Strata — A method for strategic analysis of complex systems

168 European Journal of Operational Research 24 (1986) 168-177 North-Holland

STRATA--A method complex systems

for strategic analysis of

Chris t ian S C H O L Z Institut fftr BWL, Unioersiti~t Regensburg, D 8400 Regensbur~ Germany, Fed. Rep.

Abstract: STRATA combines a specific methodology of hierarchies, the theory of membership functions, and concepts of mental data processing. It provides a heuristic method which can aid the decision maker in determining the company's situation at a given moment. To do so, STRATA helps the decision maker to construct, in an iterative mode, an individual intrasystemic hierarchy as representation of his or her cognitive structure of thought.

Keywords: Management, computers, planning, fuzzy sets, heuristics

The problem of strategic assessments

One main issue in strategic management is to determine the strategic situation of a company. By this we mean not only to assign Strategic Business Units to certain boxes in the portfolio matrix, but rather to locate the strategic strengths/weaknesses and opportunit ies/ threats of the company, as well as to determine the specific relevance of these elements with respect to the overall strategic situation.

This means that the planner has to cope with several problems at once; between others, the planner has to answer the following questions: - Which are the relevant elements? - Where to find them? - What does it mean if an element has a specific

value? - Is this value to be considered good or bad? - How do discovered elements combine into the

overall strategic situation? - How to deal with soft, fuzzy information?

What makes it even more complicated is the fact that the planner has to answer these questions simultaneously.

Received August 1983

Of course, the literature offers many suggestions, such as t h e - -b y now traditional--scanning techniques (e.g. [1]) or the theoretical framework for competitive positioning (e.g. [3]). But even though these techniques provide valuable information, still the question which specific elements (together) make up the specific strategic situation and how they work together is hard to answer.

The basic idea of STRATA

The name 'STRATA' has been derived from the goal of the approach (to do strategic analysis), and from the use of the concept of stratification which calls for a segregation of complex systems into different levels ('stratas').

STRATA is based on the idea that especially for strategic problems the intuition and the subjective judgement of the manager are extremely important. But even though the manager might have the complete strategic situation in his mind in a hofistic way, it is hard for him to articulate this picture. And it's even harder to force him to forget about fuzzy judgements and to .produce assessments which all look like hard facts. STRATA serves, in particular, two purposes: - the holistic picture the manager has in his mind

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C. Scholz / Method for strategic analysis of complex systems 169

shall be transferred into a hierarchy which reflects his picture and which is consistent; and - the manager should be allowed to make soft assessments as well as hard ones.

STRATA, therefore, is a specific method for system analysis. It helps the manager to construct an adequate picture of the situation of his company. By this we mean that the manager finds out which elements make up the particular situation and which values and weights characterize these elements.

The strategic nature of the problems we deal with results in two major characteristics of STRATA: - For strategic planning there are, in most cases, only a few hard facts available. Therefore STRATA makes use of the fuzzy set theory (e.g. [8]) which allows to deal, in particular, with soft information. - Since we focus on the strategic level, we have to deal with an extremely complex system. To reduce this complexity only state variables and certain aggregations between them are considered by STRATA. This results in a static picture of the reality, which may be described as a ' snapshot with a long exposure time'. This is a feasible procedure for analysing strategic problems.

Also we can point out two characteristics of the kind of analysis which STRATA performs: - STRATA aims at a correct picture of the (current) reality. But since there is no criterion for optimal- ity, STRATA works in an iterative mode in which the computer provides certain guidelines for the researcher to come close to what might be an appropriate picture of the reality. - In order to get those guidelines, a theoretical basis is needed. STRATA takes this underlying theory from the thoughts developed in General Sys- tems Theory about hierarchies. The procedure suggested for STRATA connects four different components: - The first component is the manager or the researcher. This planner is the one who is supposed to find out what the actual strategic situation of the company is. - The second component is the input hierarchy, which reflects his judgements on the situation. This input hierarchy consists of a specific kind of fuzzy hierarchy. - The third component is the algorithm, which performs the actual analysis. Using the internal hierarchy-model, the computer serves as a control device, which may help to correct the planner 's

MANAGER/RESEARCHER WITH COGNITIVE STRUCTURE:

J INPUT HIERARCHY

AS SPECIFIC PICTURE

I ALGORITHM

WITH ITS

INTERNAL MODEL

OUTPUT HIERARCHY

WITH STIMULATIVE

AND DIRECTIONAL

INFORMATION

Figure 1. Basic procedure for STRATA

judgements by providing stimulative as well as directional information. - The fourth component is the output hierarchy. It consists of a normalized version of the input data as well as of several variables, which serve as guidelines for the correction of the input hierarchy as well as for the interpretation of the results. These four components are then connected as shown in Figure 1.

T h e p r o c e d u r e o f STRATA

Manager/researcher

Two basic alternatives exist for the 'configura- tion' of persons working with STRATA. - The manager or the researcher (at least partly familiar with the company to be assessed) works as a planner independently from other persons in a dialogue with the system; a detailed knowledge of STRATA and especially of its indicator .variables becomes necessary. - The manager(s) or the planner(s) responsible for the assessments use(s) a researcher as an interface; this researcher (unfamiliar with the company to be assessed and therefore rather unbiased) under- stands STRATA and is able to make the manager or the planner ' ta lk about the problem' on basis of the output, in order to create 'new input'.

170 C Scholz / Method for strategic analysis of complex systems

OVERALL STRATEGIC SITUATION

INTERNAL ,0,0 ,0,7 ,3 STRATEGIC - +

SITUATION I - - o + +

,0,1,2 ,7,0 - +

- - O i + l +

,01,3,4.3,0 EXTERNAL _ + STRATEGIC - - 0 + + SITUATION

Figure 2. Fuzzy aggregations

Both alternatives seem to be possible, even though for first and heuristic analysis the second config- uration seems to be preferable.

The input hierarchy

The information which the user hands over to the algorithm is structured hierarchically. Figure 2 shows a part of such a hierarchy, to be discussed in the following with respect to elements, relations, values and weights.

STRATA uses elements which form an intrasystemic hierarchy. It is important to notice that STRATA works always only on basis of this particular type of hierarchy. In an intrasystemic hierarchy (e.g. [2, p. 52; 6, p. 177]) the elements are connected by one kind of relations only: a specific aggregation-function. For instance, the two elements 'internal strategic situation' and 'external strategic situation' may aggregate into the element called 'overall strategic situation'.

This means that for the static picture of our 'snapshot with a long exposure-time' dynamic interactions are neglected since STRATA does not consider the existing horizontal interactions between, for instance, the internal strategic situation and the external strategic situation. But it is important to notice that in an intrasystemic hierarchy no vertical interactions exist: For instance, the internal strategic situation does not influence the overall strategic situation; it is part of the overall strategic situation.

The elements of this hierarchy are interpreted by STRATA as fuzzy sets. In order to get their values, we must distinguish between other fuzzy set approaches and the approach used here by STRATA: - In other fuzzy set approaches (e.g. [10]) each

element is interpreted as one fuzzy set; for instance, to be labeled 'extremely good internal situation'; for this one fuzzy set the company's degree of membership is to be judged. - In contrast to this, STRATA takes each element as consisting of five different fuzzy sets (see [5, p. 279]; also [4, p. 119]). These five fuzzy sets for each element must be in an ordinal order and then can be labeled similar to a five-point-Likert-scale. In our figures, this scale is indicated as running from double minus to double plus, which may represent a scale reaching from extremely poor to very good. The degrees of membership indicate to which degrees the company under investigation belongs, for instance (Figure 2), to the fuzzy set labeled 'extremely poor overall strategic situation' (# = 0.0) or to the fuzzy set labeled 'good external strategic situation' (/~ = 0.3). Since we have five fuzzy sets for each element, the company's degree of membership to all five fuzzy sets must be assessed by the researcher. For instance, the hierarchy in Fig- ure 2 requires 15 judgements.

This specific feature of STRATA has two important advantages: It asks for some redundancy in the information, since, for instance, the degree of membership to one fuzzy set depends on the degree of membership to the other four sets. But even more important and as specific characteristic of STRATA, the use of five fuzzy sets for each element gives the researcher or the manager the opportunity to express his assessment of the strategic situation in an extremely distinctive way. For instance (Figure 3), - in Example A he is convinced that the company belongs exclusively to the fuzzy set labeled 'very good',

C. Scholz / Method for strategic analysis of complex systems

,0_,0.01.0 t.+ ,0,0_ !.0.5,5+ !.2_,2,2,2i,2+ - 0 + + - - 0 + + . . . . . 0 + i+

EXAMPLE A EXAMPLE B EXAMPLE C

171

Figure 3. Fuzzy assigments

- in Example B he is indifferent between 've ry good' and 'good' . This assessment reflects a situation in which the company belongs with some degree of membership to both fuzzy sets, - in Example C he is undecided, which means that he considers the company as belonging to all five fuzzy sets with the same degree of membership.

The third input we need are the weights for the elements to be aggregated. After including these, we get, for instance, the small hierarchy consisting of the internal, external, and overall strategic situation, as it was shown in Figure 2.

OVERALL STRATEGIC SITUATION ACCORDING TO INPUT HIERARCHY

.0 ,i .2 7,0 - +

- - ] 0 + + ,

INTERNAL STRATEGIC SITUATION

,0,0.0.7,3 - +

- - 0]+ +

,0,3 ;,4 ,31,0 - -i-

. . . . . O + +

The algorithm

To analyse the input hierarchy, STRATA performs three tasks:

First, STRATA normalizes the input hierarchy, because there are two requirements from the underlying fuzzy set approach to be met: One re- quirement calls for a one-peak-only situation, the other one states that the sum of the five degrees of membership for each element must equal one.

Second, STRATA builds up its own hierarchy by using the structure and the weights provided by the researcher. Then STRATA takes the given values

OVERALL STRATEGIC SITUATION ACCORDING TO STRATA

lO '2 '2 .5 'i - +

0 + +

SIGMA / I ~

',0.3.2 r.5.1 - +

..... O+ +

EXTERNAL STRATEGIC SITUATION

tit

TAU

,f

INPUT HIERARCHY

Figure4. Thealgofithm

STRATA

172

(9 @ ra-I I-s1 l-Sl rs-l

??

STRATA

Figure 5. Alternative comparisons


© f

£ N Fq D

I NPUT-H I ERARCHY STRATA

from the lowest level and aggregates them according to its internal model. STRATA, first, uses the operator TAU to perform the pairwise aggregation of the degrees of membership. After TAU has aggregated all degrees of membership for one element, SIGMA makes sure that the requirements one-peak-only and sum-equals-one are met (Figure 4).

The success of this second task depends basically on the used operators, since they are supposed to act as a substitute for a 'logical and reasonable' (e.g. [9]) human aggregation. The operators - TAU, which resembles some features of classical operators such as the geometric mean and the minimum operator, and - SIGMA, which basically performs a heuristic smoothing routine, have been found in an induc- tive approach. This generation of TAU and SIGMA as well as their mathematics and the performance test of TAU will be presented and discussed elsewhere [7]. For our discussion here it is mainly of importance that they combine descriptive and prescriptive decision theory: TAU and SIGMA, originally based on 'human' operators, now are used in STRATA as guidelines which tell how the aggregations should be done in order to be considered 'consistent'.

Also it is important that TAU is a constant operator as opposed to other operators (e.g. [9]), which are parameterized according to 'representa- tive' data bases: For the strategic problems STRATA has to deal with, it currently seems impossible to get those data bases. Therefore TAU stays constant for all aggregations, but nevertheless performs in a similar way as human operators do (see section ' test results' and [7]).

Third, STRATA evaluates the data and de- termines several indicator variables; one of them is

the consistency of the input hierarchy as compared with the artificial hierarchy created by STRATA. These differences are computed for each aggregated element twice: once for the direct aggregation as it results from the next lower level and once for the indirect aggregation as it results from the lowest level of hierarchy.

Figure 5 illustrates this idea for an input hierarchy of seven dements, A1 through A7, and shows that, for instance, the top element A7 of the input hierarchy can be compared twice: once with $7" which is the aggregation as it results according to STRATA starting from A1, A2, A3 and A4, and once with $7"* which is the value STRATA com- putes starting from A5 and A6.

Differences between $7" and A7 as well as between $7"* and A7 then indicate inconsistencies in the input hierarchy, which derive either from wrong values in A1 through A7, wrong weights, or from a wrong structure. By wrong structure we mean that the manager, for instance, aggregates implicitly other elements beside A5 and A6 into A7, which results in an inconsistency, since A7 is affected by his judgement.

Other indicators calculated by STRATA are the degree of discrimination, average softness, and variety in used softness. These indicators will al- low certain evaluations of the assessments to be discussed in the following section.

The output hierarchy

The researcher uses the results generated by STRATA as a guideline to determine the next steps to be taken (Figure 6):

First, the researcher looks at the consistency checks. If there are any parts of the hierarchy which are not consistent, a modification of the input hierarchy becomes necessary, which means


> [ INPUT HIERARCHY I +

t I +

OUTPUT HIERARCHY

CHANGE IN S T R U C T U R I ~ WEIGHTS OR VALUES~ -

VALUES

VALUES

CHANGE N ,S , / VARIETY OF

:os S.

USE OF NORMALIZED HIERARCHY AND OF INDICATOR VARIABLES

173

N,S, = "NON-SATISFYING"

S, = "SATISFYING"

Figure 6. Using the output of STRATA

that structure, weights, or values must be corrected. The new input hierarchy, again, is evaluated by STRATA.

Second, the researcher looks at the degree of discrimination, to find out if the results appear to be biased into one direction. If this possibility is

indicated, the hierarchy has to be checked against reality in order to find out if in reality really all elements go into the same positive or negative direction. If this is not the case, a more dis- criminating judgement is called for, which means that the researcher has to correct some values.

174 C. Scholz / Method for strategic analysis of complex systems

Third, the researcher looks at the average softness of the information: It is always easy to ac- complish a perfectly consistent hierarchy, if, for instance, only the assessment 'undecided' is used. Therefore, a high average softness makes the hierarchy less valuable. Again we must find out if the reality really displays this degree of softness; if it is not the case, a more specified judgement is called for.

Fourth, the researcher looks at the variety of the softness in the given information. If the manager uses the same degree of softness for all elements, those values definitely are not in accordance with reality since always some elements reflect harder facts than the other ones. Therefore, at least some variation of softness is called for. Again some values in the input hierarchy must be modified and the STRATA algorithm must analyse the hierarchy once more.

After all these four checks have produced satisfying results, the normalized hierarchy in connec- tion with indicators for the information quality is ready to be used, since it now reflects the current strategic situation of the company.

Testing STRATA

The test design

The purpose of the laboratory experiment to be reported here was only to simulate a phase in the STRATA procedure, in which a specific hierarchy

already has been agreed upon. This hierarchy (elements, but no values) has been constructed by a small number of students and faculty so that it was able to work with a short Business Policy case study.

The experiment has been run with 43 students, mostly from the area of Business Administration; they had, from 1 to 9 semester, academic experience; some had also work experience. None of the test persons knew anything about contents, aim, or procedure of the test, nor have they been familiar with any information about STRATA. The experiment took about 90 minutes. No team effort was intended, which means, all test persons worked completely on their own. After about 10 minutes of instructions concerning the kind of assessments STRATA calls for, they moved on to two warm-up exercises (which served also as statistical controls) and then to the Business Policy case. To each element of the hierarchy a one-sentence descrip- tion was attached, which gave a slight impression of the common strategic management interpretation. The hierarchy itself is shown (translated from German) in Figure 7.

The test persons had been divided into three groups: Two groups received test-booklets, which enabled them only to assign values to selected variables, which means that one group worked top-down, the other one bot tom-up; the persons in the third group had the opportunity to answer quasi-simultaneously by working on one single paper.

OVERALL STRATEGIC SITUATION

INTERNAL EXTERNAL STRATEGIC STRATEGIC SITUATION SITUATION

IMMATERIAL ORGANIZATIONAL ECONOMIC NON-ECONOMIC ASSETS CAPITAL STRUCTURE ASPECTS ASPECTS

H U M A ~ M A N P O ~ LEGISLATIVE SOCIO- RESOURCES TECHNOLOGY AVAILABILITY RESOURCES MARKET ASPECTS CULTURAL

STATE FLEXIBILITY STATE FLEXIBILITY COMPETITION AVAILABILITY COMPETITION SIZE & QUALITY

Figure 7. Example for a STRATA hierarchy


Table 1 Differences between input hierarchy and output hierarchy

175

Aggregation DIFF

normalized non-normalized

average max. min. average max. min.

From next lower level 0.087 0.04 0.17 0.135 0.06 0.21

From lowest level 0.094 0.04 0.16 0.147 0.07 0.25

The test results

As to the consistency of aggregation we wanted to find out the differences DIFF between the test persons' aggregation and STRATA'S aggregation. DIVE was computed, according to the regular output of STRATA, a s the difference between the values of both elements divided by the number of fuzzy sets per element (five). The maximum value therefore is 0.4 for the normalized aggregation, and 1.0 for the non-normalized aggregation, which STRATA provides as additional output. As men- tioned before, we compare each element aggregated by the test person once with STRATA'S aggregation from the next lower level and once with STRATA'S aggregation from the lowest level (see Figure 4).

But it is important to notice that an outcome in which both aggregations are identical would be as valueless as an outcome where both aggregations differ completely. In the first case STRATA does not tell the researcher anything, in the latter case STRATA has too much a mind of its own.

Table 1 gives the average difference between the input hierarchies and STRATA'S aggregations; it also shows DIFF for the test persons who were closest and farest to STRATA as well as the average over all 43 persons.

From Table I we can see that some (not all) test persons worked similar as STRATA. Also DIVE turned out rather small, despite the fact that the test persons had only 17 discrete steps to choose (yielding margins of 0.058) while STRATA aggregated into a continuous number-space.

DIFF becomes smaller when the number of semesters increases ( r = - 0 . 3 5 , s=0 .01) , which means that advanced students (and probably even more practitioners) are closest to the STRATA

suggestions. Several factors affected parts of the aggregation

in different ways, which leads the way to a possible team approach. To give some of the specifics of our experiments: - Students with work experience had a surprising high difference in the aggregation which produces the market assessment, which derives from the fact that they considered one subelement (e.g. driving force) missing on the lower level but implicitly integrated in the aggregated element (r = 45, s = 0.001). - Advanced students had a rather low difference with the part dealing with the evaluation of the technology (r -- - 0.41, s = 0.003). - The fictive case had been made look like (at least) one specific German company. Students who believed to know the company brought in additional information, which resulted in a more cons i s ten t p ic ture ; especial ly the supply aspec ts - - impor tan t for this company- -were aggregated similar to STRATA (r = --0.45, s ---- 0.002).

The direction of filling-out plays an important role: The t o p - d o w n approach yields more STRATA-like aggregations than the b o t t o m - u p approach (Table 2). One possible explanation is an effect, according to which the sub-elements are assessed similarly as the upper element, which means that the top-down approach produces slightly more similar curves. Because of this, the b o t t o m - u p approach is highly recommended in dealing with STRATA, since the forces in the

Table 2 Influence on difference and softness

DIFF (normalized) Softness

next lower level lowest level

T o p - d o w n 0.081 0.090 46% Bo t tom-up 0.092 0.095 37% Simultaneous 0.088 0.098 42%

All 43 0.087 0.094 41%

176 C Scholz / Method for strategic analysis of complex systems

top-down approach towards similarities through imitation contradict the heuristic intention of STRATA.

The variable 'softness' reveals a second point against the top-down approach for assessments of complex systems; 'softness' according to STRATA ranges from 0%, when one fuzzy set achieves the degree of membership 1.0 (Figure 3, Example A), to 100%, when all fuzzy sets have the same degree of membership (Figure 3, Example C): The data from Table 2 suggest that top-down assessments produce statements which are softer (fuzzier) than in bo t tom-up assessments. The rea- son for this effect is that, when the manager works his way top-down, the reality he has to assess appears rather unspecific since his understanding of the involved elements is smaller than in bottom-up assessments, in which he knows at least a little about the elements to be aggregated.

To sketch another result of the experiments with STRATA: The test persons showed rather dis- tinctly different attitudes towards the way of ex- pressing their perceived softness (fuzzyness): - The average ranges from persons with 18% to persons with 61%, still for the Business Policy case. This means that some test persons considered the described situation extremely less soft than other test persons. Keeping in mind the purpose of STRATA as a heuristic device, this outcome must be considered desirable, since it indicates the sensitiv- ity of STRATA to the perceived quality of information. - Also important is the variety of used softness (as standard deviation to average softness); it ranges from 5 to 30. Usually a large variety of used softness is desirable or a person assessing a strategic system, since the variety of used softness reflects the variety of the quality of information in the reality. This could mean that some persons are a little more able to work with STRATA in the intended way than the other ones; but it definitely shows that STRATA reacts quite sensitively to different users, which again must be considered desirable.

Only a small portion of the complete statistical analysis (included in [7]) is presented here. All results together indicate that STRATA, with its operators TAU and SIGMA as well as with suggested procedures for analysis, is: - valid as a descriptive tool, since it comes close to the human aggregations, and

- suitable as a prescriptive tool, since it produces meaningful and sensitive results.

Therefore, even though further research is needed especially with respect to different types of persons dealing with STRATA, the results of the experiments must be considered promising, independently from the limitations of a laboratory test-design.

A p p l i c a t i o n s for STRATA

STRATA may be used in several different ways. To name a few:

Individual hierarchy

One single manager or researcher interacts with the computer and constructs step-by-step the searched-for picture of his own cognitive structure. In this case, the basic procedure as presented above will be followed.

Collective hierarchy

The basic procedure will also be followed when a group of managers or researchers aims at their conjoint assessment. In this case, the group agrees on one input hierarchy; after the STRATA'S output is received, the complete group discusses the results according to Figure 6 and then agrees on one corrected input hierarchy.

Delphi-like procedure

Again a group of persons is involved. But this time everyone enters his own input hierarchy and receives his specific output hierarchy plus average values over the assessments of the other persons. Then he may modify his assessment not only according to the basic procedure (Figure 6) but also by considering the data reflecting the assessments of the other planners. In addition to this, personal communications between the different persons may be provided; but nevertheless always each planner enters for each round his own values and weights until the assessments converge.

Merging of partml assessments

The three applications above had one thing in common: structure, values, and weights, all are to

C. Scholz / Method for strategic analysis of complex systems 177

be determined. But after once the hierarchy is agreed upon, in the future often only the bottom level needs to be assessed; starting from this, the complete hierarchy can be built up by STRATA. This means also that independent researchers can make partial judgements and STRATA provides for the synthesis.

rather the individual who does the analysis: STRATA evaluates him or her not only with respect to the 'correct' judgement, but also with respect to internal consistency, to his dealing with fuzzy, soft information and to his ability to differentiate in his judgements.

Strategic actions

Until now we assessed only the current situa- tions of the company under investigation. But it is also possible to construct hierarchies each repre- senting a different point of time: After one assessment of the strategic situation which describes the current position has been made, it may be compared with a second hierarchy; this hierarchy which reflects a desired situation is also developed with STRATA and therefore consistent as well as feasible. The comparison of both hierarchies then may lead to the definition of strategic actions.

Non-strategic applications

STRATA is not restricted to strategic problems, even though its characteristics are tuned into this direction. It may also be used, for instance, as part of an Assessment Center, known from human resource management. For this application, STRATA does not intend to assess a specific situation, but

References

[1] Aguilar, F.J., Scanning the Business Environment, Macmil- lan, New York, 1967.

[2] Laszlo, E., Introduction to Systems Philosophy, Gorden and Breach, New York-London-Paris, 1972.

[3] Porter, M.E., Competitive Strategy, Free Press, New York-London, 1980.

[4] Scholz, C., Betriebskybernetische Hierarchiemethodik, Lang, Frankfurt-Bern, 1981.

[5] Scholz, C., "Aufbau hierarchischer Kontrollsysteme mit PYRAMID", in: R. Pfeiffer, H. Lindner eds., Syste~ntheorie und Kybernetik in Wirtschaft und Verwaltung, Duncker & Humblot, Berlin 1982, 263-281.

[6] Scholz, C., "The architecture of hiearchy", Kybernetes 11 (1982) 175-181.

[7] Scholz, C. "Gedanken zur Unsch~fe", Research Report 1985, forthcoming.

[8] Zadeh, L.A., "Fuzzy sets", Information and Control 8 (1965) 338-353.

[9] Zimmermann, H.-J., and Zysno, P., "Latent connectives in human decision making", Fuzzy Sets and Systems 4 (1980) 37-51.

[10] Zimmermann, H.-J., and Zysno, P. "Ein hierarchisches Bewertungssystem far die Kreditwiardigkeitsp~fung im Konsumentenkreditgesch'aft", Die Betriebswirtschaft 42 (1982) 403-417.

Strata — A method for strategic analysis of complex systems

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