A New Approach to Portfolio Matrix Analysis for Marketing Planning

A NEW APPROACH TO PORTFOLIO MATRIX ANALYSIS FOR STRATEGIC MARKETING PLANNING 1 2 Vladimir Dobric , Boris Delibasic capacity of constitutional science, emailprotected rs 2 Faculty of validational science, delibasic. emailprotected rs 1 Abstract Portfolio hyaloplasm is probably the most important tool for strategical foodstuffing planning, especi ally in the dodge selection stage. Position of the organization in the portfolio matrix and its corresponding marketing strategy depends on the compendium of cherishs of relevant strategic factors. Traditional snuggle to portfolio matrix analysis uses averaging start as an gathering operator.This cost is very limited in realistic line of products environment characterized by complex relations among strategic factors. An innovative approach to portfolio matrix analysis, presented in this paper, flowerpot be used to express complex interaction amidst strategic factors. The new approach is based on the ratiocinative ingathering operator, a generalized collection operator from which other aggregation operators can be obtained as special baptistrys. Example of tralatitious approach to portfolio matrix analysis given in this paper all the way projects its inherited limitations.The new approach applied to the kindred example eliminates weaknesses of traditional one and facilitates strategic marketing planning in realistic avocation environment. Key words Portfolio matrix analysis, strategic marketing planning, logical aggregation, aggregation operator. 1. INTRODUCTION The portfolio matrix analysis is widely used in strategic management 2, 3, 6. It offers a view of the part of the organization in its environment and suggests generic strategies for the incoming. Some of the most frequently used portfolio matrices are the ADL (developed by Arthur D.Little), the BCG (Boston Consulting Group) and the GE (General Electric) McKinsey matrix. Other models that can be considered as versions or adaptations of the original GE McKinsey matrix are the Shell directional policy matrix and McDonalds directional policy matrix (DPM) that is used in this paper. The lotion of any of these portfolio matrices can be, roughly, divided into dickens stages the first stage, which includes the analysis of the barter prepare of the organization, and the second stage in which the strategies that should be used in future are recommended based on the estimated target.The difference in the midst of aforementioned matrices lies in number and meaning of factors used in the analysis process as wellspring as in the number and generality of recommended strategies. It is common for all the portfolio matrices that the stick of the organization in a portfolio matrix is based on estimated determine of ii factors the one describing external environment (market attractiveness in DPM) and the other describing inner characteristics of the organization compared to the major competitors ( demarcation strengths/ congeal in DPM).On the basis of portfolio matrix analysis , a generic marketing strategy is recommended based on an organizations position in the portfolio matrix. In the portfolio matrix analysis, values of two factors describing external and interior environment are estimated as aggregations of values of strategic factors influencing respective environment. The choice of the most adequate aggregation divisions depends on the condition in which organization operates, i. e. an aggregation functions describing external and inner environment should have a behaviour which models organizations external and internal environment conditions respectively.In the traditional approach to portfolio matrix analysis, weight down arithmetic mean is comm scarcely used as an aggregation function. This aggregation operator describes an averaging behaviour, thus, it can be used to model bloodline environment in which high and low values of strategic factors average each other. In the realistic bu siness environment strategic factors can interact in a more complex port, i. e. they can average each other, reinforce or weaken each other (disjunctive or conjunction behaviour), or exhibit conglomerate forms of mixed interactions 2, 3, 6.It is clear that the use of burthen arithmetic mean as an aggregation operator cant express all the feasible interactions between strategic factors that exist in a realistic business environment. This explains why the traditional approach to portfolio matrix analysis is highly limited, with the inherited weaknesses that cant be overcome without substantial modification. Therefore, under previous conditions, it is obvious that a new approach to portfolio matrix analysis is needed.This new approach must dribble in consideration all the viable forms of interactions between strategic factors that can occur in a realistic business environment. These interactions can be explicit with a logical aggregation operator, so a new approach to portfolio matrix analysis can be based on this operator. W eighted arithmetic mean and other known aggregation operators are just, as we will see in the following sections, special cases of logical aggregation operator. 2. THE MCDONALDS directional POLICY MATRIX (DPM)Although the DPM, like other models of portfolio matrices, attempts to define an organizations strategic position and strategy alternatives, this objective cant be met without considering what is meant by the term organization. The accepted level at which an organization can be analysed using the DPM is that of the strategic business unit. The most common comment of an SBU is as follows 3 (1) It will have common segments and competitors for most of the products (2) It will be a competitor in an external market (3) It is a discrete, separate and recognizable unit 4) Its manager will have control over most of the areas critical to success. DPM has two dimensions each built up from a number of factors (1) securities industry at tractiveness and (2) Business strengths/position. Using these factors, and some scheme for charge them according to their importance, strategic business units are classified into one of nine cells in a 3 X3 matrix. Each cell is connected to a generic strategy recommended by the DPM. Factors used to form aggregated dimensions of DPM vary according to concrete share in which SBU operates. remonstrate that previous explanations taken rom 3 suggest weighted arithmetic mean as an aggregation operator, thus, traditional approach to DPM analysis only considers a case of averaging behaviour between strategic factors. That is only one of the possible interactions between strategic factors that can occur in realistic business environment. Other possible interactions like conjunction, disjunction or mixed interaction can t be modelled by using weighted sum of factors as an aggregation operator. Definitions of market attractiveness and business strengths/positions dimensions are g iven in 3. Market attractiveness is a measure of the market ass potential to yield growth in sales and profits. It is important to highlight the need for an objective assessment of market attractiveness using data from the organizations external environment. The criteria themselves will, of course, be inflexible by the organization carrying out the exercise and will be relevant to the objectives the organization is trying to achieve, but they should be independent of the organizations position in its m arkets 3. Business strengths/position is a measure of organizations actual strengths in the marketplace (i. . the degree to which it can take utility of a market opportunity). Thus, it is an objective assessment of an organizations ability to satisfy market needs congress to competitors. DPM, together with generic marketing strategy options is groundn in Picture 1. Picture 1 Directional policy matrix 3. TRADITIONAL APPROACH TO DIRECTIONAL POLICY MATRIX ANALYSIS In this section, traditional a pproach to DPM analysis using simple example will be presented, highlighting its inherited limitations originating from using non-adequate aggregation functions.Tables 1 and 2 are slight modification of tables that are used in DPM analysis example in 3 on pages 202 and 203, where market attractiveness and business strengths/position are evaluated by using weights and tons of relevant strategic factors. The only modification applied on tables in 3 is the normalization of weights, scores and corresponding evaluations to 0, 1 interval. This is done with simple transformation, which is cover in the following sections. Table 1 Market attractiveness evaluation Strategic factor (Fi) Score (si) numerate (M) 0. 25 0. 25 0. 5 0. 15 0. 1 0. 1 1. Growth 2. Profitability 3. Size 4. Vulnerability 5. Competition 6. Cyclicality W eight (wi) 0. 6 0. 9 0. 6 0. 5 0. 8 0. 25 0. 15 0. 225 0. 09 0. 075 0. 08 0. 25 Total 1 0. 645 Table 2 Business strengths/position evaluation Strategic factor (Fi) 7. Pr ice 8. Product 9. Service 10. count on Total W eight (wi) 0. 5 0. 25 0. 15 0. 1 1 You company Competitor A Competitor C Score (si) Total (B) Score Total (A) Score Total (C) 0. 5 0. 6 0. 8 0. 6 0. 25 0. 15 0. 12 0. 06 0. 6 0. 8 0. 4 0. 5 0. 3 0. 2 0. 06 0. 05 0. 4 1 0. 6 0. 3 0. 2 0. 25 0. 09 0. 03 . 58 0. 61 0. 57 Market attractiveness (M) and business strengths/position (B) are evaluated using weighted arithmetic mean as an aggregation function of scores s1, , s6 and s7, , s10 given for relevant strategic factors F1, , F10 using weights w1, , w10 M = w1 s1 + w2 s2 + w3 s3 + w4 s4 + w5 s5 + w6 s6 = 0. 645 (1) B = w7 s7 + w8 s8 + w9 s9 + w10 s10 = 0. 58 (2) The aforementioned(prenominal) equations can be given in matrix form M = W M SM (3) B = W B SB (4) where M and B are market attractiveness and business strengths/position evaluation respectively, W M = w1, T , w6 and SM = s1, , s6 are weighting and scoring vectors for market attractiveness strategic factors , T and W B = w7, , w 10 and SB = s7, , s10 are weighting and scoring vectors for business strengths/position strategic factors. Notice that the exact position of the organization on the DPM is non given with business strengths/position value (B), but the relative business strengths/position value (BR), since business strengths/position is actually a measure of organizational abilities (B) (internal environment) relative to the competitors (i. e. respective abilities of market leader) 3.In our example market leader is Competitor A (from Table 2), thus, organizations relative business strengths/position value (BR) is careful as BR = B/A (5) Relative business strengths/position value (BR) is then(prenominal) plotted on the horizontal axis of the DPM using a logarithmic scale 3. These explanations are not of importance for the domain of our investigation, so no futher considerations regarding relative business strengths/position value (BR) and DPM plotting are given. In the rest of this paper, the only c onsideration will be given to market attractiveness (M) and business strengths/position (B) evaluation.W eighted arithmetic mean used for an aggregation function assumes that the interactions between strategic factors show averaging behavior, i. e. it is used to model business environment in which values of strategic factors average each other. This is the mayor drawback of traditional DPM analysis. Realistic business environment demands more modelling power for more complex factors interactions. Besides averaging, strategic factors can reinforce or weaken each other (disjunctive or conjunctive behaviour respectively), or exhibit heterogeneous forms of interactions which are neither strictly averaging, conjunctive or disjunctive, but mixed, i. . aggregation function exhibits different behaviour on different parts of the domain (mixed behaviour). Under these circumstances, it is obvious that a new approach to portfolio matrix analysis demands an usage of different aggregation operat or, the one capable of modelling all the possible interactions between strategic factors that can take place in a realistic business environment. The paper presents an approach to portfolio matrix analysis, using logical aggregation operator, which eliminates weaknesses of traditional one. If we return to ur example shown in Tables 1 and 2, we can restate possible business external and internal environment conditions in the following way 1) It is possible that interactions between market attractiveness or business strengths/position strategic factors show averaging behaviour, i. e. scores s1, , s6 or s7, , s10 given to strategic factors F1, , F10 can average each other using weights w1, , w10. In this case market attractiveness and business strengths/position are evaluated as shown in equations (1) and (2) , or in their matrix equivalents (3) and (4). ) It is possible that interactions between market attractiveness or business strengths/position strategic factors show conjunctive be haviour, i. e. scores s1, , s6 or s7, ,s10 given to strategic factors F1, , F10 can weaken each other. In this case market attractiveness and business strengths/position evaluation depends upon the lowest score among the relevant factors M = min(s1, , s6) (6) B = min(s7, , s10) (7) 3) It is possible that interactions between market attractiveness or business strengths/position strategic factors show disjunctive behaviour, i. e. cores s1, , s6 or s7, , s10 given to strategic factors F1, , F10 can reinforce each other. In this case market attractiveness and business strengths/position evaluation depends upon the highest score among the relevant factors M = max(s1, , s6) (8) B = max(s7, , s10) (9) 4) It is possible that interactions between market attractiveness or business strengths/position strategic factors show mixed behaviour. For example, scores s1, ,s6 or s7, ,s10 given to strategic factors F1, , F10 can average, reinforce and weaken each other depending on their values.Thus, t he aggregation function can be conjunctive for low scores, disjunctive for high scores, and perhaps averaging when some scores are high and some are low (different behaviour of aggregation function on different parts of the domain). Example for this kind of aggregation functions behaviour will be given in the following sections. arranged aggregation operator can express all previous types of interactions, so it naturally imposes itself as a replacement to weighted arithmetic mean aggregation operator in the new approach to portfolio matrix analysis.Notice that interactions between strategic factors from organizations external environment (market attractiveness factors) and those from organizations internal environment ( business strengths/position factors) are not recognized in traditional approach to DPM analysis 3. If those interactions can be recognized, they can easily be integrated into the model in the new approach. In the following section basic theory of logical aggregation will be briefly examined. afterward examining the theory, a simple example of new approach to portfolio matrix analysis using Tables 1 and 2 will be presented. . LOGICAL AGGREGATION gathering functions are functions with special properties. The purpose of aggregation functions (they are also called aggregation operators, both terms are used interchangeably in the existing literature) is to accept inputs and produce output, where the inputs are typically interpreted as degrees of preference, strength of evidence or support of hypothesis 1. If we consider a finite set of inputs I = i1, , in, we can aggregate them into single representative value by using infinitely many aggregation functions.They are grouped in various families such as means, triangular norms and conor ms, Choquet and Sugeno integral, uninorms and nullnorms, and many others 1. The question arises how to chose the most suitable aggregation function for a specific application. This question can be answered by choosi ng logical aggregation function a generalized aggregation operator that can be reduced to any other known one. Logical aggregation is an aggregation method that combines inputs and produces output using logical aggregation operator 4, 5.In a general case logical aggregation is carrried out in two distinct steps 1) Normalization of input values which results in a generalized logical and/or 0, 1 value of analyzed input ij ? ? ? I 0, 1 (10) 2) accretion of normalized values of inputs into resulting globaly representative value with a logical aggregation operator n Aggr 0, 1 0, 1 (11) The first step explains the reason for modification of tables from 3 in previous section, in order to obtain Tables 1 and 2 with normalized values of strategic factors scores on which logical aggregation operator can be applied.Operator of logical aggregation in a general case (Aggr ) is a pseudo-logical function ( ), a linear convex combination of generalized Boolean polynomials ( ) 4, 5 Aggr (? i1? , , ? in? ) = (? i1? , , ? in? ) = ? wj? j? (? i1? , , ? in? ) (12) where (? ) is a generalized product operator and (? ) is an aggregation measure as defined in 4, 5. Generalized Boolean polynomial is a value realization of Boolean logical function ?. Boolean logical function is an element of Boolean algebra of inputs ? (i1, , in) ?BA(I), to which corresponds uniquely a generalized Boolean polynomial (? i1? , , ? in? ) as its value 0, 1 0, 1 n (13) Logical aggregation operator depends on the chosen measure of aggregation (? ) and operator of generalized product (? ). By a corresponding choice of the measure of aggregation (? ) and generalized product (? ) the known aggregation operators can be obtained as special cases 4, 5, e. g. for additive aggregation measure (? = ? add) and generalized product (? = min) logical aggregation operator reduces to weighted arithmetic mean Aggradd in (? i1? , , ? in? ) = ? wj (? ij? ) (14) After considering basic theory of logical aggreg ation, we can return to the domain of our investigation. In the following section the new approach to portfolio matrix analysis will be presented thoroughly using the same data from Tables 1 and 2. 5. A NEW APPROACH TO PORTFOLIO MATRIX ANALYSIS If we consider again Tables 1 and 2, and four cases of possible business environment conditions as defined in Section 3, we can design new aggregation functions that model all the aforementi oned conditions using logical aggregation operator.In this section an example to all four types of strategic factors interactions will be given, together with logical functions modeling them. A starting point for the new approach to portfolio matrix anal ysis is a finite set of strategic factors F = F1, , F10 and a Boolean algebra BA(F), defined over it. The task of logical aggregation in DPM analysis is the fusion of strategic factors scores into resulting market attractiveness and business strengths/position values using logical tools. Logical aggregat ion has two steps (1) Normalization of strategic factors scores (score Sj corresponds to factor Fj as its predefined value) ? ? Sj 0, 1 (15) that results in a logical and/or score sj ? 0, 1 of analyzed strategic factor Fj (j = 1.. F). Normalization of scores in S is done with simple transformation. In the original tables in 3, score (Sj) of strategic factor (Fj) belongs to interval 0.. 10, e. g. Strategic factor Growth (F1) has score S1 = 6 in the original table in 3. The normalized score (s1) for this factor (F1) is given in Table 1 with the following equation s1 = 6/10 = 0. 6 (16) The same transformation is applied to the rest of the strategic factors in tables in 3, resulting in Tables 1 and 2. 2) Aggregation of normalized scores s1, , s6 and s7, , s10 of factors F1, , F10 into resulting market attractiveness (M) and business strengths/position (B) values with a logical aggregation operator M = Aggr (s1, , s6) (17) B = Aggr (s7, , s10) (18) Aggregation of scores s1, , s6 and s7, , s10 for strategic factors F1, , F10 is accomplished using generalized Boolean polynomials (? M? ) and (? B? ) Aggr (s1, , s6) = ? M? (s1, , s6) = ? M(F1, , F6)? (19) Aggr (s7, , s10) = ? B? (s7, s10) = ? B(F7, , F10)? (20) Generalized Boolean polynomials ? M? (s1, , s6) and ? B? (s7, , s10) are value realizations of Boolean logical functions ? M(F1, , F6) and ? B(F7, , F10), which belong to Boolean algebra of strategic factors BA(F). Notice that interactions between strategic factors from organizations external environment (market attractiveness factors) and those from organizations internal environment (business strengths/position factors) are not stated in 3. If they exist, they can easily be integrated into the model.Adequate generalized product operator (? ) in the domain of portfolio matrix analysis is min operator (? = min). If we return to the possible business environment conditions stated in Section 3, we can formulate logical functions to express corr esponding types of interactions between the strategic factors 1) If the interactions between market attractiveness or business strengths/position strategic factors show averaging behaviour, then the new approach to portfolio matrix analysis reduces to traditional one, as stated in equations (1) and (2), or matrix equivalents (3) and (4). ) If the interactions between market attractiveness or business strengths/position strategic factors show conjunctive behaviour, they are expressed in the following way ? M = F1 ? F2 ? F3 ? F4 ? F5 ? F6 (21) ?B = F7 ? F8 ? F9 ? F10 (22) Market attractiveness and business strengths/position evaluation are given with corresponding generalized Boolean polynomial (? = and, ? = min) M = Aggrand (s1, , s6) = ? M min B = Aggrand min = F1 ? F2 ? F3 ? F4 ? F5 ? F6 min (s7, , s10) = ? B min min = F7 ? F8 ? F9 ? F10 min(s1, s2, s3, s4, s5, s6) = 0. 25 (23) min (24) = min(s7, s8, s9, s10) = 0. 5 3) If the interactions between market attractiveness or business strengths/position strategic factors show disjunctive behaviour, they are expressed in the following way ? M = F1 ? F2 ? F3 ? F4 ? F5 ? F6 (25) ?B = F7 ? F8 ? F9 ? F10 (26) Market attractiveness and business strengths/position evaluation are given with corresponding generalized Boolean polynomial (? = or, ? = min) M = Aggror (s1, , s6) = ? M min min = F1 ? F2 ? F3 ? F4 ? F5 ? F6 min max(s1, s2, s3, s4, s5, s6) = 0. 9 (27) B = Aggror (s7, , s10) = ? B min min = F7 ? F8 ? F9 ? F10 min = max(s7, s8, s9, s10) = 0. 8 (28) 4) If the interactions between market attractiveness or business strengths/position strategic factors show mixed behaviour (aggregation function exhibits different behaviour on different parts of the domain), they can be modelled with the following logical functions, e. g. realistic external and internal business environment, where strategic factors show mixed behaviour, can be modelled as ?If the external environment conditions are that profitabilty (F2), size (F3) and cyclicality (F6) are important, but if the profitability (F2) is not high enough, growth (F1), exposure (F4) and competition (F5) are important, we can write the following expression ?M = (F2 ? F3 ? F6) ? (c(F2) ? F1 ? F4 ? F5) (29) ? If the internal environment conditions are that impairment (F7) and product (F8) are important, but if the price (F7) and product (F8) are not competitive, service (F9) and image (F10) are important, we can write the following expression ?B = (F7 ? F8) ? (c(F7 ? F8) ?F9 ? F10) (30) Market attractiveness and business strengths/position evaluation, for organizations external and internal environment conditions respectively, are given with corresponding generalized Boolean polynomial (? = min) M = Aggr? (s1, , s6) = ? M = (F2 ? F3 ? F6) ? (c(F2) ? F1 ? F4 ? F5) = = s2 ? s3 ? s6 + (1 s2) ? s1 ? s4 ? s5 s2 ? s3 ? s6 ? (1 s2) ? s1 ? s4 ? s5 = 0. 25 (31) B = Aggr? (s7, , s10) = ? B = (F7 ? F8) ? (c(F7 ? F8) ? F9 ? F10) = = s7 ? s8 + (1 (s7 ? s8)) ? s9 ? s10 s7 ? s8 ? (1 (s7 ? s8)) ? s9 ? s10 = 0. 6 (32) min min min min min minRemember that when plotting the DPM, the exact position of the organization on the business strengths/position axis (horizontal) is calculated using relative business strengths/position value (BR) and logarithmic scale (see equation (5)), for all aforementioned types of strategic factors interactions . 5. CONCLUSION Traditional approach to portfolio matrix analysis uses weighted arithmetic mean as an aggregation function, thus, it can only be used to model business environment in which strategic factors interactions show averaging behavior. This is only one of the four cases of realistic business environment conditions, i. . strategic factors interactions showing conjunction, disjunction or mixed behavior are not covered in the traditional approach. The new approach uses generalized aggregation function operator of logical aggregation. This operator can model all the possible business environment con ditions types of interactions between the strategic factors. This paper shows that traditional approach to portfolio matrix analysis is just a special case of the new one, since the weighted arithmetic mean is actually a special case of logical aggregation operator.Usage of logical aggregation operator in the new approach clearly improves the traditional one, allowing more modeling power for complex relations among the strategic factors. Since the new approach to portfolio matrix analysis covers all four types of strategic factors interactions, it facilitates strategic marketing planning in a realistic business environment. 5. BIBLIOGRAPHY 1 Beliakov G. , Pradera A. , Calvo T. , Aggregation functions A guide for practitioners , Springer-Verlag, Berlin Heilderberg, 2007. 2 Leibold M. Probst G. J. 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