discounting

seems, to the authors, to be irrelevant so long as the aim is to maximise effectiveness within

fixed fiscal limits. However, there are alternative views, and the arguments for and against

discounting in defence procurement in the U.S.A. are forcefully debated by Clark,1,2 Blandin and Frederiksen3 and Thaler.4

CONCLUDING REMARKS

The arguments put forward in this paper have been concerned with the balance between

flows of cost and effectiveness. The principal objective has been to discuss the way in which

costs are measured and then compared with effectiveness values when trying to determine

which projects offer the best value for money. Nothing has been said about the problems of measuring effectiveness. This is deliberate. Defence analysts spend much of their time

in trying to devise suitable measures and in constructing models to assess their numerical

values. It is simply assumed in this case that this type of work has been successful.

The example has served to illustrate that a simplistic approach to comparing costs with

effectiveness or utility provides little or no information. Some projects can be weeded out, but generally all that is learnt is that the more effective programmes cost more than the

less effective ones. The usual ways out of this dilemma are either to attempt to compare the costs of programmes of equal effectiveness or to compare the effectiveness of pro?

grammes of equal cost?the so-called constant effectiveness and constant cost approaches. The way in which cost should be modelled depends very much on which approach is

adopted. The experience of the authors has been that the latter approach is more likely,

certainly in a defence context, since programmes generally have to be fitted into a tightly controlled spending profile. A mathematical programming technique has been devised to

199




select equipment programmes by both type and quantity over a period of years, which

maximises effectiveness within annual budgetary limits. In this scheme there is no

requirement to discount future costs, and the conclusions drawn on the relative merits of

programme options are quite different from those implied by the simplistic approach. Whether mathematical programming is the right technique to aid day-to-day decision-

making is open to question. Simple heuristics developed with hindsight may suffice.

However, it is salutary to discover that there are no obvious, easy solutions and that

decisions on 'the best buy' are heavily dependent upon context.

In this paper the authors have claimed that Government activities differ from those of

Industry in two ways. One is that Government activities cannot generally be measured in

money terms. The other is thatTndustry has free recourse to borrow. However, they do

not believe the distinction in a real world is likely to be so clear-cut. They wonder to what extent Industry has policy appraisal problems akin to those they have ascribed solely to

Government.

DISCLAIMER

The views expressed are those of the authors and do not necessarily represent those of the Ministry of Defence.

REFERENCES

lR. H. Clark (1978) Should defence managers discount future costs? Defense Management Journal, Office of the Assistant Secretary of Defense, Washington, March 1978, pp. 13-17.

2R. H. Clark (1979) Counterpoint on discounting. Defense Management Journal, Office of the Assistant Secretary of Defense, Washington, March-April 1979, pp. 44-45.

3J. S. Blandin and P. C. Frederiksen (1978) The role of discounting in problems of choice. Defense Management Journal, Office ofthe Assistant Secretary of Defense, Washington, November 1978, pp. 13-15.

4R. Thaler (1979) Why discounting is always right. Defense Management Journal, Office of the Assistant Secretary of Defense, Washington, September-October 1979, pp. 3-5.

200



cost and utility: where does the balance lie for governments?

Documents