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A practical example of a multi-attribute decision aiding technique
OMEGA Int. J. of Mgmt Sci., Vol. 18, No. 2, pp. 139-t49, 1990
0305-0483 90 53.00 + 0.00 Copyright C 1990 Pergamon Press pie
Printed in Great Britain. All rights reserved
A Practical Example of a Multi-Attribute Decision Aiding Technique JB KIDD Aston Management Centre, UK SP P R A B H U Prabhu and Associates, Surrey, UK (Received February 1989; in revised form October 1989) The marketing and business development representatives of major construction firms operating abroad experience difficulties from being remote from their decision-making executives. Even with modern communications the physical distances involved, with their attendant time zone differences, present many problems for decision-making. One objective of these representatives is to identify construction business opportunities and pursue these through all phases including tendering competitively. A typical policy is for a major decision to he referred to 'head-office' which introduces delays often unacceptable to the clients and which may reduce the competitive advantage of the tendering firm. A study was undertaken in conjunction with a major contracting firm who wishes to remain anonymous. This was to derive a decision-making process for its overseas representatives which would help on-the-spot decisions to comply with corporate policies whilst a bid is being presented to the client by the due date. The firm is divisionalised and operates in overseas territories as one single division using sub.contractots, or with co-operating divisions, or at group level. As the tendering personnel are one of the firm's scarce resources and also a most valuable resource, it is clear that they should he 'used' to the best advantage. This paper presents the decision aiding technique proposed by Keency and Raiffa, in a restricted format, to illustrate how firms may better utilise their scarce marketing and business development resources and in doing so boost their chances of success in a competitive situation.
Key words--bidding, tendering, strategy, multi-attribute decision analysis
INTRODUCTION THE MAJOR ENTERPRISE which provided the data for this paper operates in many overseas countries and has several specialist divisions. If a project is small, one of the divisions will evaluate it, and perhaps offer to tender with the aid of a local sub-contractor. Sometimes a division will perceive that the task needs the services of one or more of the other divisions. In such cases, further extended tender analysis has to take place, meetings arranged, and joint evaluations undertaken. In some cases, the potential workload calls for the total groulffto-be in the tendering partnership, maybe even entering into a consortium agreement with other OME 1 5 , 2 ~
major firms (at times overseas companies), especially manufacturers of capital plant and equipment. As one may imagine, any venture (other than the simplest) calls for quite lengthy evaluation time. The tender period is usually limited by the client so the time available needs to be utilised effectively by the tenderer. One of the most effective operations at this stage is to be decisive on the question of whether to bid or not. If the division singly, or in partnership, or at group level, finds the affirmative answer quickly, more time will be available to prepare a better bid document, leading hopefully to winning a greater proportion of all tenders proposed. The technique of decision aiding developed by 139
140
Kidd, Prabhu--A Multi-Attribute Decision Aiding Technique
Keeney and Raiffa [1] appears to be an ideal mechanism to evaluate the question--"to bid or not to bid"? The proposed procedure which is based on an easily applied rule is essential, as contractors are often tempted by large schemes in developing countries and tend to overcommit scarce business development and marketing resources in pursuit of these schemes. Often potential developments have built-in attractions such as: - - o p p o r t u n i t y to generate cash; - - o p p o r t u n i t y to utilise resources; - - o p p o r t u n i t y for further business; all of which have different levels of attractiveness at different times to the parent firm. A quick, understandable and consistent mechanism to evaluate these factors would be of interest to multi-national corporations. We do not claim this technique should replace the intuition of the senior executives based on their knowledge of their business plans, goals and missions. Rather, we hope the technique will aid their judgement. Managers generally acknowledge that they should spend more time on developing strategies and this theme is promoted across a broad spectrum of management literature. For instance Keen [2] argues that managers have above all to remain competitive through the use of modern technological aids. We are aware that a reduction in the time available for a decision increases the pressure to take risky decisions and the contracting business, being no exception, is full of risks and uncertainty. We suggest that systematic analysis can help identify the range of uncertainty within which contractors have to work. Such a procedure can evaluate categories such as: (i) uncertainty about the facts at hand; (ii) the subjective assessment facts;
of these
(iii) the future consequences of present decisions based on the facts. METHODOLOGY
-
A senior marketing manager at director level was interviewed to ascertain his responses to the
several facets of the method. (These facets will be reviewed in turn as we build up a multi-attribute equation that will act as a decision filter. This equation will be used to generate overall values that will allow easy adjudication of the worth of tendering at a given opportunity.) He agreed that sometimes marketing executives are a little over enthusiastic over some projects, being concerned with their own prestige, and as a consequence, may become involved with something 'not in line' with corporate policy. Later analysis showed these 'pet' projects have led to a wastage of scarce tendering resources in order to support projects on which the contractor had no expertise. Table 1 shows the project business opportunities 'chased' by the firm. Only 51% of the project business could be classified as associated with company knowhow. The rest was wrongly pursued so deploying the organisation's scarce human assets with no reasonable chance of success. Wastage of time necessarily spread throughout the firm as senior managers attempted later to extricate the firm from the ensuing difficult situation. He agreed that there was a primafacie case for the provision of a decision aiding tool which should save managerial time by aligning decisionmaking with corporate policy. The technique has five stages of analysis and requires considerable discussion between the 'analyst' and the client. Much of this discussion will have to be taken for granted in the nature of this paper--but example conversations will be reported. These time-consuming procedures must be followed to ensure the correct derivation of a robust equation that will be used as a surrogate for the (human) decision-maker. Initially, and usually with the help of the consultant, the decision-maker has to ascertain which variables are within his control and which are extraneous to the firm. Then a small number of the controllable variables have to be selected so as to properly describe the 'problem' but not to include too much surplus detail. Following this selection there is an initial analysis to check that the attributes of the decision are independent and do not 'colour' each other through the ensuing discussions. If there is some overlap in the decision-maker's mind between these attributes it will not be possible to determine if more or less of one attribute in particular is of vital importance when the other attributes get in the way, as it were. Once independence is
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Table I. Classification of projects
Class of project Power generation and/or distribution (civil/electrical/mechanical) Process and chemical industries Civil engineering based Assortment of projects Projects needing general co-operation Totals
proven, the way is clear to the development of an equation that links all attributes to the utilities that the decision-maker has about him/her individually and globally. The equation is the objective of the long elicitation process-once found it may be used as a fast decision support tool, even as a surrogate decisionmaker if the manager is absent for some reason and the client is pressing for an answer. We will now illustrate the stages of deriving the decision aiding equation.
Numbers
Percent of total
Projects associated with the firm's know-how (%)
41
34
34
39 22 9 9
33 17 8 8
nil 17 nil nil
120
100
51
All attributes have to be measured. Their scales have to capture the full range of permissible values that will be acceptable by the decision-maker. Individual values outside these ranges, while they may be feasible in some other circumstances, will be deemed for this analysis to generate a utility of zero. Hence they have been excluded from further discussion. The ranges of the attributes and their graduations for the example are given in Table 2.
Stage 2--The independence of the attributes Stage 1--The attribute list The total number of attributes in a decision process are often thought by decision-makers to be too many, diverse and impossible to quantify. In fact often only a few are of real significance: they are diverse, but they are quantifiable. Later on we will see that they can be traded-off in magnitude terms against other attributes and against some ideal point. Clearly, the greater the numbers of attributes the longer is the initial task of evaluating their indifference. Nevertheless, a sufficient number are needed to capture the full sensitivity of the problem space. There is a need to discuss this aspect with the client so as to derive a valid starting set of attributes. In practice, seven to eleven attributes seem to capture the richness of most problem scenarios. In this example, derived from a detailed case study, we will use only three attributes to reduce the complexity of the analysis simply for the purpose of illustration. These attributes are: X l - - t h e opportunity to generate cash; X2--resource utilisation; X3--opportunity for future business.
It is possible to obtain a reliable equation linking all the attributes by undertaking a full combinatorial evaluation of the effects of varying each and every attribute in the study, but this is a very time-consuming task. It is virtually impossible when there are more than five attributes to consider. The method developed by Keeney and Raiffa checks for attributes that are co-related in the decision-maker's viewpoint, although originally they may have been proffered as though independent. Once independence is established, only a few combinations of the attributes are then needed to ascertain the overall utility equation. Although we refer to the definitions given by Keeney and Raiffa in their exemplary book, there are several introductory examples given in Kaufman and Thomas [3]. Step l mPreference independence check. The details of the procedure are given in Table 3 for one pair of attribute checks. Here, we will concentrate on the rationale of the checking. In order to establish the independence between the attributes, an initial check is undertaken to see if there is any variation in a hypothetical trade-off between two attributes under very different circumstances--namely, when all the other attributes are each at their worst, or alternatively, are all at their best
x3 Opportunity for future business
x2 Rcsouroc utilisation
XI Opportunity to generate cash
Attributes
o
_.2
|
¢
Opp. for extension of the project
20
o
No opp. for future work
,I .I
Up to 20% divisional staff can be utilised
20
5% profit no down payment
41 H
Very little opp. to Use own resources
o
Negative cash flow and no profit
Opp. for PiE work only in the territory
Up to 70% divisional staff can he utilised
5% profit 10% down payment
4o
~ s
40
.I,
40
I ,K
,JR
Opp. for managing Contract or type of work
- - ,
Input from two divisions
•°
10% profit 15% down payment
Measure
611
'I
60
I•
I
8O
Opp. for main contracts work
~0
, °M
Input from four divisions
80
15% profit 20% down payment
Opp. for sub-contracts work
L
Input from three divisions
I
10% profit 20% down payment
Table 2. Ranges and lists of attributes
.,
I
.12
Opp. for all types of work
IN
use the group's resources
O p p . to
I00
20% profit 20% down payment
No opp. for future work
Very little opp. to use own resources
Negative cash flow
Worst
Best
Opp. for all types of work
Opp. to use the group resources
20% profit and 20% down payment
Levels
B=
i
g:
I
Omega. Vol. 18, :Vo. 2
143
Table 3. Preference independence check Consider the pair XI and X2 - - a n d assume X3 is at its WORST level 100
G F
Indifference
Question-From point (A,H) would you rather move towards N or towards G? That is--N = (Xl at worst, X2 at best) or G = ( X I at best. X2 at worst)? 100 bst
(X21
DM: (answer) I am personally in favour of cash generation and would prefer to go for point G (i.e. 20% down payment and 20% profit) with H on X2 (showing little opportunity to use our own resources) rather than the policy at point N. Q: Would you consider point E? DM: Yes--I would still prefer a good profit level and a good down payment--even if it means using outside resources. Q: How about point D? DM: Again ' Y e s ' - - b u t these policy changes are becoming less attractive. Q: At what level of cash generation would you be in a dilemma? That is--when would it be difficult to choose between XI and X2? DM: I think if XI is at B (i.e. 5% profit and no down payment and no opportunity to use the groups resources) then it would be too low. At that stage I would rather go for the use of the groups own resources. So . . . point C would be my indifference point. Q: So, at this level you have no preference between XI and X2? DM: That is correct.
values. When independence is proven, we may be confident that later in the procedure the decision-maker will be able to make real-valued trade-offs no matter what levels are taken by the other attributes (because none of the attributes are co-related). The check is continued to cover all pair-wise combinations of the attribute set. Non-independence will be noted when there is a substantial difference between the two indifference points found in the two trade-offs: the case when all attributes are at their 'best', and secondly, when they are all at their 'worst' values. At this point it is necessary to consider both the analytic and the subjective interactions in order to choose which attribute to 'drop' from the evaluation. By removing an attribute which is acting in a co-varying way with another of the attributes, one removes the perceptual confusion caused by non-independence. In Table 3 we find indifference pairs at points C and N. Here the manager is indifferent between: C: a policy of pricing at 5% profit and seeking a 10% down-payment--but with little opportunity to use the firm's own resources. and N: a policy having negative cash flow and no profit, but with opportunity to utilize the whole group's resources.
As can be imagined, the complexity of the individual scale descriptions require considerable discussion in order to achieve a clear, meaningful and stable trade-off position. The role of the analyst is of paramount importance here; and, while it is difficult to recount on paper, one must not forget the importance of wide-spanning conversations between the analyst and the client to ensure the derivation of unequivocal results. Table 3 covers only attributes X1 and X2; we have the further need in this exposition to relate X3 with one of XI, or X2, to have examined all the combinations--but in the full analysis (not quoted here), there were more pairs to consider given that there were nine attributes. Step 2inUtility independence check. Here the procedure is similar to the above, but we now consider only one attribute at a time. Table 4 illustrates the procedure for the first attribute, XI. Once more, the task is to check if there is any substantive variation of the indifference point as the background changes: that is, as all attributes other than the one specified are changed from their best to their worst levels. If there is a substantive difference in the indifference point, then there is some underlying co-relation that has to be eradicated so that the decision-maker can be clear-headed about individual changes in the magnitudes of the attributes later in the analysis. When there are several attributes, the
Kidd, Prabhu--A Multi-Attribute Decision Aiding Technique
144
Table 4. Utility independence check Consider attribute Xl only --with all others at their BEST G
A
X ? ; b e s t rover. ( 2 0 */, downpaymen~ Clnd 2 0 * / , grofit)
X l : ~ors~ LevoL. (LO. neqotive CaSh fkOW)
BorCDEF? •.
for s u r e . .
Q:
Consider the lottery above. This gives you a 50% chance that XI would be at its best level, and a 50% chance that it would be at its worst level, Remember--X2 and X3 are at their best levels. Would you prefer the gamble, or point B? DM: With a 50/50 chance of the best leveE, I would rather go for the lottery. Q: How about point C if it were sure? DM: No. The lottery is still of interest. Q: Now what of having point D for sure? That is 10% profit and 15% down payment. DM: In this case I would be indifferent.
potential for conflict is high; in this example we assume the three attributes are independent both in a preference and in a utility sense.
Stage 3--Evaluation of the individual utility functions Table 5 indicates the procedure for the X1 attribute. These graphs are needed to translate the eventual real-valued tenders on say, the scale of X1, into the utility value of Xl, i.e. U(X1). In other words, we are asking how the decisionmaker views the continuum from the minimum to the maximum of X I. Are all increments equally desired? Or, are unit increases on one part of the scale more highly 'valued' than at other parts of the XI magnitude scale? More simply, this represents the usual human tradeoff o f . . . "the more you have the less welcome is the increment, but it continues to be a positive welcome". In utility theory (well covered in texts such as Keeney and Raiffa [1]), there is no absolute requirement that the individual curves be concave, convex or even straight, lines. They are representations of the decision-maker's perceptions and feelings at the point of time of the analysis. These graphs take into account all the surrounding factors t o o - - t h e state of his or her peer group, the state of the firm and of the market--even the state of the nation. This means that the utility curve of another person may be quite different. But nonetheless we are
saying that the exposition of a personal statement will lead to more enlightenment and more discussion than would be the case if there was no modelling of the decision problem. Within this study of multi-attribute decision analysis there is the assumption that the individual decision-maker such as the director of marketing represents the totality of the organisational viewpoint. It is known that to incorporate the views of many individuals, some of whom will be concerned with attributes that others consider trivial, is a complex and as yet unsolved problem. We pose this method as one that should lead to discussion and development in the enterprise by the simple fact that a model is used, and it is presented 'on the table' for agreement, or for contradiction, but importantly for the overall betterment of the decision process. In general terms, the type of business and organisational structure will have some influence on the ease of developing discussions on the model and its parameters.
Stage 4--Derivation of the multi-attribute equation The earlier stages have been concerned with evolving and agreeing a valid data set--the attributes that independently describe the problem space. Now we wish to assess the impact of potential real trade-offs between the valid attributes. It makes sense at this stage to the decision-maker to assess trade-offs firstly
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145
Table 5. Utility curves
Eraluation of individual utility curves Starting with XI Assign utility values of 1.0 to point G and 0.0 to point A. REMEMBER: no other attribute will interact with this assessment as we have found them all to be independent.
X100 U:~O
F
XI~AU:O0
Q:
relative to the various descriptions of the X I scale what would your indifference be in comparison to the gamble illustrated.'?
For the first evaluation we have U(B) = 0.5 ( l . 0 ) + 0.5 (0.0)=0.5 DM: Point B--because I would not wish to receive the downside costs of the worst case outcome at its 50% chance. Q: Now we have moved B to be the downside risk. What would your indifference point be? DM: Now I guess it is point C.
J Fcs~°
x~oou:,.o
For the second gamble we have u ( c ) = 0.5 (1.0) + 0.5 (0.5) = 0.75 X1 @ 8U : 0 5
Now point A is substituted into the gamble instead of point G and this yields a certainty equivalent about half way between point A and point B. U('p') = 0.5 (0.0) + 0.5 (0.5) = 0.25 It is possible to plot these Certainty Equivalent resulting from the gambles against their Utility values as follows. 1
P
B
C
O
E
F
G
Votue ( X l )
between the attributes that are perceived to be the most important, followed by the attributes deemed to be of less importance. There are thus two steps to this process: Step I--Ranking of attributes. This is a relatively simple task. Initially, attributes have to be imagined to be at their worst values. Following this, the decision-maker is asked to choose which attribute to raise first to its best value (if that were a possible scenario); then the second, then the third, and so on along the list. The resulting ranked list provides the guidance for the subsequent analysis of pair-wise trade-offs. Previously, in Stage 2, the pair-wise comparisons have been against a con_venient list, X1 to X2 to X3 etc. But now we have a list of importance rankings that shows that there is a perceived distance between the attributes
that will make comparisons more (or less) meaningful. For example: a comparison of 'chickens and eggs' may be easier than 'chickens and gross tonnages of boats'--some attributes are linked naturally in a decision problem. Applying this analogy to the construction industry we feel a comparison of 'design or construct a power plant' against a 'procurement contract' may be easier than 'design a power plant' and 'mining for coal'. Too wide a range in the allowable set of comparisons becomes meaningless in assessing trade-offs--the decision-maker would not (truly) be able to make reasonable comparisons as they are not the usual comparisons that are made, whereas attributes that are close in the decision space may have trade-offs undertaken realistically. In the case example, the rank order
Kidd. Prabhu--A Multi-Attribute Decision Aiding Technique
146
is of little importance over the three attributes, thus we will assume the order X1, X2, X3 is preferred, with XI being the most preferred. In the real background problem there was a large perceived distance between the first and the last attribute in this ranked list.
Step 2--Assessing the relative trade-off magnitudes. This procedure follows from Step 1 wherein the rank order of the attributes was evaluated. As we know the attributes are independent (from Stage 2) we can allow pair-wise consideration of the attributes to be undertaken without reference to any other attribute. Table 6 indicates the form of questioning that can take place to derive and quantify the relative weights to assign to each attribute. In this example there are two equations linking the three attributes, but in general for 'n' attributes, there will be ' n - 1 ' equations. To provide a solution for this set of equations we have to seek one absolute value of a weighting, say upon the premier attribute. Then it will be possible to cascade the calculations through the
interconnected set of equations to obtain a full set of numerically defined weights, wz, w2. . . . . w,. It is only at this stage that we may ascertain if we have a linear relationship between the attributes or a more complex multiplicative relationship. By definition, described in Keeney and Raiffa, if the sum of the 'w' weights is approximately unity, the relationship is linear. Again the judgment is subjective: a linear relationship is easier to explain to most clients, but must not be used when the mathematical 'truth' indicates the use of a more complex equation.
Stage 5--Revision of the attribute rankings Following the insights gleaned through the detailed analysis many clients revise their opinion of the most important attributes (the ranked set). This rearrangement will affect the derivation of the individual weights within the overall utility function. Thus the latter two stages have to be undertaken once more to revise the tradeotis and derive new weighting coefficients.
Table 6. Scaling constants
Assessing the scaling c o n s t a n t s The relative weights of each attribute are evaluated by assessing the trade-offs between the independent attributes. The affects of the other attributes do not matter. Consider the attributes XI and X2
N
L
tndi f. pair K X2
M--__7 J
1
H
Q: DM: Q: DM: Q:
A
B
C
0 Xl
[
F
G
The point (A,H) represents the WORST case of both attributes. So what policy change would you prefer? To go to N or to G? To G. But if we had to reduce G to F would you accept this? Yes: in fact right down to D---then [ would be puzzled as C is to me less desirable than point N. OK. So let's say you are indifferent between the two policies of (A,N) and (DoH). This is equivalent to--U:(A,N) = UK(D.H) Or we may say ... w: ffi wlul(D) since the utility of X2 at N is 1.00 Reference to the diagram in Table 4 shows u~ (D) = 0.84 (approx.).
Following the remainder of pair-wise comparisons we find that w: = 0,701 w b and % = 0.754 w~. Now one absolute value for a 'w" has to be found from the next gamble structure. AU. o t t r i b u t l l
¢11 D i l l
ODtiOn 1 a r t a t t r i ~ u l : e l a t wort~:
X l at: b l l t , r l l t 01~ worlr.
I
Alter the value of the probability to check the indifferent choice of option.
I ere with P = 0 . 8 there is a - balance point.
Substituting in the above equations results in Ut(Opt)= Lt't*=0.8 and thus a'2--" 0.701 and w3 = 0.754. The total utility = 2.25, well over unity. We have therefore to use the muhiplicative equation.
Omega, Vol. 18. No. 2
Finally we should have established an equation that will be capable of aiding the decision process. It has been elicited from an agreed list of attributes which have been proved to be independent. And, after ranking the attributes, there followed the development of an equation that will simulate the perceptions of the decision-maker. This equation could be used as a surrogate 'decision-maker' in order to evaluate, at any instant, any new information within the domain of its competence. AN EXAMPLE OF THE TENDER PROCESS
147
and so k = - 0 . 7 4 . The assessment was repeated to see if the value of k differed through the newly acquired insights about the value tradeoffs, but it remained at - 0 . 7 4 .
Comparison o f
Attribute XI
As we mentioned above, the firm wishes to remain anonymous, and so the example has been heavily disguised. In Table 2 we set out three attributes that must suffice to illustrate the development of the technique. These attributes have their worst and their best values noted and there are intermediate values noted as policy B or K or T for instance. These policies were 'calibrated' with respect to two measures of 'cash flow' in X l; to the origin of the resources in X2; and to the types of future work possibility in X3. The scale break-downs are not linear, but represent meaningful descriptive phases. One should note that the quoted policies A - U encompass real examples which are illustrated below as projects 1-9. The theory underpinning this form of multiple attribute analysis (see Keeney and Raiffa) says that if the sum of the weights equals unity we may use an additive m o d e l - -
tender offers
We have now found the components of an equation that capture the feelings, trade-offs and utility of the decision-maker so we are now in a position to use the equation for evaluating the differences between tender offers. As an initial example, note the following two tender offers:
X2
Project I
Project 2
5% profit margin 10% down payment i.e. point C Input from four Divisions
10% profit 20% down pa?ment i.e. point E Up to 70% divisional staff can be utilized on project i.e. point K Opportunity for PIE work onl}
i.e. point N Opportunity for extension of the project i.e. point R
X3
By interpolation from the individual utility curves developed as in Table 5 we find for project 1: U(Point C) = 0.75, U(N) = 0.75. and U(R) = 0.04. And as we know all Wi and the scaling constant K, we may calculate the utility of the project. From the multiplicative equation we have [1 + ( - 0 . 7 4 )
U ( X I . . . X3)] = [I - (-0.74)(0.75)(0.80)] • [I - (-0.74)(0.75)10.70)] • [I - (1 - 0.74)(0.04)(0.754)] = 0.668
u ( x t . . , x°) = s[wt.u(x , ) + w.,.u(x,)... + w, .x(u, )1
but if the sum exceeds unity, as in this example where the Z(weights)= 2.25, then we must use a multiplicative m o d e l - I +k'U(X
I ...X,)
= ~[I + k ' w , ' u ( x t)]
where k is a further scaling constant that has to be computed as follows: If we say that all attributes in the above equation are at their best values, then U(X~, )(2, )(3) and u(xi) are all equal to unity, we have 1 + k = i - t n~ (1 + k ' w I) = (1 + 0.8k)(l + 0 . 7 k ) ( l + 0.75k)
with the w~ being derived through the comparisons illustrated in Table 6. That is: with . . . wt = 0.80, w., = 0.70, w3 = 0.75
i.e. point Q
and so the overall utility becomes U ( X I , X2. X3) = 0.90 for project I, a n d likewise U ( X I , X2. X3) = 0 . 9 3 for project 2
This is continued for all projects to form the following list: Individual (raw) attribute utilities Pr~ect
ul
u2
u3
ZU
Weighted project utility
Scaled project utility
I 2 3 4
0.75 0.95 0.50 0.50
0.75 0.50 0.55 0.35
0.04 0.06 0.0 0.06
1,54 1,51 1,05 0,91
0.9 0.9 0.67 0.6
0.75 0.75 0.54 0.49
5 6 7 8 9
0.88 0.0 0.0 0.97 1.00
0.0 0.63 0.50 0.75 1.00
0.0 0.0 0.14 0.50 1.00
0.88 0.63 0.64 2.23 3.00
0.65 0.43 0.41 1.09 1.23
0.52 0.35 0.33 0.89 1.00
Kidd, Prabhu--A Multi-Attribute Decision Aiding Technique
148
It should be noted that the evaluations above are derived from a 'what if' search. The individual attribute utilities have been systematically varied to highlight slightly fictitious projects to review a spectrum of results within which socalled real projects will lie. These data may better be expressed in graphical form to show the cut-off in project utility; see Fig. i. Through a retrospective review of successes and failures in tendering, the management decided that any project not conforming to a weighted utility of 0.9 or more should not be considered for the tender development process. The graph shows both the raw scores and the scaled (weighted) utility score. There is a clear point below which potential projects are of no interest to the firm. Conversely, for high scoring tenders, resources may be put quickly to those projects that have shown a utility value above the cut-off point. CONCLUSION Several methodologies have been proposed in the literature on the topic of 'evaluation'. One, based on Linear Programming, Turner [4] derives a quasi-optimal solution for contract tender evaluations. Some judgment is allowed upon the acceptable commercial tender, but the method relies mainly on the use of a 'hard' technique. Another example, Cook et al. [5], is based on the methodology of multi-criteria analysis. Here the authors use a modified version of ELECTRA (see Roy [6]), called SELECTRA. We do not recommend this method in so far as it captures little of the managers' preferDecision aiding graph DispLay of u t i L i t y ~
1.o
(1) Ensuring a thorough and consistent review of the process of "tendering'.
(2) Making clear the policies and issues to
0.8 2~ff-Here, the onty ._~ •~.,
ences over the alternatives. A different illustration of the evaluation of alternatives is given by Brooks and Kirkwood [7]. Here they use the multi-attribute method, which we favour, to aid a selection procedure when all vendor offers are known within a purchasing problem. Finally, we wish to mention a paper supporting the use of researched and negotiated subjective values. Khan and Shih [8] show that jud~nental decision models perform well in environments that have high intrinsic variability. Thus we are confident that the method and case work which we have discussed above was rigorous enough to offer a good management support tool. Through the long process of discussion and evaluation of feasible attributes, their trade-offs and the derivation of each attribute's weighting we have derived an equation that is a model of the decision-maker. It may even be a surrogate of the decision-maker. This model has been exposed to public scrutiny within the firm and within the group to further expose its assumptions to the assumptions held by other managers--both with respect to the model of the decision-making process and to the manner in which the weightings were developed through one person's subjectivity. This process of refinement has resulted in an equation that can act as a filter against potential overload of the manager responsible for initiating the tender evaluation. Furthermore, it can act as though it 'were' that person if the manager were unavailable for some reason, perhaps detained on other business. It can thus materially reduce the variety and uncertainty that does exist. Thus we could summarise the benefits as--
all involved in the process, be they local or remote in the organisation.
projects as
.~ :5
0.6
candidates for
tendering are
"o
1,2,8 and 9
(3) The creation of an equation that
0.4
openly incorporates the subjectivity of the decision-makers following negotiated trade-offs.
SuitabLe
0.2
projects .1
0
0.5
1.0
1.5
I
2.0
-I 2.5
Total row utilities
Fig. 1. Graphical display of project utilities.
I
3.0
(4) The reduction of the 'mystique' of decision-making through the substitution of systematic analysis within a wellfounded scientific framework.
Omega, Vol. 18, No. 2
Clearly, by creating this equation and obtaining the support of management in its use we have helped to develop a strategy for competing in time and thus we have aided the time management and the human resource management of the whole firm. The construction industry in which the above technique was tested has unique characteristics such as projects which are exposed to many elements and politics outside the control of the contractor. Hence the technique is not intended to replace the senior executive's intuition which would be based on his knowledge of business and the immediate environment. But it is to be seen as an aid to sharpen judgement. Nor, we may add, is 'our' multi-attribute technique presented as the only method applicable in these circumstances. We see increasing effort being put in to the support of persons concerned with large scale projects. For instance A1-Khayat and Edwards [9] have suggested an options-choice methodology which combines a problem structuring approach with one based in multi-criteria decision analysis. Within their decision analysis section their clients, like ours, have to make strategic selections, or rank orderings of their preferences. For this it has been suggested that the Analytic Hierarchy Process (AHP) is appropriate. This method was originally formulated by Saaty [10]; it looks essentially at pair-wise comparisons of options against criteria within some overall focus wherein the client can rank the options and so develop a set of weights in the face of potential inconsistencies. Other approaches lean towards the application of Expert Systems to elucidate the knowledge base of the field consultants, see for instance King and Phythian [11]. In all these cases, ours included, we see that there is a very strong element of 'modelling' involved. The consultants are concerned to present a system to their clients that allows the client to be more consistent, and helps support decision-making in a more timely fashion. All
1-19
the methods are concerned to extract the subjective rules that are used in practice so as to offer a consistent decision aid to the firm. But to derive the final decision aid all methods involve the client in considerable discussion and thus are time-consuming. Yet, based on this strong framework, it is suggested that tendering firms will be able to offer better researched tenders which will result in more successful outcomes. This was certainly true in our case, and as Fig. 1 indicates, we can offer a very simple graphical aid to answer the question "to bid or not to bid"?
REFERENCES 1. Keeney RL and Raiffa H (1976) Decisions witil Multiple Objectives. Wiley, NY. 2. Keen PGW (1988) Competing in Time: using Telecommunications for Competitive Advantage. Ballinger, Cambridge, MA. 3. Kaufman GM and Thomas H (1977) Modern Decision Analysis. Penguin, Harmondsworth. 4. Turner I (1988) An independent system for the evaluation of contract tenders. J. Opl Res. Soc. 39(6), 551-56 I. 5. Cook WD, Golan I, Kazakov A and Kress M (1988) A case study of a non-compensatory approach to ranking transportation projects. J. Opl Res. Soc. 39(10). 901-910. 6. Roy B (1978) La m~thode ELECTRE II. METRA Direction Scientifique, Note de Travail 142, pp. 161-182. 7. Brooks DG and Kirkwood CW (1988) Decision analysis to select a microcomputer networking strategy: A procedure and a case study. J. Opl Res. Soc. 39(1). 23-32. 8. Khan AM and Shih C-T (1988) "Judgemental decision models as alternatives to optimisation: The case of spousal selection. J. Opl Res. Soc. 39(5), 435-457. 9. AI-Khayat FHM and Edwards JS (1986) An optionschoice methodology for technological projects in developing countries. Systems Res. 3(3), 123-133. I0. Saaty TL (1980) The Analytic Hierarchical Process. McGraw-Hill, NY. I1. King M and Phythian G (1989) Expert systems in competitive tendering--a case study. A presentation to the 31st ORS Annual Conference, Southampton, 12-15 September 1989. l~fr JB Kidd, Information Management Division, Aston Business School, Universit)' of Aston, Birmingham, B4 7ET, UK.
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0305-0483 90 53.00 + 0.00 Copyright C 1990 Pergamon Press pie
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A Practical Example of a Multi-Attribute Decision Aiding Technique JB KIDD Aston Management Centre, UK SP P R A B H U Prabhu and Associates, Surrey, UK (Received February 1989; in revised form October 1989) The marketing and business development representatives of major construction firms operating abroad experience difficulties from being remote from their decision-making executives. Even with modern communications the physical distances involved, with their attendant time zone differences, present many problems for decision-making. One objective of these representatives is to identify construction business opportunities and pursue these through all phases including tendering competitively. A typical policy is for a major decision to he referred to 'head-office' which introduces delays often unacceptable to the clients and which may reduce the competitive advantage of the tendering firm. A study was undertaken in conjunction with a major contracting firm who wishes to remain anonymous. This was to derive a decision-making process for its overseas representatives which would help on-the-spot decisions to comply with corporate policies whilst a bid is being presented to the client by the due date. The firm is divisionalised and operates in overseas territories as one single division using sub.contractots, or with co-operating divisions, or at group level. As the tendering personnel are one of the firm's scarce resources and also a most valuable resource, it is clear that they should he 'used' to the best advantage. This paper presents the decision aiding technique proposed by Keency and Raiffa, in a restricted format, to illustrate how firms may better utilise their scarce marketing and business development resources and in doing so boost their chances of success in a competitive situation.
Key words--bidding, tendering, strategy, multi-attribute decision analysis
INTRODUCTION THE MAJOR ENTERPRISE which provided the data for this paper operates in many overseas countries and has several specialist divisions. If a project is small, one of the divisions will evaluate it, and perhaps offer to tender with the aid of a local sub-contractor. Sometimes a division will perceive that the task needs the services of one or more of the other divisions. In such cases, further extended tender analysis has to take place, meetings arranged, and joint evaluations undertaken. In some cases, the potential workload calls for the total groulffto-be in the tendering partnership, maybe even entering into a consortium agreement with other OME 1 5 , 2 ~
major firms (at times overseas companies), especially manufacturers of capital plant and equipment. As one may imagine, any venture (other than the simplest) calls for quite lengthy evaluation time. The tender period is usually limited by the client so the time available needs to be utilised effectively by the tenderer. One of the most effective operations at this stage is to be decisive on the question of whether to bid or not. If the division singly, or in partnership, or at group level, finds the affirmative answer quickly, more time will be available to prepare a better bid document, leading hopefully to winning a greater proportion of all tenders proposed. The technique of decision aiding developed by 139
140
Kidd, Prabhu--A Multi-Attribute Decision Aiding Technique
Keeney and Raiffa [1] appears to be an ideal mechanism to evaluate the question--"to bid or not to bid"? The proposed procedure which is based on an easily applied rule is essential, as contractors are often tempted by large schemes in developing countries and tend to overcommit scarce business development and marketing resources in pursuit of these schemes. Often potential developments have built-in attractions such as: - - o p p o r t u n i t y to generate cash; - - o p p o r t u n i t y to utilise resources; - - o p p o r t u n i t y for further business; all of which have different levels of attractiveness at different times to the parent firm. A quick, understandable and consistent mechanism to evaluate these factors would be of interest to multi-national corporations. We do not claim this technique should replace the intuition of the senior executives based on their knowledge of their business plans, goals and missions. Rather, we hope the technique will aid their judgement. Managers generally acknowledge that they should spend more time on developing strategies and this theme is promoted across a broad spectrum of management literature. For instance Keen [2] argues that managers have above all to remain competitive through the use of modern technological aids. We are aware that a reduction in the time available for a decision increases the pressure to take risky decisions and the contracting business, being no exception, is full of risks and uncertainty. We suggest that systematic analysis can help identify the range of uncertainty within which contractors have to work. Such a procedure can evaluate categories such as: (i) uncertainty about the facts at hand; (ii) the subjective assessment facts;
of these
(iii) the future consequences of present decisions based on the facts. METHODOLOGY
-
A senior marketing manager at director level was interviewed to ascertain his responses to the
several facets of the method. (These facets will be reviewed in turn as we build up a multi-attribute equation that will act as a decision filter. This equation will be used to generate overall values that will allow easy adjudication of the worth of tendering at a given opportunity.) He agreed that sometimes marketing executives are a little over enthusiastic over some projects, being concerned with their own prestige, and as a consequence, may become involved with something 'not in line' with corporate policy. Later analysis showed these 'pet' projects have led to a wastage of scarce tendering resources in order to support projects on which the contractor had no expertise. Table 1 shows the project business opportunities 'chased' by the firm. Only 51% of the project business could be classified as associated with company knowhow. The rest was wrongly pursued so deploying the organisation's scarce human assets with no reasonable chance of success. Wastage of time necessarily spread throughout the firm as senior managers attempted later to extricate the firm from the ensuing difficult situation. He agreed that there was a primafacie case for the provision of a decision aiding tool which should save managerial time by aligning decisionmaking with corporate policy. The technique has five stages of analysis and requires considerable discussion between the 'analyst' and the client. Much of this discussion will have to be taken for granted in the nature of this paper--but example conversations will be reported. These time-consuming procedures must be followed to ensure the correct derivation of a robust equation that will be used as a surrogate for the (human) decision-maker. Initially, and usually with the help of the consultant, the decision-maker has to ascertain which variables are within his control and which are extraneous to the firm. Then a small number of the controllable variables have to be selected so as to properly describe the 'problem' but not to include too much surplus detail. Following this selection there is an initial analysis to check that the attributes of the decision are independent and do not 'colour' each other through the ensuing discussions. If there is some overlap in the decision-maker's mind between these attributes it will not be possible to determine if more or less of one attribute in particular is of vital importance when the other attributes get in the way, as it were. Once independence is
Omega, Vol. 18. No. 2
141
Table I. Classification of projects
Class of project Power generation and/or distribution (civil/electrical/mechanical) Process and chemical industries Civil engineering based Assortment of projects Projects needing general co-operation Totals
proven, the way is clear to the development of an equation that links all attributes to the utilities that the decision-maker has about him/her individually and globally. The equation is the objective of the long elicitation process-once found it may be used as a fast decision support tool, even as a surrogate decisionmaker if the manager is absent for some reason and the client is pressing for an answer. We will now illustrate the stages of deriving the decision aiding equation.
Numbers
Percent of total
Projects associated with the firm's know-how (%)
41
34
34
39 22 9 9
33 17 8 8
nil 17 nil nil
120
100
51
All attributes have to be measured. Their scales have to capture the full range of permissible values that will be acceptable by the decision-maker. Individual values outside these ranges, while they may be feasible in some other circumstances, will be deemed for this analysis to generate a utility of zero. Hence they have been excluded from further discussion. The ranges of the attributes and their graduations for the example are given in Table 2.
Stage 2--The independence of the attributes Stage 1--The attribute list The total number of attributes in a decision process are often thought by decision-makers to be too many, diverse and impossible to quantify. In fact often only a few are of real significance: they are diverse, but they are quantifiable. Later on we will see that they can be traded-off in magnitude terms against other attributes and against some ideal point. Clearly, the greater the numbers of attributes the longer is the initial task of evaluating their indifference. Nevertheless, a sufficient number are needed to capture the full sensitivity of the problem space. There is a need to discuss this aspect with the client so as to derive a valid starting set of attributes. In practice, seven to eleven attributes seem to capture the richness of most problem scenarios. In this example, derived from a detailed case study, we will use only three attributes to reduce the complexity of the analysis simply for the purpose of illustration. These attributes are: X l - - t h e opportunity to generate cash; X2--resource utilisation; X3--opportunity for future business.
It is possible to obtain a reliable equation linking all the attributes by undertaking a full combinatorial evaluation of the effects of varying each and every attribute in the study, but this is a very time-consuming task. It is virtually impossible when there are more than five attributes to consider. The method developed by Keeney and Raiffa checks for attributes that are co-related in the decision-maker's viewpoint, although originally they may have been proffered as though independent. Once independence is established, only a few combinations of the attributes are then needed to ascertain the overall utility equation. Although we refer to the definitions given by Keeney and Raiffa in their exemplary book, there are several introductory examples given in Kaufman and Thomas [3]. Step l mPreference independence check. The details of the procedure are given in Table 3 for one pair of attribute checks. Here, we will concentrate on the rationale of the checking. In order to establish the independence between the attributes, an initial check is undertaken to see if there is any variation in a hypothetical trade-off between two attributes under very different circumstances--namely, when all the other attributes are each at their worst, or alternatively, are all at their best
x3 Opportunity for future business
x2 Rcsouroc utilisation
XI Opportunity to generate cash
Attributes
o
_.2
|
¢
Opp. for extension of the project
20
o
No opp. for future work
,I .I
Up to 20% divisional staff can be utilised
20
5% profit no down payment
41 H
Very little opp. to Use own resources
o
Negative cash flow and no profit
Opp. for PiE work only in the territory
Up to 70% divisional staff can he utilised
5% profit 10% down payment
4o
~ s
40
.I,
40
I ,K
,JR
Opp. for managing Contract or type of work
- - ,
Input from two divisions
•°
10% profit 15% down payment
Measure
611
'I
60
I•
I
8O
Opp. for main contracts work
~0
, °M
Input from four divisions
80
15% profit 20% down payment
Opp. for sub-contracts work
L
Input from three divisions
I
10% profit 20% down payment
Table 2. Ranges and lists of attributes
.,
I
.12
Opp. for all types of work
IN
use the group's resources
O p p . to
I00
20% profit 20% down payment
No opp. for future work
Very little opp. to use own resources
Negative cash flow
Worst
Best
Opp. for all types of work
Opp. to use the group resources
20% profit and 20% down payment
Levels
B=
i
g:
I
Omega. Vol. 18, :Vo. 2
143
Table 3. Preference independence check Consider the pair XI and X2 - - a n d assume X3 is at its WORST level 100
G F
Indifference
Question-From point (A,H) would you rather move towards N or towards G? That is--N = (Xl at worst, X2 at best) or G = ( X I at best. X2 at worst)? 100 bst
(X21
DM: (answer) I am personally in favour of cash generation and would prefer to go for point G (i.e. 20% down payment and 20% profit) with H on X2 (showing little opportunity to use our own resources) rather than the policy at point N. Q: Would you consider point E? DM: Yes--I would still prefer a good profit level and a good down payment--even if it means using outside resources. Q: How about point D? DM: Again ' Y e s ' - - b u t these policy changes are becoming less attractive. Q: At what level of cash generation would you be in a dilemma? That is--when would it be difficult to choose between XI and X2? DM: I think if XI is at B (i.e. 5% profit and no down payment and no opportunity to use the groups resources) then it would be too low. At that stage I would rather go for the use of the groups own resources. So . . . point C would be my indifference point. Q: So, at this level you have no preference between XI and X2? DM: That is correct.
values. When independence is proven, we may be confident that later in the procedure the decision-maker will be able to make real-valued trade-offs no matter what levels are taken by the other attributes (because none of the attributes are co-related). The check is continued to cover all pair-wise combinations of the attribute set. Non-independence will be noted when there is a substantial difference between the two indifference points found in the two trade-offs: the case when all attributes are at their 'best', and secondly, when they are all at their 'worst' values. At this point it is necessary to consider both the analytic and the subjective interactions in order to choose which attribute to 'drop' from the evaluation. By removing an attribute which is acting in a co-varying way with another of the attributes, one removes the perceptual confusion caused by non-independence. In Table 3 we find indifference pairs at points C and N. Here the manager is indifferent between: C: a policy of pricing at 5% profit and seeking a 10% down-payment--but with little opportunity to use the firm's own resources. and N: a policy having negative cash flow and no profit, but with opportunity to utilize the whole group's resources.
As can be imagined, the complexity of the individual scale descriptions require considerable discussion in order to achieve a clear, meaningful and stable trade-off position. The role of the analyst is of paramount importance here; and, while it is difficult to recount on paper, one must not forget the importance of wide-spanning conversations between the analyst and the client to ensure the derivation of unequivocal results. Table 3 covers only attributes X1 and X2; we have the further need in this exposition to relate X3 with one of XI, or X2, to have examined all the combinations--but in the full analysis (not quoted here), there were more pairs to consider given that there were nine attributes. Step 2inUtility independence check. Here the procedure is similar to the above, but we now consider only one attribute at a time. Table 4 illustrates the procedure for the first attribute, XI. Once more, the task is to check if there is any substantive variation of the indifference point as the background changes: that is, as all attributes other than the one specified are changed from their best to their worst levels. If there is a substantive difference in the indifference point, then there is some underlying co-relation that has to be eradicated so that the decision-maker can be clear-headed about individual changes in the magnitudes of the attributes later in the analysis. When there are several attributes, the
Kidd, Prabhu--A Multi-Attribute Decision Aiding Technique
144
Table 4. Utility independence check Consider attribute Xl only --with all others at their BEST G
A
X ? ; b e s t rover. ( 2 0 */, downpaymen~ Clnd 2 0 * / , grofit)
X l : ~ors~ LevoL. (LO. neqotive CaSh fkOW)
BorCDEF? •.
for s u r e . .
Q:
Consider the lottery above. This gives you a 50% chance that XI would be at its best level, and a 50% chance that it would be at its worst level, Remember--X2 and X3 are at their best levels. Would you prefer the gamble, or point B? DM: With a 50/50 chance of the best leveE, I would rather go for the lottery. Q: How about point C if it were sure? DM: No. The lottery is still of interest. Q: Now what of having point D for sure? That is 10% profit and 15% down payment. DM: In this case I would be indifferent.
potential for conflict is high; in this example we assume the three attributes are independent both in a preference and in a utility sense.
Stage 3--Evaluation of the individual utility functions Table 5 indicates the procedure for the X1 attribute. These graphs are needed to translate the eventual real-valued tenders on say, the scale of X1, into the utility value of Xl, i.e. U(X1). In other words, we are asking how the decisionmaker views the continuum from the minimum to the maximum of X I. Are all increments equally desired? Or, are unit increases on one part of the scale more highly 'valued' than at other parts of the XI magnitude scale? More simply, this represents the usual human tradeoff o f . . . "the more you have the less welcome is the increment, but it continues to be a positive welcome". In utility theory (well covered in texts such as Keeney and Raiffa [1]), there is no absolute requirement that the individual curves be concave, convex or even straight, lines. They are representations of the decision-maker's perceptions and feelings at the point of time of the analysis. These graphs take into account all the surrounding factors t o o - - t h e state of his or her peer group, the state of the firm and of the market--even the state of the nation. This means that the utility curve of another person may be quite different. But nonetheless we are
saying that the exposition of a personal statement will lead to more enlightenment and more discussion than would be the case if there was no modelling of the decision problem. Within this study of multi-attribute decision analysis there is the assumption that the individual decision-maker such as the director of marketing represents the totality of the organisational viewpoint. It is known that to incorporate the views of many individuals, some of whom will be concerned with attributes that others consider trivial, is a complex and as yet unsolved problem. We pose this method as one that should lead to discussion and development in the enterprise by the simple fact that a model is used, and it is presented 'on the table' for agreement, or for contradiction, but importantly for the overall betterment of the decision process. In general terms, the type of business and organisational structure will have some influence on the ease of developing discussions on the model and its parameters.
Stage 4--Derivation of the multi-attribute equation The earlier stages have been concerned with evolving and agreeing a valid data set--the attributes that independently describe the problem space. Now we wish to assess the impact of potential real trade-offs between the valid attributes. It makes sense at this stage to the decision-maker to assess trade-offs firstly
Omega. Vol. 18, No. 2
145
Table 5. Utility curves
Eraluation of individual utility curves Starting with XI Assign utility values of 1.0 to point G and 0.0 to point A. REMEMBER: no other attribute will interact with this assessment as we have found them all to be independent.
X100 U:~O
F
XI~AU:O0
Q:
relative to the various descriptions of the X I scale what would your indifference be in comparison to the gamble illustrated.'?
For the first evaluation we have U(B) = 0.5 ( l . 0 ) + 0.5 (0.0)=0.5 DM: Point B--because I would not wish to receive the downside costs of the worst case outcome at its 50% chance. Q: Now we have moved B to be the downside risk. What would your indifference point be? DM: Now I guess it is point C.
J Fcs~°
x~oou:,.o
For the second gamble we have u ( c ) = 0.5 (1.0) + 0.5 (0.5) = 0.75 X1 @ 8U : 0 5
Now point A is substituted into the gamble instead of point G and this yields a certainty equivalent about half way between point A and point B. U('p') = 0.5 (0.0) + 0.5 (0.5) = 0.25 It is possible to plot these Certainty Equivalent resulting from the gambles against their Utility values as follows. 1
P
B
C
O
E
F
G
Votue ( X l )
between the attributes that are perceived to be the most important, followed by the attributes deemed to be of less importance. There are thus two steps to this process: Step I--Ranking of attributes. This is a relatively simple task. Initially, attributes have to be imagined to be at their worst values. Following this, the decision-maker is asked to choose which attribute to raise first to its best value (if that were a possible scenario); then the second, then the third, and so on along the list. The resulting ranked list provides the guidance for the subsequent analysis of pair-wise trade-offs. Previously, in Stage 2, the pair-wise comparisons have been against a con_venient list, X1 to X2 to X3 etc. But now we have a list of importance rankings that shows that there is a perceived distance between the attributes
that will make comparisons more (or less) meaningful. For example: a comparison of 'chickens and eggs' may be easier than 'chickens and gross tonnages of boats'--some attributes are linked naturally in a decision problem. Applying this analogy to the construction industry we feel a comparison of 'design or construct a power plant' against a 'procurement contract' may be easier than 'design a power plant' and 'mining for coal'. Too wide a range in the allowable set of comparisons becomes meaningless in assessing trade-offs--the decision-maker would not (truly) be able to make reasonable comparisons as they are not the usual comparisons that are made, whereas attributes that are close in the decision space may have trade-offs undertaken realistically. In the case example, the rank order
Kidd. Prabhu--A Multi-Attribute Decision Aiding Technique
146
is of little importance over the three attributes, thus we will assume the order X1, X2, X3 is preferred, with XI being the most preferred. In the real background problem there was a large perceived distance between the first and the last attribute in this ranked list.
Step 2--Assessing the relative trade-off magnitudes. This procedure follows from Step 1 wherein the rank order of the attributes was evaluated. As we know the attributes are independent (from Stage 2) we can allow pair-wise consideration of the attributes to be undertaken without reference to any other attribute. Table 6 indicates the form of questioning that can take place to derive and quantify the relative weights to assign to each attribute. In this example there are two equations linking the three attributes, but in general for 'n' attributes, there will be ' n - 1 ' equations. To provide a solution for this set of equations we have to seek one absolute value of a weighting, say upon the premier attribute. Then it will be possible to cascade the calculations through the
interconnected set of equations to obtain a full set of numerically defined weights, wz, w2. . . . . w,. It is only at this stage that we may ascertain if we have a linear relationship between the attributes or a more complex multiplicative relationship. By definition, described in Keeney and Raiffa, if the sum of the 'w' weights is approximately unity, the relationship is linear. Again the judgment is subjective: a linear relationship is easier to explain to most clients, but must not be used when the mathematical 'truth' indicates the use of a more complex equation.
Stage 5--Revision of the attribute rankings Following the insights gleaned through the detailed analysis many clients revise their opinion of the most important attributes (the ranked set). This rearrangement will affect the derivation of the individual weights within the overall utility function. Thus the latter two stages have to be undertaken once more to revise the tradeotis and derive new weighting coefficients.
Table 6. Scaling constants
Assessing the scaling c o n s t a n t s The relative weights of each attribute are evaluated by assessing the trade-offs between the independent attributes. The affects of the other attributes do not matter. Consider the attributes XI and X2
N
L
tndi f. pair K X2
M--__7 J
1
H
Q: DM: Q: DM: Q:
A
B
C
0 Xl
[
F
G
The point (A,H) represents the WORST case of both attributes. So what policy change would you prefer? To go to N or to G? To G. But if we had to reduce G to F would you accept this? Yes: in fact right down to D---then [ would be puzzled as C is to me less desirable than point N. OK. So let's say you are indifferent between the two policies of (A,N) and (DoH). This is equivalent to--U:(A,N) = UK(D.H) Or we may say ... w: ffi wlul(D) since the utility of X2 at N is 1.00 Reference to the diagram in Table 4 shows u~ (D) = 0.84 (approx.).
Following the remainder of pair-wise comparisons we find that w: = 0,701 w b and % = 0.754 w~. Now one absolute value for a 'w" has to be found from the next gamble structure. AU. o t t r i b u t l l
¢11 D i l l
ODtiOn 1 a r t a t t r i ~ u l : e l a t wort~:
X l at: b l l t , r l l t 01~ worlr.
I
Alter the value of the probability to check the indifferent choice of option.
I ere with P = 0 . 8 there is a - balance point.
Substituting in the above equations results in Ut(Opt)= Lt't*=0.8 and thus a'2--" 0.701 and w3 = 0.754. The total utility = 2.25, well over unity. We have therefore to use the muhiplicative equation.
Omega, Vol. 18. No. 2
Finally we should have established an equation that will be capable of aiding the decision process. It has been elicited from an agreed list of attributes which have been proved to be independent. And, after ranking the attributes, there followed the development of an equation that will simulate the perceptions of the decision-maker. This equation could be used as a surrogate 'decision-maker' in order to evaluate, at any instant, any new information within the domain of its competence. AN EXAMPLE OF THE TENDER PROCESS
147
and so k = - 0 . 7 4 . The assessment was repeated to see if the value of k differed through the newly acquired insights about the value tradeoffs, but it remained at - 0 . 7 4 .
Comparison o f
Attribute XI
As we mentioned above, the firm wishes to remain anonymous, and so the example has been heavily disguised. In Table 2 we set out three attributes that must suffice to illustrate the development of the technique. These attributes have their worst and their best values noted and there are intermediate values noted as policy B or K or T for instance. These policies were 'calibrated' with respect to two measures of 'cash flow' in X l; to the origin of the resources in X2; and to the types of future work possibility in X3. The scale break-downs are not linear, but represent meaningful descriptive phases. One should note that the quoted policies A - U encompass real examples which are illustrated below as projects 1-9. The theory underpinning this form of multiple attribute analysis (see Keeney and Raiffa) says that if the sum of the weights equals unity we may use an additive m o d e l - -
tender offers
We have now found the components of an equation that capture the feelings, trade-offs and utility of the decision-maker so we are now in a position to use the equation for evaluating the differences between tender offers. As an initial example, note the following two tender offers:
X2
Project I
Project 2
5% profit margin 10% down payment i.e. point C Input from four Divisions
10% profit 20% down pa?ment i.e. point E Up to 70% divisional staff can be utilized on project i.e. point K Opportunity for PIE work onl}
i.e. point N Opportunity for extension of the project i.e. point R
X3
By interpolation from the individual utility curves developed as in Table 5 we find for project 1: U(Point C) = 0.75, U(N) = 0.75. and U(R) = 0.04. And as we know all Wi and the scaling constant K, we may calculate the utility of the project. From the multiplicative equation we have [1 + ( - 0 . 7 4 )
U ( X I . . . X3)] = [I - (-0.74)(0.75)(0.80)] • [I - (-0.74)(0.75)10.70)] • [I - (1 - 0.74)(0.04)(0.754)] = 0.668
u ( x t . . , x°) = s[wt.u(x , ) + w.,.u(x,)... + w, .x(u, )1
but if the sum exceeds unity, as in this example where the Z(weights)= 2.25, then we must use a multiplicative m o d e l - I +k'U(X
I ...X,)
= ~[I + k ' w , ' u ( x t)]
where k is a further scaling constant that has to be computed as follows: If we say that all attributes in the above equation are at their best values, then U(X~, )(2, )(3) and u(xi) are all equal to unity, we have 1 + k = i - t n~ (1 + k ' w I) = (1 + 0.8k)(l + 0 . 7 k ) ( l + 0.75k)
with the w~ being derived through the comparisons illustrated in Table 6. That is: with . . . wt = 0.80, w., = 0.70, w3 = 0.75
i.e. point Q
and so the overall utility becomes U ( X I , X2. X3) = 0.90 for project I, a n d likewise U ( X I , X2. X3) = 0 . 9 3 for project 2
This is continued for all projects to form the following list: Individual (raw) attribute utilities Pr~ect
ul
u2
u3
ZU
Weighted project utility
Scaled project utility
I 2 3 4
0.75 0.95 0.50 0.50
0.75 0.50 0.55 0.35
0.04 0.06 0.0 0.06
1,54 1,51 1,05 0,91
0.9 0.9 0.67 0.6
0.75 0.75 0.54 0.49
5 6 7 8 9
0.88 0.0 0.0 0.97 1.00
0.0 0.63 0.50 0.75 1.00
0.0 0.0 0.14 0.50 1.00
0.88 0.63 0.64 2.23 3.00
0.65 0.43 0.41 1.09 1.23
0.52 0.35 0.33 0.89 1.00
Kidd, Prabhu--A Multi-Attribute Decision Aiding Technique
148
It should be noted that the evaluations above are derived from a 'what if' search. The individual attribute utilities have been systematically varied to highlight slightly fictitious projects to review a spectrum of results within which socalled real projects will lie. These data may better be expressed in graphical form to show the cut-off in project utility; see Fig. i. Through a retrospective review of successes and failures in tendering, the management decided that any project not conforming to a weighted utility of 0.9 or more should not be considered for the tender development process. The graph shows both the raw scores and the scaled (weighted) utility score. There is a clear point below which potential projects are of no interest to the firm. Conversely, for high scoring tenders, resources may be put quickly to those projects that have shown a utility value above the cut-off point. CONCLUSION Several methodologies have been proposed in the literature on the topic of 'evaluation'. One, based on Linear Programming, Turner [4] derives a quasi-optimal solution for contract tender evaluations. Some judgment is allowed upon the acceptable commercial tender, but the method relies mainly on the use of a 'hard' technique. Another example, Cook et al. [5], is based on the methodology of multi-criteria analysis. Here the authors use a modified version of ELECTRA (see Roy [6]), called SELECTRA. We do not recommend this method in so far as it captures little of the managers' preferDecision aiding graph DispLay of u t i L i t y ~
1.o
(1) Ensuring a thorough and consistent review of the process of "tendering'.
(2) Making clear the policies and issues to
0.8 2~ff-Here, the onty ._~ •~.,
ences over the alternatives. A different illustration of the evaluation of alternatives is given by Brooks and Kirkwood [7]. Here they use the multi-attribute method, which we favour, to aid a selection procedure when all vendor offers are known within a purchasing problem. Finally, we wish to mention a paper supporting the use of researched and negotiated subjective values. Khan and Shih [8] show that jud~nental decision models perform well in environments that have high intrinsic variability. Thus we are confident that the method and case work which we have discussed above was rigorous enough to offer a good management support tool. Through the long process of discussion and evaluation of feasible attributes, their trade-offs and the derivation of each attribute's weighting we have derived an equation that is a model of the decision-maker. It may even be a surrogate of the decision-maker. This model has been exposed to public scrutiny within the firm and within the group to further expose its assumptions to the assumptions held by other managers--both with respect to the model of the decision-making process and to the manner in which the weightings were developed through one person's subjectivity. This process of refinement has resulted in an equation that can act as a filter against potential overload of the manager responsible for initiating the tender evaluation. Furthermore, it can act as though it 'were' that person if the manager were unavailable for some reason, perhaps detained on other business. It can thus materially reduce the variety and uncertainty that does exist. Thus we could summarise the benefits as--
all involved in the process, be they local or remote in the organisation.
projects as
.~ :5
0.6
candidates for
tendering are
"o
1,2,8 and 9
(3) The creation of an equation that
0.4
openly incorporates the subjectivity of the decision-makers following negotiated trade-offs.
SuitabLe
0.2
projects .1
0
0.5
1.0
1.5
I
2.0
-I 2.5
Total row utilities
Fig. 1. Graphical display of project utilities.
I
3.0
(4) The reduction of the 'mystique' of decision-making through the substitution of systematic analysis within a wellfounded scientific framework.
Omega, Vol. 18, No. 2
Clearly, by creating this equation and obtaining the support of management in its use we have helped to develop a strategy for competing in time and thus we have aided the time management and the human resource management of the whole firm. The construction industry in which the above technique was tested has unique characteristics such as projects which are exposed to many elements and politics outside the control of the contractor. Hence the technique is not intended to replace the senior executive's intuition which would be based on his knowledge of business and the immediate environment. But it is to be seen as an aid to sharpen judgement. Nor, we may add, is 'our' multi-attribute technique presented as the only method applicable in these circumstances. We see increasing effort being put in to the support of persons concerned with large scale projects. For instance A1-Khayat and Edwards [9] have suggested an options-choice methodology which combines a problem structuring approach with one based in multi-criteria decision analysis. Within their decision analysis section their clients, like ours, have to make strategic selections, or rank orderings of their preferences. For this it has been suggested that the Analytic Hierarchy Process (AHP) is appropriate. This method was originally formulated by Saaty [10]; it looks essentially at pair-wise comparisons of options against criteria within some overall focus wherein the client can rank the options and so develop a set of weights in the face of potential inconsistencies. Other approaches lean towards the application of Expert Systems to elucidate the knowledge base of the field consultants, see for instance King and Phythian [11]. In all these cases, ours included, we see that there is a very strong element of 'modelling' involved. The consultants are concerned to present a system to their clients that allows the client to be more consistent, and helps support decision-making in a more timely fashion. All
1-19
the methods are concerned to extract the subjective rules that are used in practice so as to offer a consistent decision aid to the firm. But to derive the final decision aid all methods involve the client in considerable discussion and thus are time-consuming. Yet, based on this strong framework, it is suggested that tendering firms will be able to offer better researched tenders which will result in more successful outcomes. This was certainly true in our case, and as Fig. 1 indicates, we can offer a very simple graphical aid to answer the question "to bid or not to bid"?
REFERENCES 1. Keeney RL and Raiffa H (1976) Decisions witil Multiple Objectives. Wiley, NY. 2. Keen PGW (1988) Competing in Time: using Telecommunications for Competitive Advantage. Ballinger, Cambridge, MA. 3. Kaufman GM and Thomas H (1977) Modern Decision Analysis. Penguin, Harmondsworth. 4. Turner I (1988) An independent system for the evaluation of contract tenders. J. Opl Res. Soc. 39(6), 551-56 I. 5. Cook WD, Golan I, Kazakov A and Kress M (1988) A case study of a non-compensatory approach to ranking transportation projects. J. Opl Res. Soc. 39(10). 901-910. 6. Roy B (1978) La m~thode ELECTRE II. METRA Direction Scientifique, Note de Travail 142, pp. 161-182. 7. Brooks DG and Kirkwood CW (1988) Decision analysis to select a microcomputer networking strategy: A procedure and a case study. J. Opl Res. Soc. 39(1). 23-32. 8. Khan AM and Shih C-T (1988) "Judgemental decision models as alternatives to optimisation: The case of spousal selection. J. Opl Res. Soc. 39(5), 435-457. 9. AI-Khayat FHM and Edwards JS (1986) An optionschoice methodology for technological projects in developing countries. Systems Res. 3(3), 123-133. I0. Saaty TL (1980) The Analytic Hierarchical Process. McGraw-Hill, NY. I1. King M and Phythian G (1989) Expert systems in competitive tendering--a case study. A presentation to the 31st ORS Annual Conference, Southampton, 12-15 September 1989. l~fr JB Kidd, Information Management Division, Aston Business School, Universit)' of Aston, Birmingham, B4 7ET, UK.
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