Journal of Forecasting. Vol. 7, 31-47 (1988)

A New Method of Scenario Analysis forStrategic Planning*

JUTTA BRAUERS**

MARTIN WEBER*'Aachen University, FRG

ABSTRACT

We first present scenario analysis as a qualitative forecasting techniqueuseful for strategic planning. Then we develop an overview of the twoclasses of methods for scenario analysis described in the literature. Basedon both classes, a new method is developed which especially fits the needsof strategic planning. The method can be divided into three stages: 1.Determination of compatible scenarios, 2. Determination of scenarioprobabilities, and 3. Determination of main scenarios. An example is givento illustrate the method.

KEY WORDS Scenario analysis Cross-impact analysisStrategic planning

Strategic planning, the major building block of strategic management, has the goal of guidingand coordinating the long-term development of an organization and its environment (Trux andKirsch 1979). Because planning is directed towards the future, predictions are indispensablecomponents of planning and doubtless the most important form of information that can beproduced and used in the planning process (Wild 1981). New demands for forecasting methodshave arisen as changes in the planning process in organizations lead to increasing emphasis onthe strategic aspects of the planning process.

More traditional methods, i.e. quantitative forecasting methods such as time-series analysis,try to extrapolate new ideas about future developments based on knowledge of and experiencewith the past and present (Makridakis and Wheelwright, 1978, Opitz 1985). These methodsusually imply that frameworks developed in the past are also applicable to the future, and rarelyuse the qualitative, subjective knowledge of local managers involved. However, extrapolationcan easily allow one to overlook new opportunities and risks facing the organization, especiallyin times of rapidly changing internal and external conditions. What is needed are forecastingtechniques which address the special requirements of strategic planning to supplementtraditional methods.

'This paper is based upon an earlier publication, 'Szenarioanalyse als Hilfsmittel der strategischen Planung:Vlethodenvergleich und Darstellung einer neuen Methode. Zeiischrift fUr Beiriebswirtscha/l, volume 56 (1986).**Lehr-und Forschungsgebiet Allgemeine Beiriebswirtschaftslehre, RWTH Aachen, Templergraben 64, D-5100Aachen, West Germany.0277-6693/88/010031 -17$O8.5O Received February 1987© 1988 by John Wiley & Sons, Ltd. Revised July 1987

32 Journal of Forecasting Vol. 7, Iss. No. I

Scenario analysis techniques as a qualitative forecasting methodWe would like to propose scenario analysis as a forecasting method to support the strategicplanning process. We consider a scenario to be a description of a possible future state of anorganization's environment considering possible developments of relevant interdependentfactors in this environment. We can find analogous definitions in the literature (see for example,Becker, 1983; Geschka and von Reibnitz, 1979; Godet, 1983; Oberkampf, 1976; Sarin, 1978).Scenario analysis techniques characteristically synthesize quantitative and qualitativeinformation, constructing multiple scenarios or alternate portraits of the future (von Reibnitz,1981). The experience and intuition of the manager will be reflected in the qualitativeinformation used.

To illustrate, let us contrast scenario techniques with the more traditional quantitativeforecasting methods. While the latter conceptually deal mostly with the existence of a singlefuture state which they predict, scenario techniques attempt to ascertain alternative futurestates and calculate their probabilities (i.e. the probability we can assign now to their futureoccurrence). Put into decision theory terms, scenario techniques are a strategic planning toolfor decision making under risk (i.e. choosing among strategic alternatives,) for determiningpossible future environmental situations and their probabilities. Since the future-orientedscenario techniques should operate without making direct extrapolations from past situationsand frameworks, they require the consideration of qualitative, subjective information requiringthe close collaboration of management in the building of scenarios.

Once we have determined a set of possible future states using scenario techniques, thesescenarios can be included in different phases of the strategic planning process (Becker, 1983;Gomez, 1982; von Reibnitz, 1983; Wilde, 1982). They can now form a basis for the evaluationand selection of potential strategies, i.e. we can now produce an estimation considering theprobabilities and risks involved with each individual strategy. In the simplest case, in everyscenario the same strategy will have a higher objective function value when compared toalternative strategies and therefore will be chosen. The different scenarios will demonstrate defacto, the way to its success or failure. If we monitor certain aspects of the scenarios with an'early warning system' we may be able to recognize any potential failures and may be able toavoid them entirely. Another advantage of scenario techniques arises in large organizations,where planning is at least partially decentralized. Here scenarios represent the results of acoordination process for determining possible future states, i.e. they represent a common basisfor further planning within the organization.

There are primarily two types of scenarios. The first are 'corporate scenarios* which aredeveloped internally, targeting a specific goal or problem of the organization. Scenariosentitled, for example, 'Our Company in the Year 2000' a sales or marketing scenario, wouldfall under this category. The second type of scenarios are those which are not tailored to aspecific concern of an organization. These include so-called 'world scenarios' (Kahn andWiener, 1967), 'energy scenarios', scenarios concerning an entire sector (Rao, 1984) and trafficscenarios (Mitchell et al. 1979).

Although these latter scenarios have enjoyed almost twenty years of increasing popularity,the corporate scenarios we consider in this article have only recently entered the realm ofstrategic planning. In an empirical study Linneman and Klein (1983) determined that prior to1974, only a few American companies used scenario techniques in their planning process. Asurvey conducted in 1981 found that 108 out of 215 responding Fortune 1000 companies usedscenario techniques. Malaska et al. (1984) conducted a similar study in Europe sending out 1100surveys, from which 116 answers were received, 36 per cent of which indicated the use ofscenario techniques. Only 12 per cent of these companies used this methodology before 1973.

Jutta Brauers and Martin H'eber Scenario Analysis for Strategic Planning 33

Eighty-three percent of those who use scenario techniques support the premise of this paper,that they are a useful element of the strategic planning process.

OutlineAlthough scenarios are an important tool in the strategic planning process, and are increasinglyused in the business world in this capacity, there is no single generally accepted method forconstructing them. We can summarize the requirements of scenarios in the planning process asfollows. Their purpose is to reflect possible alternative developments which are constructedusing quantitative data as well as the experience and intuition of managers. Existinginterdependencies between future developments must also be considered. Practically, betweentwo and tour scenarios should be produced, along with a current starting assessment of theirlikelihoods considering the possible future states of their environment.

Selected methods of scenario development from the literature are discussed in light of theserequirements. In the following sections a new procedure is presented which meets therequirements described above. Finally, an example using this new procedure is given.

SCENARIO ANALYSIS METHODOLOGIES: DESCRIPTION AND COMPARISONS

Scenario analysis consists of three basic stages (see, for example. Gomez and Escher, 1980):analysis phase; description of future states of environmental subsystems; and synthesis phase.

In the first stage, the analysis phase (von Reibnitz, 1981), we will come up with an exactdefinition for the entity of our investigation, so that all participants in the analysis have asimilar understanding of the problem at hand. Based on this consensus the problem can befurther bounded and structured.

The problem analysis is followed by a subsystem analysis which consists of the identificationof relevant external influences (the environmental subsystems) on the entity being investigated.Possible subsystems include 'the economy' "raw material acquistion' 'the working world''society' and 'technology' From every subsystem we choose a few representative influencingfactors relevant to the problem at hand. For 'the economy* we might determine that 'economicgrowth' is one representative factor, for 'society we may indicate 'dominant political opinion'To aid us in the analysis phase we should employ a variety of creative methods (such asmorphological analysis, brainstorming, brainwriting, and the delphi technique).

In the second stage of scenario analysis we define possible development paths of theinfluencing factors already discussed. In the third stage we consider the existinginterdependencies between the factors and establish alternative scenarios through the synthesisof these different future states. There are two basic methodologies for implementing the secondand especially the third stage of scenario analysis. One, the 'cross-impact analysis' technique,is primarily used and presented in English-language publications. The other, the 'Battellemethod' from the Battelle Institute in Frankfurt, is primarily a German approach.

Cross-impact analysisCross-impact analysis techniques (Gordon and Hayward, 1968; Sarin, 1978, 1979) makeassumptions about the future developments in the environment of an organization, in whichcertain events influencing the entities under investigation are identified and either occur ( = T )or do not occur (= '0'). Methods used in this third stage of scenario analysis range from theinterpretation of the literature, to conventional forecasting techniques (for example trendextrapolation), to the creativity techniques previously used in the analysis phase.

34 Journal of Forecasting Vol. 7, Iss. No. I

Starting with a finite set of events e,(/= 1,.... /i) scenarios consisting of combinations ofoccurring and non-occurring events are constructed in the synthesis phase. Additionalinformation must be specified (Jackson and Lawton 1976; Dalkey 1972): (1) the marginal(absolute) probability pii) (the probability that event et occurs) and (2) estimates of theinterdependencies between different events in the format of a cross-impact matrix.

In older cross-impact analysis models (Wechsler, 1978; Welters, 1977; Duval et al., 1975),these interdependencies (cross-impacts) were estimated as likelihood ratios. By using thecross-impacts we can transform the marginal probabilities pii) into conditional probabilitiespii\j) (the probability that event e, will occur given that event ej has occurred). Each scenariowill be constructed by simulating occurrence or non-occurrence for every event in the event list,and for the rest of the events, through probability transformations based on cross-impacts.After many simulation runs, the relative frequency will determine the probability of eachscenario (Martino, 1972; Mertens and Plattfaut, 1985).

More recent approaches employing cross-impact analysis have modelled theinterdependencies directly in the form of conditional probabilities pii\j)- By usingprogramming methods and/or systems of equations, scenario likelihoods or bounds aredetermined from the marginal and conditional probabilities. We shall continue by looking atthe two most recent methods for the determination of the scenario probabilities, the interactivemodels by Sarin (1978, 1979) and by De Kluyver and Moskowitz (1984). Both models use thefollowing notation: the combination of n given events ei en, produces N = 2" scenarios(see Table 1).

The likelihood or probability of a scenario is designated by the variable ys, the column vectorof the scenario probability by y, and the corresponding transposed probability vector by y'The 'O'/'l' column vector in Table 1 are abbreviated as ai,...,an.

Table 1. List of scenarios

Scenario

12

7 V - 1N

Probability

yi 11

00

e2

11

00

Event

*•/I ^ L

11

00

en

10

10

T : Event ei occurs '0 ' : Event e, does not occur

Sarin's ModeiSarin (1978, 1979) determines scenario probabilities interactively. If experts estimate onlymarginal probabilities pii), then the limits for the joint probabilities pii'j) or conditionalprobabilities pii \ j) can be calculated for these experts using standard probability theory.ipii'J) = pi'\J)' PiJ) is defined as the joint probability that events e, and ej both occur.)Experts can then supply additional estimates within these particular limits. When allprobabilities pii) and pii'J) have been determined, the bounds for further joint probabilities,firstly those for the next level pii'j-k), can be calculated and in turn used by the experts. Thisinteractive procedure should be continued until the final estimate of the joint probability

2'... /I) has been determined.

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 35

From Table 1 we see that the marginal and joint probabilities can be expressed in the form ofscenario probabilities and therefore can lead to the following system of linear equations: (Notethe ' •' operation produces a vector of components where each component is the product of therespectively indexed components of the vectors being operated upon.)

y'-ai =Pii), i=l,...,n

= Pii'J-k), /•= \,...,n-2, j> i, k> j

y'-iai'... an) = p ( l ...-n).

The following relationship must hold for all scenario probabilities ys'.N

YJ ys-A' .Vs ^ 0, for all s.5 = I

Since all terms on the right-hand side of these equations are specified by Sarin's interactiveprocedure, we can now calculate the scenarios' probabilities. This allows us to order thescenarios and to select probable scenarios for further analysis.

De Kluyver's and Moskowitz's ModelFor this model (De Kluyver and Moskowitz, 1984), experts must estimate the conditionalprobabilities pii\J) in addition to the marginal probabilities pii). Since estimation of theformer often ends up violating axioms of probability theory, they introduce final, theoreticallyaccurate conditional probabilities p*(/ j J) which fulfill these axioms. The 'difference variables'dij and dij measure the difference between the theoretically accurate and the estimatedconditional probabilities p*ii \ j) + dij- dij = pii \ J), where p*(/1 f) and pii \ J) both must liewithin the bounds pii | J)~ and pii\ j)* respectively. The maximum of all individual differencevariables is represented as '</'

The object of this method is to determine a starting solution for the variables ys,p*ii | j), dijand dij. To do this we must minimize the maximum difference between the theoreticallyacceptable and the elicited conditional probabilities:

min dsubject

y' ai

y''iai'

s = I

pOlyrP*(i\J)O^dJ,

to:

aj)

-I

^ i

+ a

= P

p\i\UJ-a+ ^a

(0.*0|y)-

y) ^ pi

^ij = Pii!

PU)

[i\J)

\J)

The interactive nature of this procedure is employed only after the starting solution has beendetermined. The decision maker can now suggest corrections, the effect of which can beexamined by a sensitivity analysis.

36 Journal of Forecasting Vol. 7. Iss. No. I

The Battelle methodThe Battelle method (Geschka and Reibnitz, 1979; Oberkampf, 1976; von Reibnitz, 1981, 1983)arises from a different way of defining future states of the environmental subsystems. Here,factor outcomes (alternate future states) for the critical factors (the subworld representationswhich do not have one clearly defined future state) are specified mutually exclusively butexhaustively. If we try to determine possible outcome values for, for example, the societalfactor SI: 'dominant political opinion', then the following list of mutually exclusive butexhaustive outcomes could result: Sll: 'socialist' S12: 'liberal' or S13: 'conservative'

In the synthesis stage, individual compatible outcomes will be combined into a single bundlefree of contradictions. The Battelle method explicitly does not use probabilities. To determinethe interdependence between the individual outcomes, experts are asked how compatible theoutcomes e, and ejij = 1,...,«) are. These subjective estimates give us a 'compatibility matrix'comprised of compatibility values kij which take on integer values from 1 to 5. If two outcomesare incompatible they are assigned the value 1. A compatibility rating of 5 indicates that theyare very compatible. The inbetween values 2, 3 and 4 represent increasing compatibility. Sincethis compatibility matrix is symmetric, ikij = kji), it can therefore be represented as a triangularmatrix. This matrix can be programmed onto a computer and used to prune the number ofpossible outcome combinations (scenarios) down to the number of compatible scenarios. Ascenario is considered compatible when none of its outcome pairs ikij) has a value of 1. Thisfurther analysis should be applied to between three and five selected scenarios which have a highinternal compatibility rating, but which are externally dissimilar to one another (Reibnitz,1981), thus covering the range of plausible scenarios.

Comparison and evaluation of the proposed methodsCross-impact analysis requires marginal and conditional probabilities for the pairs of events asinput. High demands are therefore placed on the decision maker's ability and willingness tomake estimates. Since these estimates often do violate probability theory axioms, consistencytests and corrections are often required (Dalkey, 1972; Duval et al., 1975; Sarin, 1978).Cross-impact analysis outputs a ranking of scenarios in order of their likelihoods. Since theseprobabilities are often very small (Duperrin and Godet, 1975) it is suggested that individualscenarios be grouped together (Martino and Chen, 1978).

The Battelle method, contrasting with cross-impact analysis, requires much simpler input:the compatibility estimates for every possible pair of factor outcomes. The output is a range ofcompatible scenarios and their average compatibility values (or weights). Since the Battellemethod does not employ probabilities and only certain individual scenarios are chosen forfurther investigation, it is possible that scenarios will be selected which have startingprobabilities so small that these scenarios cannot practically be the basis of a meaningfulplanning effort.

A NEW METHOD FOR SCENARIO DETERMINATION

Before we present this new method of scenario determination, we should describe the inputrequirements and the resulting outputs. We adopted the position of the manager who, wesuggest based on our experience, is not very interested in the mathematical aspects of ascenario's analysis.

Analogous to the methods described above, we will assume that factors, factor outcomes andcompatibility values (1-5) have been defined in earlier stages of the scenario analysis according

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 37

to the Battelle method. Here the factors are the relevant external factors which influence theproblem. The factor outcomes are possible future states of the factors. The compatibility valuesrepresent estimates of the interdependencies existing between individual outcomes. Of course itwould be theoretically advantageous if these interdependencies were described as conditional orjoint probabilites; however we want to keep the information demanded of managers as simpleas possible. As mentioned previously, a critical factor in cross-impact analysis is its need forestimates of the conditional probabilities (Mitchell and Tydeman, 1978). An empirical study byMoskowitz and Wallenius (1984) showed that, depending on the format of the survey questionsused, up to 50 per cent of all estimates of conditional and joint probabilities violate simpleaxioms of probability theory. For a study of improving the consistency of conditionalprobability assessment see Moskowitz and Sarin (1983).

Our method also requires marginal probabilities on the occurrence of factor outcomes. Sinceevery factor usually only has two or three outcomes, these probabilities are easy to determine(Spetzler and Stael von Holstein, 1976). If this determination of probabilities is too difficult formanagers, the estimation could also be done by other experts, or one could assume that alloutcomes of a factor have equal probabilities.

As a result of our method, managers obtain a number (usually two to four) of alternativemafor development directions (scenarios) and their respective probabilities. This creates a basisfor further stages of scenario analysis, and therefore for strategic planning.

The following methodology can be split into three stages:

(1) determination of compatible scenarios;(2) determination of scenario probabilities through linear programming and(3) determination of some main scenarios using cluster analysis

In the second stage we will determine the probabilities for possible combinations of factoroutcomes (scenarios) based on their (marginal) probabilities and their compatibility values. Forthis we will further develop De Kluyver's and Moskowitz's model described earlier. Sincedetermining scenario probabilities for normal-sized problems is already cumbersome due to thesheer number of computations necessary (our example will require a linear program withapproximately 600 variables and 500 constraints), we will be determining all compatiblescenarios in stage 1 using an enumeration procedure. In larger problems these compatiblescenarios, or at least a portion of them, will provide the starting data for stage 2. This is basedon the hypothesis that typically very small probabilities (or even ys = 0) would be determined inthe second stage for incompatible scenarios with non-extreme marginal probabilities. In stage 3,we will use cluster analysis to synthesize the selected scenarios into a few main scenarios. Theprobability of a main scenario is calculated as the sum of the probabilities of the scenarios fromwhich it is comprised.

The three stages of this method have been implemented in the computer system'KONMACA' (compatible scenario, matrix generator for linear programming, cluster analysis— von Nitzsch et al. 1985).

Determination of compatible scenariosBased on the compatibility matrix developed in the Battelle method (i.e. on the factor outcomesand the compatibility values), the compatible scenarios are determined in the first stage of ourprocedure. These scenarios are found through simple bounded enumeration of all possiblecombinations of factor outcomes. Every combination is checked to see if its outcome pair hasthe compatibility rating of 1 assigned to it. If so this combination will be classified as

38 Journal of Forecasting Vol. 7, Iss. No. 1

belonging to an incompatible scenario and excluded from further examination. (For aprogramming implementation see von Nitzsch et al., 1985.)

With larger problems it is possible that so many compatible scenarios will exist, that foreconomic reasons only a subset (practically less than 50) can be considered in stage 2. In thesecases we would try to choose the scenarios with the fewest number of compatibility ratings of 2and/or which have the highest average compatibility values. We do this because, if we assumenon-extreme marginal probabilities, both of these selection criteria tend to exclude onlyscenarios with typically very small probabilities.

Determination of scenario probabilities using iinear programmingAfter the first step, where the number of possible scenarios is reduced to the number ofcompatible scenarios, and in some cases, further pruned to a subset of these, the decision makerhas the option to reintroduce any especially interesting scenarios which were excluded due totheir deemed incompatibility.

The probabilities of the selected scenarios are determined by the use of a linear programmingmodel (referred to hereafter as LP), which is based on the De Kluyver and Moskowitz modeldiscussed above.

De Kluyver's and Moskowitz's procedure requires marginal and conditional probabilities.On the other hand, in addition to the marginal probabilities, our procedure only needs simplecompatibility estimates of the outcome pairs. Since these compatibility estimates are integersbetween 1 and 5, they must be transformed into probabilities before the LP can use them tocalculate scenario likelihoods. To do this we have two options: we can translate them (1) intoconditional probabilities p(i \ j); or (2) into joint probabilities p(i' j). We reject the first optionbecause the symmetry of the compatibility matrix tells us that k,j = kji and therefore would alsoapply to the conditional probabilities p{i\ j) = pU\ ')• This condition is only fulfilled whenp{i) = p(j), i.e. when all marginal probabilities of the individual outcomes for each outcomepair are equal. The second option has the advantage that there is symmetry between the jointprobabilities, i.e. pii-J) = p(j- i). In the first part of the second stage, the compatibility valueskij will thus be transformed into similar joint probabilities p(i -J). The upper and lower boundsof these joint probabilities p(i-j) will be calculated (Stover and Gordon 1978) according toprobability theory axioms, and thus:

These bounds are illustrated in the following example. If /?(;) = 0.7 and pij) = 0.8 then thejoint probability pii'j) cannot be 0.4 because this would violate the lower bound ofl,j = 0.5 ^ pii'j). Alternatively, the joint probability cannot be 0.9 because of the upper boundUij = 0.1^pit-j).

The transformation of the compatibility values k,j into joint probabilities pii'j) is done asfollows:

This equation is based on the concept of splitting the difference between the upper and lowerbounds of the joint probabilities according to the compatibility ratings. If kij = 1 then the jointprobability p(i-j) will take the value of the lower bound /,>; if kij= 5 then pii'j) - Uij. Thepreceding equations give us the folJowing results:

kij= 1 -• pii'j) = lij (in the example: 0.5);kij = 5 -• pii'j) = Uij (in the example: 0.7);1 < /Cy < 5 - lij ^ pii -j) ^ Uij.

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 39

However, these equations are linear interpolations over the range from 1 to 5 and have thedisadvantage that if ku = 3 then it is possible that pii-j) ^ pii) - pij). To avoid this we couldmake the following change:

/?(/ -y) = Pii)' PiJ) + I iuu - Pii) - PiJ)) - iku - 3)/2),

where kij ̂ 3 with a respective equation for A: ^ 3. This gives us two linear interpolations, for1 ^ A: ^ 3 and for 3 ̂ A- < 5.

The joint probabilities pii-j) calculated using the equations above are entered into the LP asso-called preliminary joint probabilities. They are referred to as preliminary probabilitiesbecause they generally violate another important condition and therefore will eventually have tobe corrected. This condition states that the probability of each outcome must be equal to thesum of the joint probabilities for this o.utcome, and every other outcome both occurring andnot occurring pii) = pii-j) + pii' ~ j), where pii- ~ j) is the joint probability that outcomeei will occur and that ej will not. From this we can establish a final joint probability p*ii'j) forthe determination of the scenario probabilities, which fulfills the conditionspii) = P*ii'j) + P*ii' ~- y)i and whose distance from the joint probability pii'j) is measuredusing the difference variables dfj and du. The objective of this LP model is to minimize thedifference between preliminary and final joint probabilities, where the scenario probabilitieswill be determined as by-products. (For an overview of goal programming see Ignizio, 1976.)

The LP model has the following form for K selected scenarios:

min Y.uidiJ+ dij) + M-d where A/ is a large value, say 10,000

subject to:

(1) y''ai ^ pii),il) y''iai-aj)-p*ii-j) ^0

(3) IJ ys ^ 1

(4) p*ii'j) + dij- dij = Pii'j)

(6) d-di} ;d- dij '•

il) ys,dij,di},d ;

'Notes on the LP Model:Objective Function: The variable d is equal to the maximum of all individual differencevariables dj and dij. Becaus'e of the relatively large objective function coefficient d, first themaximum difference between the preliminary and final joint probabilities is minimized and thenthe sum of the individual deviations is minimized. Our objective function therefore combinestwo alternative objective functions: minE(flfy-i- dy) and min d.

Constraints (1) and (2): This could be illustrated in a small example where we have two factors(A and B), each with two outcomes (Al, A2 and BI, B2) and one factor (C) with three resultingoutcomes (C1,C2,C3). These outcomes give 2*2*3 =12 possible outcome groupings orscenarios (see Table 2).

40 Journal of Forecasting Vol. 7, Iss. No. I

Table 2.

Scenario

Possible scenarios

Probability

(example)

Al A2 BI

Outcome

B2 Cl C 2 C3

1 yi 1 0 1 0 1 0 02 yz 1 0 0 1 1 0 03 yi 0 1 1 0 1 0 04 y4 0 1 0 1 1 0 05 ys 1 0 1 0 0 1 06 yt 1 0 0 1 0 1 07 >», 0 1 1 0 0 1 08 ys 0 1 0 1 0 1 09 y9 1 0 1 0 0 0 1

10 >',o 1 0 0 1 0 0 111 yn 0 1 1 0 0 0 112 vi2 0 1 0 1 0 0 1

The probability of outcome Al can be expressed in terms of scenario probabilities yi + yi+ ys + J6 H- ;'9 + yio = P ( A 1 ) , i.e., the sums of the probabilities for the scenarios comprising

outcome Al are added. Accordingly, the joint probability of Al and BI in this example is thesum of probabilities of scenarios including both of these scenarios: yi + ys + y9^ P(A1 BI).

If our representation of marginal and joint probabilities pii) and pii'j) includes only asubset of all possible scenarios (for example, all compatible scenarios), then we replace theequal sign with a greater than or equal sign ( ^ ) . This results in the vector notations ofconstraints (1) and (2) in the LP model.

Constraint (3): If N is the number of all possible scenarios, then S>'s=l is=\,...,N).However if we only are considering K scenarios, where K ^ N, then Zys < 1 (5 = 1,..., K).

Constraint (4): This constraint determines the difference between the preliminary and final jointprobabilities. When p*ii'j) < pii'j), then the difference is dij. When p*ii'j)>pii-j) thenthe difference is dij. When p*ii'j) = pii'j) then dij= dij = 0.

Constraint (5): To explain constraint (5) we shall use the example in Table 2. We find:

piAl) = p*iA\ B\) + p*iAl BI)piAl) = p*iA\ -C\) + p*iAl - C2) + p*iA\' C3)

piC3) = p*iC3 • Al) + p*iC2' Al)* * *ipiC3) = p*iC3' BI) + p*iC3' BI)

The probability of each outcome must equal the sum of the joint probabilities for this outcome,and every other outcome both occurring and non-occuring.

Constraints (6) and (7): Constraint (6) defines the generalized difference variable d as an upperlimit, i.e. maximum of all individual distance variables dij And rf,^ during the minimization.Constraint (7) ensures that all variables must be hon-negative.

The linear program outputs the scenario probabilities ysis= I, ...,K), the final joint prob-abilities p*ii'j), the individual differences between preliminary and final joint probabilities duand du, and their maximum d. Finally, the corrections to the joint probabilities (and thus the

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 41

compatibility values) are based on the attempt to bring the original estimates in line with thelaws of probability theory.

As a result of the LP model described above, we have obtained scenario probabilities whichfulfill our chosen objective function's demand for minimized difference between preliminaryand final joint probabilities. After determining this first optimal solution, we should follow upwith a post-optimality analysis. Here we will examine each scenario probability to determine therange in which it could fluctuate without the final objective function value changing.

If there is no available standard procedure for post-optimality analysis (sensitivity analysis),then the sensitivity range of the scenario probability Vs could be calculated by minimizing thisvariable once and maximizing it once. With an additional constraint the objective function ofthe first LP model can be set equal to OFl, where OFlmin is the minimal objective functionvalue of the first LP model:

Min v, then Max \\

subject to:

Constraints (l)-(7)

Constraint (8): S,,(£/,7+c?,)) + 10,000-c^= OFl ^m, s=\,...,K.

As an input value for the third stage, the cluster analysis, the simplest method is to take thearithmetic mean of the upper and lower bound of each scenario probability.

Determination of a few main scenarios using cluster analysisAfter completing stages 1 and 2 of our procedure we have many scenarios with, at best very lowstarting probabilities. In strategic planning it is practical only to consider a small number ofmajor scenarios. Cluster analysis gives us the option to combine this multitude of scenarios intoa small number of main scenarios. Without going into the details of cluster analysis procedureshere (see Bohler, 1977; Martino and Chen, 1978; Steinhausen and Langer, 1977), we will onlyaddress a few details important to our examination.

We turn to cluster analysis to be able to recognize important characteristics of the str^uctureof the synthesis of a multitude of individual pieces of data (Steinhausen and Langer, 1977). Todo this we attempt to organize homogeneous groupings of scenarios where the groups are asheterogeneous among themselves as possible. We therefore cannot make any general assertionsabout the number of clusters (usually two to four), which is dependent on the structure of theproblem. The selection of a measure of distance which defines homogeneity and heterogeneity,must be in accordance with the scaling of the factor outcomes (usually a nominal scale).Sometimes a rescaling will be necessary. Note, that the basis for clustering is similarity definedby the Euclidian distance between pairs of scenarios. Potential consequences of scenarios arenot taken into account. However, alternative clustering criteria seem possible.

The theoretical 'centre' of clusters calculated by cluster analysis algorithms can be viewed asrepresenting the possible major final states. A probability, consisting of the sum of theprobabilities of the scenarios belonging to the cluster is associated with each 'centre* Thesecentres do not usually correspond entirely to possible real scenarios. If, for example, a factor'dominant political opinion' has the outcomes: 'liberal' with a value of 2, and 'conservative'with a value of 3, then the center could formally be given the value 2.8. We can now follow oneof two procedures. One close-lying scenario can be defined as a representation of the centre.Alternatively, a vague outcome for a factor could be an indicator of the range of variance ofthis factor in the cluster. In many cases it may be important not to describe a major future state

42 Journal of Forecasting Vol. 7, Iss. No. I

too exactly because the method and the data may not support such precision. It is especiallyimportant in this last phase, with its final description of the main scenarios, to encourage stronginteractions with management.

EXAMPLE

In the following example we consider three environmental subsystems relevant to a fictitiousproblem: 'society', 'technology' and 'the economy* The subsystem 'society' is described by afactor (SI) with three outcomes (S11,S12,S13) and three factors (S2,S3,S4), each with twooutcomes (HiS/1 and H2S/2 where / = 2,3,4). 'Technology' is represented by the factor (TI)with two outcomes. The subsystem 'the economy' has two factors (El and E2) with two andthree outcomes respectively.

Table 3 describes all the data necessary to run through this new procedure:

(1) a list of all factor outcomes e, (/ = 1 16)(2) the determined compatibility values ku for every 2 outcomes e, and ej (where A:y = 1,..., 5)(3) the estimated probabilities pii) for the individual outcomes e,.

In this example there are 2 ' 3^ = 288 possible outcome combinations (scenarios). In the firststage of the new procedure, all compatible scenarios (i.e. those without a value of 1) are

Table

Pii)

0.30.40.5

0.60.4

0.60.4

0.70.3

p p

to. bo

0.20.8

0.30.50.2

3. Data for the example

Factor

SI: DominantPolitical Opinion

S2: Gov't Influenceon the Economyand Society

S3: ConsumerSpending

S4: EnvironmentalProtection

TI: Rate of TechnicalInnovation

El: EconomicGrowth

E2: Unemployment

Outcomes

Sll*;S12:S13:

S21:S22:

S31:S32:

S41:S42:

Til:T12:

Ell:E12:

E21:E22:E23:

: socialistliberalconservative

strongweak

strongweak

strongweak

highlow

risingstagnating

risingno changefalling

SI

1

X

1**1

51

24

51

24

24

2 .34

2

X

1

15

Ul Ul

ro ro

52

42

1 Ul Ul Ul

3

X

33

42

25

Ul Ul

Ul Ul

243

S2

1

X

1

33

33

Ul Ul

23

234

2

X

ut Ul

Ul Ul

Ul Ul

43

432

S3

1

X

1

14

52

52

234

2

X

42

25

14

432

S4

1

X

1

42

23

243

2

X

Ul Ul

43

1 Ul Ul Ul

TI

1

X

1

53

234

2

X

13

432

El

1

X

1

135

2

X

531

E2

1 2 3

X

1 X1 1 X

Xij = Outcome j of factor Xi Compatibility Ratings

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 43

determined using the first part of the computer program KONMACA (von Nitzsch et al., 1985).In our example there are 46 scenarios. To simplify our investigation, we will examine only someof these compatible scenarios. The following criteria will guide our selection: (a) the number of2 ratings (denoted as 'mistakes* in Table 4) should be less than 4; or (b) the scenario weighting(defined as the average compatibility rating of the scenario) should be greater than or equal to3.286.

Table 4 shows the result of this selection process: the block of columns marked 'outcomes'shows which outcomes will be accepted for any given scenario (1 to 32) for each factor (SIthrough E2).

Every compatible scenario can be represented as an overview table using the KONMACAsystem. For example take scenario 4̂ the scenario with the highest weighting. Table 5 exhibitsthe estimated compatibility values for the individual outcome pairs and the factor outcomes forscenario 4. It gives, among other things, a simple localization of Table 4's 2 ratings (i.e.mistakes).

In the second stage of this procedure we calculate the probabilities of the scenarios chosen inthe first stage. Here we use the second part of the KONMACA program. It consists of a matrixgenerator which, based on the compatibility values and marginal probabilities of the individualoutcomes, produces the input data set according to the LP model described above. The LP forthe example contains 549 constraints and 328 + K variables. K is the number of scenarioprobabilities considered, where K < 288. Since we selected A =̂ 32 scenarios in the first stage,the solution LP now contains 360 variables. Based on the solution of this LP, upper and lowerbounds for all scenario probabilities and when appropriate, the arithmetic mean, arecalculated. (Table 6 shows the mean scenario probabilities ys (as a percentage) for the selectedscenarios, where s=\, ...,32.)

The cluster analysis is performed using the PKM-program from the BMDP package (o. V.,1981; von Nitzsch et al., 1985). We calculated solutions for two sets of trials with two, three.

Table 4. Selected compatible scenarios

Scenario

123456789

10111213141516

S1

1122222222333333

Outcomes

S S S T E2 3 4 1 1

1 2 1 1 21 2 1 2 22 1 2 1 12 1 2 1 12 1 2 1 22 2 1 1 22 2 1 2 22 2 2 1 22 2 2 2 22 2 2 2 21 1 2 1 11 1 2 1 11 1 2 1 21 1 2 2 21 2 1 1 21 2 1 2 2

E2

2223222212232222

'Mistakes'

2101223333111233

Weight

3.3813.5243.6673.8103.2383.2863.1903.0953.3333.0953.5243.7143.2863.1433.0953.143

Scenario

17181920212223242526272829303132

S1

3333333333311222

Outcomes

S S S T E2 3 4 1 1

1 2 2 1 21 2 2 2 22 1 2 1 12 1 2 1 12 1 2 1 22 1 2 2 22 2 1 1 22 2 1 2 22 2 2 1 22 2 2 2 22 2 2 2 21 2 1 1 21 2 1 2 22 1 2 1 22 2 1 1 22 2 1 2 2

E2

2223222221211111

'Mistakes'

3201123333264444

Weight

3.0483.1903.6193.7143.2863.1433.0953.1433.0483.3333.1903.2863.5243.2863.3333.333

For example: Scenario 4 = (S12, S22, S3i, S42, Til , EH, E23)

44 Journal of Forecasting

Table 5. Scenario 4

Vol. 7. Iss. No. I

Dominant Pol. OpinionGov't InfluencesConsumer SpendingEnvironmental ProtectionRate of Techn. InnovationEconomic GrowthUnemployment

liberalminimalstrongweakhighhigherfalling

S12S22*S31S42Ti lEllE23

S12

5**33543

S21

33342

S31

4554

S41

343

Ti l

54

El l

5

E23

*Xij: outcome j for factor Xi iji Compatibility rating values

Table 6. Scenario probabilities as arithmetic means of the upper and lower bounds

s

12345678

ys

7.505.003.752.503.75

10.000.003.75

s

910111213141516

ys

0.000.003.753.753.752.503.753.75

s

1718192021222324

ys

3.753.753.752.503.752.503.753.75

5

2526272829303132

ys

3.753.753.753.753.753.757.500.00

four and five clusters each. In one set of trials, three cluster centres were predefined. The otherset had no predefined cluster centres. Using a predefined centre is one method of incorporatingpossible knowledge of experts or managers regarding the structure of the problem as a startingsolution for cluster analysis. Generally, of course, increasing the number of clusters increasesthe homogeneity within a cluster but thus reduces the heterogeneity between clusters. With thedata given, it seems logical to construct three clusters, as four or five would not produce anynew (in terms of heterogeneity) main scenarios. Since the results with and without predefinedcentres do not strongly differ, those representations with predefined centres will be used.

The appointed starting cluster contains the highly contrasting scenarios 3( = 22 1 2 1 1 1),27( = 3 2 2 2 2 2 2) and 28(= 1 12 1 12 1). We then alter the scaling of the factors with twooutcomes (S2, S3, S4, Tl, El) and assign the value 3 to the second outcome. In this way thedifference between the extreme outcomes is the same for each factor. Table 7 shows the resultsof a cluster analysis, three clusters with the distance of the scenarios to the centre.

We should emphasize the calculated cluster probabilities. If we assume equal probabilities foreach scenario, then cluster 2 occurs with approximately 47% probability (i.e. p-incorrect) andcluster 3 occurs with only about 22% probability. However, when talcing into account theresults from stage 2 we see that cluster 3 (p = 37%) is actually more probable than cluster 2(p = 33%). Table 8 displays the centres for the first cluster for our example.

The maximums and minimums define the ranges of the factor outcomes.

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 45

Table 7. Results of the cluster analysis

Cluster IScenario

345

11121319202130

p-incorrect31.25

Probabilities

Distance

.18

.411.48.67

[.841.89.09.34.41

1.89

P30.7

in percentages

Cluster 2Scenario

789

101416171822232425262732

p-incorrect46.875

Distance

1.701.851.471.252.452.102.221.762.042.101.601.761.351.111.87

P32.8

Cluster 3Scenario

126

15282931

p-incorrect21.875

Distance

1.071.691.651.691.141.731.69

P36.5

Table 8. Centres for the First Cluster

Factor

1 SI —2 S 2 -3 S3 -4 S4 -5 Tl -6 El -7 E 2 -

POL.OINFLUCONSU

• ENVIR- INNOV

ECON- UNEMP

Minimum

2.00001.00001.00003.00001.00001.00001.0000

Centre

2.60002.40001.00003.00001.00001.80002.2000

Maximum

3.00003.00001.00003.00001.00003.00003.0000

CONCLUDING REMARKS

In this paper we proposed a new method for scenario analysis. Starting with relatively simpledata obtained from managefs, this procedure determines possible alternate main future states(scenarios) and their probabilities. The scenarios developed thus serve as starting points forfurther investigations in the strategic planning process.

A part of this methodology (stage 1) was successfully tested in a workshop attended bystudents and faculty. Stages 1 and 3 of the new procedure were validated as part of their firstpractical application in the strategic planning process at a large German company. We wereencouraged by the reactions to the use of a formal methodology as part of a process generallybased on experience and intuition.

46 Journal of Forecasting Vol. 7. Iss. No. 1

ACKNOWLEDGEMENTS

We gratefully acknowledge the help of Mr. Rudiger von Nitzsch for his assistance withcomputer-related aspects of this research. We would also like to thank Michael Bieber at theWharton School for translating this paper from the original German.

REFERENCES

Becker, H. A. 'Scenarios: a tool of growing importance to policy analysts in government and industry*,Technological Forecasting and Social Change, 23 (1983), 95-120.

Bohler, H., 'Methoden und Modelle der Marktsegmentierung, Stuttgart, Poschel, 1977.Dalkey, N. C , *An elementary cross-impact model' Technological Forecasting and Social Change, 3

(1972), 341-351.De Kluyver, C. A. and Moskowitz, H., 'Assessing scenario probabilities via interactive goal

programming. Management Science, 30 (1984), 273-278.Duperrin, J. C. and Godet, M., 'SMIC 74 — A method for constructing and ranking scenarios' Futures,

7 (1975), 302-312.Duval, A., Fontela, E. and Gabus, A., 'Cross-impact analysis: A handbook on concepts and

applications' In Baldwin, M. M. (Ed.) Portraits of Complexity, pp. 202-222. Columbus, Ba HelleMemorial Institute, 1975.

Geschka, H. and Reibnitz, U. von, 'Zukunftsanalysen mit Hilfe von Szenarien — erlautert an einemFallbeispiel "Freizeit im Jahr 2000" ', Politische Didaktik, 4 (1979), 71-101.

Godet, M., 'Reducing the blunders in forecasting', Futures, 15 (1983), 181-192.Gomez, P., 'So verwenden wir Szenarien fur Strategieplanung und Friihwarnsystem* Management —

Zeitschrift Industrielle Organisation, 51 (1982), 9-13.Gomez, P and Escher, F., 'Szenarien als Planungshilfen', Management — Zeitschrift Industrielle

Organisation, 49 (1980), 416-420.Gordon, T. J. and Hayward, H., 'Initial experiments with the cross impact matrix method of forecasting'

Futures, 1 (1968), 100-116.Ignizio, J. P., Goal-programming and Extensions, Lexington, 1976.Jackson, J. E. and Lawton, W. H., 'Some probability problems associated with cross-impact analysis'

Technological Forecasting and Social Change, 8 (1976), 263-273.Kahn, H. and Wiener, A., The Year 2000, New York, Collier Macmillan, 1967.Kneschaurek, F., 'Szenarioanalysen' In Buchinger, G. (Ed.) Konzeptionen-Praxis-

Entwicklungstendenzen, pp. 311-326, Wien, Signum, 1983.Linneman, R. E. and Klein, H. E., 'The use of multiple scenarios by U.S. industrial companies: A

comparison study, 1977-1981' Long Range Planning, 16 (1983), 94-101.Malaska, P., Malmivirta, M., Meristo, T. and Hansen, St.-O., 'Multiple scenarios in strategic

management', Long Range Planning, 17 (1984), 45-49.Makridakis, S. and Wheelwright, S. C , Forecasting Methods and Applications, New York, John Wiley &

Sons, 1978.Martino, J. P., Technological Forecasting for Decision Making, New York, American Elsevier, 1972.Martino, J. P. and Chen, K.-L., 'Cluster analysis of cross impact model scenarios' Technological

Forecasting and Social Change, 12 (1978), 61-71.Martens, P. and Plattfaut, E., 'Ansatze zur DV-Unterstutzung der Strategischen Unternehmensplanung'

Die Betriebswirtschaft, 45 (1985) 19-29.Mitchell, R. B. and Tydeman, J., 'Subjective conditional probability modelling' Technological

Forecasting and Social Change, 11 (1978), 133-152.Mitchell, R. B., Tydeman, J. and Georgiades, J., 'Structuring the future—application of a scenario-

generation procedure'. Technological Forecasting and Social Change, 14 (1979), 409-428.Moskowitz, H. and Sarin, R. K., 'Improving the consistency of conditional probability assessments for

forecasting and decision making', Management Science, 29 (1983), 735-749.Moskowitz, H. and Wallenius, J., 'Conditional versus joint probability assessments'. Paper No. 851,

Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana (1984).

Jutta Brauers and Martin Weber Scenario Analysis for Strategic Planning 47

Nitzsch, R. von, Weber, M. and Wietheger, D., 'KONMACA: Ein Programmsystem zur Unterstutzungder Szenarioanalyse', Working Paper No. 85-03, Institut fur Wirtschaftswissenschaften, RWTHAachen, Aachen (1985).

Oberkampf, V., 'Szenario-Technik, Darstellung der Methodik' Manuskript, Battelle-Institut e.V.,Frankfurt/Main (1976).

Opitz, O., 'Modelle und Verfahren der Prognose', Die Betriebswirtschaft 45 (1985), 83-95.o. V. BMDP — Statistical Software, Berkeley, Los Angeles, London, 1981.Rao, T. R., 'Scenarios for the Indian iron and steel industry'. Long Range Planning, 17 (1984), 91-101.Reibnitz, U. von, 'So konnen auch Sie die Szenario-Technik nutzen' Marketing-Journal, 14 (1981),

37-41.Reibnitz, U. von, 'Szenarien als Grundlage strategischer Planung' Harvard Manager, 1 (1983).Sarin, R. K., *A sequential approach to cross-impact analysis', Futures, 10 (1978), 53-62.Sarin, R. K., 'An approach for long-term forecasting with an application to solar electric energy'

Management Science, 25 (1979), 543-554.Spetzler, C. S. and Stael von Holstein, C. A., 'Probability encoding in decision analysis' Management

Science, 22 (1975), 340-358.Steinhauser, D. and Langer, K., Clusteranaiyse, Berlin, New York, De Gruyter, 1977.Stover, J. G. and Gordon, T. J. 'Cross-impact analysis' In Fowles, J. (Ed.) Handbook of Future

Research, pp. 301-328, Westport, London, 1978.Trux, W. and Kirsch, W., 'Konzeptionelle Gesamtsicht und Fruhaufklarung als zentrale Probleme des

strategischen Managements' In Roventa, P (Ed.) Portfolio Analyse und Strategisches Mangement,pp. xix-xxxiii, Munchen, Planungsschriften, 1979.

Wechsler, W., Delphi-Methode. Munchen, V. Florenz, 1978.Welters, K. 'Cross-Impact Analyse als Instrument der Unternehmungsplanung' Betriebswirtschaftliche

Forschung und Praxis, 29 (1977), 557-568.Wild, J., Gundlagen der Unternehmungsplanung, 3rd Edn, Opladen, Westdeutscher Verlag, 1981.Wilde, K. D., 'Langfristige Prognosen in der strategischen Planung: Methodik und Verfahrensvergleich

anhand praktischer Beispiele' Zeitschrift fur Betriebswirtschaft, 52 (1982), 923-941.

Authors' biographiesJutta Brauers is working in the planning department of a large German company. She holds a Master inBusiness (Dipl.-Kfm.) from Aachen University. During her study she worked as a research assistant at theSchool of Management at Aachen. Currently she is developing a computer-based information system.

Martin Weber is an Assistant Professor (Wissenschaftlicher Mitarbeiter), School of Management, AachenUniversity. He received a Master in Mathematics (Dipl.-Math.) and Business (Dipl.-Wirtschaftsmath.)and a Ph.D. in Business (Dr.rer.pol.) from Aachen University. He has held visting appointments atHelsinki School of Economics, Graduate School of Management, UCLA and the Wharton School,University of Pennsylvania. His research interests are in planning, decision making and finance.

Authors' addressesJutta Brauers, Kronenstr 2, 4000 Dusseldorf 1, West Germany

Martin Weber, Lehr-und Forschungsgebiet Allgemeine Betriebswirtschaftslehre, RWTH Aachen,Templergraben 64, 5100 Aachen, West Germany.

Please address all correspondence to Martin Weber at the above address.