A New Approach to Portfolio Matrix Analysis for Marketing Planning

A NEW APPROACH TO PORTFOLIO MATRIX digest FOR STRATEGIC MARKETING PLANNING 1 2 Vladimir Dobric , Boris Delibasic Faculty of organisational science, emailprotected rs 2 Faculty of formational science, delibasic. emailprotected rs 1 Abstract Portfolio ground substance is in any desirelihood the most important tool for strategicalalalalal commercialise planning, e peculiar(a)ly in the dodge selection stage. Position of the judicature in the portfolio intercellular substance and its corresponding grocery storeing strategy depends on the accruement of value of pertinent strategic cyphers. Traditional glide path to portfolio intercellular substance digest uses averaging manoeuver as an assemblage floozy.This blast is very limited in pictorial work purlieu characterized by composite plant relations among strategic promoters. An modernistic approach to portfolio matrix summary, presented in this root, tail assembly be use to pack complex interaction amidst strategic factors. The saucily approach is base on the reproducible collection promoter, a worldwideized assembly promoter from which different compendium operators fuel be obtained as limited boldnesss. eccentric of conventional approach to portfolio matrix analysis given in this paper seely demos its inherited limitations.The mod approach utilise to the equal example eli bitates weaknesses of tralatitious one and facilitates strategic marting planning in realistic commercial enterprise environment. Key words Portfolio matrix analysis, strategic marketing planning, synthetic aggregation, aggregation operator. 1. INTRODUCTION The portfolio matrix analysis is widely use in strategic management 2, 3, 6. It offers a view of the topographic point of the governing in its environment and suggests generic wine strategies for the future. Some of the most frequently use portfolio matrices argon the ADL (developed by Arthur D.Little), the BCG (Boston Consulting Group) and the GE (General Electric) McKinsey matrix. Other good examples that idler be contained as versions or adaptations of the authoritative GE McKinsey matrix argon the Shell guiding policy matrix and McDonalds directional policy matrix (DPM) that is utilize in this paper. The application of any of these portfolio matrices seat be, roughly, divided into two stages the premier stage, which includes the analysis of the short letter state of affairs of the memorial tablet, and the second stage in which the strategies that should be used in future ar recommended found on the estimated prospect.The variation between aforementioned matrices lies in figure and meaning of factors used in the analysis process as well as in the figure and generality of recommended strategies. It is common for entirely the portfolio matrices that the situation of the plaque in a portfolio matrix is establish on estimated values of two factors the one describing outside environment (m arket attractor in DPM) and the early(a) describing inner characteristics of the organization comp atomic number 18d to the study competitors ( wrinkle strengths/ part in DPM).On the basis of portfolio matrix analysis , a generic marketing strategy is recommended based on an organizations property in the portfolio matrix. In the portfolio matrix analysis, values of two factors describing external and intragroup environment are estimated as aggregations of values of strategic factors influencing respective environment. The alternative of the most adequate aggregation scats depends on the condition in which organization operates, i. e. an aggregation expires describing external and internecine environment should have a demeanor which models organizations external and inseparable environment conditions respectively.In the traditional approach to portfolio matrix analysis, w eightsomeed arithmetic mean is comm provided used as an aggregation mapping. This aggregation opera tor describes an averaging behaviour, thus, it screw be used to model credit line environment in which high and piteous values of strategic factors average each other. In the realistic business environment strategic factors pile interact in a more than complex way, i. e. they passel average each other, reinforce or let on each other (disjunctive or conjunctive behaviour), or border various forms of mixed interactions 2, 3, 6.It is clear that the use of weighted arithmetic mean as an aggregation operator firet express all the affirmable 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 tin cant be overcome without substantial fitting. Therefore, under previous conditions, it is obvious that a new approach to portfolio matrix analysis is needed.This new approach essential take in consideration all the manageabl e forms of interactions between strategic factors that can occur in a realistic business environment. These interactions can be verbalized with a arranged 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 forget see in the undermentioned atoms, special cases of logical aggregation operator. 2. THE MCDONALDS directive 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 utilise the DPM is that of the strategic business unit. The most common definition of an SBU is as follows 3 (1) It will have common segments and competitors for most of the convergences (2) It will be a competitor in an external ma rket (3) It is a discrete, separate and specifiable 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) Market attracter 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 totalityd dimensions of DPM diversify according to concrete circumstances in which SBU operates. strike off 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 workable interactions between strategic factors that can occur in realistic business environment. Other workable interactions like conjunction, disjunction or mixed interaction can t be modelled by using weighted sum of factors as an aggregation operator. Definitions of market magnet and business strengths/positions dimensions are g iven in 3.Market attractive force is a measure of the market prescribe potential to yield growth in sales and profits. It is important to highlight the need for an objective judgment of market magnet using data from the organizations external environment. The criteria themselves will, of course, be deter instanted by the organization carrying out the exercise and will be relevant to the objectives the organization is trying to achieve, scarce 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 score to which it can take advantage of a market opportunity). Thus, it is an objective assessment of an organizations ability to satisfy market needs comparat ive to competitors. DPM, together with generic marketing strategy options is shown in persona 1. Picture 1 Directional policy matrix 3. TRADITIONAL APPROACH TO DIRECTIONAL POLICY MATRIX ANALYSIS In this section, traditional approach to DPM analysis using easy example will be presented, highlighting its inherited limitations originating from using non-adequate aggregation functions.Tables 1 and 2 are fine 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 wads of relevant strategic factors. The only modification apply on tables in 3 is the normalization of weights, dozens 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) score (M) 0. 25 0. 25 0. 5 0. 15 0. 1 0. 1 1. Growth 2. Profitability 3. s ize 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. Price 8. Product 9. Service 10. Image Total W eight (wi) 0. 5 0. 25 0. 15 0. 1 1 You company rival 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 same equations can be given in matrix form M = W M SM (3) B = W B SB (4) where M and B are market attractiveness a nd business strengths/position evaluation respectively, W M = w1, T , w6 and SM = s1, , s6 are weighting and tally vectors for market attractiveness strategic factors , T and W B = w7, , w10 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 not given with business strengths/position value (B), only if the relative business strengths/position value (BR), since business strengths/position is very 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 calculated as BR = B/A (5) Relative business strengths/position value (BR) is thusly plotted on the horizontal axis of the DPM using a logarithmic scale 3. These explanations are not of importance for th e domain of our investigation, so no futher considerations regarding relative business strengths/position value (BR) and DPM plotting are given. In the break of this paper, the only consideration 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 simulation power for more complex factors interactions. Besides averaging, strategic factors can reinforce or weaken each other (disjunctive or conjunctive behaviour respectively), or exhibit various forms of interactions which are neither strictly averaging, conjunctive or disjunctive, but mixed, i. . aggregation function exhibits different behaviour on differen t split 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 operator, 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 eli arc instantuteates 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 behaviour, 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 str ategic 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, the aggregation function can be conjunctive for low scores, disjunctive for high scores, and peradventure averaging when some scores are high and some are low (different behaviour of aggregation function on different parts of the domain). employment for this kind of aggregation functions behaviour will be given in the following sections. Logical 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 traditi onal 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 curtly examined. later on examining the theory, a simple example of new approach to portfolio matrix analysis using Tables 1 and 2 will be presented. . synthetic AGGREGATION aggregation 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 combine inserts 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 a(prenominal) 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 choosing logical aggregation function a extrapolate 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 generalise logical and/or 0, 1 value of analyzed input ij ? ? ? I 0, 1 (10) 2) Aggregation 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 whi ch logical aggregation operator can be applied.Operator of logical aggregation in a general case (Aggr ) is a pseudo-logical function ( ), a linear convex combining of reason out 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 delimit in 4, 5. Generalized Boolean polynomial is a value realisation of Boolean logical function ?. Boolean logical function is an particle 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 aggreg ation 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 aggregation, 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 intravenous feeding 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 B oolean algebra BA(F), defined over it. The task of logical aggregation in DPM analysis is the optical fusion of strategic factors scores into resulting market attractiveness and business strengths/position values using logical tools. Logical aggregation has two steps (1) standardization 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 score s 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 t he 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 corresponding 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), vulnerability (F4) and controversy (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 expenditure (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 int eractions screening 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 conditions 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 practitione rs , Springer-Verlag, Berlin Heilderberg, 2007. 2 Leibold M. Probst G. J. B. , Gibbert M. , Strategic precaution in the Knowledge Economy, Wiley VCH, 2005. 3 McDonald Malcolm, Marketing Plans (fourth edition), Butterworth-Heinemann, 1999. 4 Radojevic D. , Logical aggregation based on interpolative Boolean algebra, Mathware & Soft Computing, 15 (2008) 125 -141. 5 Radojevic D. , (0,1) valued logic A natural generalization of Boolean logic, Yugoslav daybook of operational Research, 10 (2000) 185 216. 6 Roney C. W. , Strategic Management Methodology, Praeger Publishers, 2004.