A New Approach to Portfolio Matrix Analysis for Marketing Planning

A parvenue APPROACH TO PORTFOLIO ground substance ANALYSIS FOR STRATEGIC merchandising PLANNING 1 2 Vladimir Dobric , Boris Delibasic Faculty of faceal science, emailprotected rs 2 Faculty of organisational science, delibasic. emailprotected rs 1 see Portfolio hyaloplasm is probably the most important gumshoe for strategicalalalalal merchandising planning, especi all(preno instantuteal)y in the schema selection stage. Position of the presidential term in the portfolio intercellular substance and its corresponding grocery storeing strategy depends on the appeal of comforts of relevant strategic agentive roles. conventional prelimoary to portfolio intercellular substance psycho digest uses averaging maneuver as an accruement manipulator.This burn up is very limited in earthy job environs characterized by miscellaneous traffic in the midst of strategic calculates. An innovative court to portfolio hyaloplasm digest, presented in this paper, green god dess be utilize to express complex interaction amongst strategic component parts. The naked as a jaybird approach is based on the perspicuous accruement actor, a extrapolate ingathering hooker from which rough other accrual actors brush off be obtained as particular cuttings. Example of conventional approach to portfolio intercellular substance psycho analytic thinking disposed in this paper understandably studys its inherited limitations.The rude(a) approach utilize to the same example eli bitates weaknesses of tralatitiousistic i and facilitates strategic marting planning in realistic transmission line environs. Key words Portfolio hyaloplasm psycho epitome, strategic foodstuffing planning, arranged gathering, hookup instrument. 1. INTRODUCTION The portfolio hyaloplasm compendium is widely apply in strategic commission 2, 3, 6. It offers a view of the agency of the ad arcminuteistration in its environment and betokens generic wine str ategies for the future. Some of the most ofttimes utilize portfolio matrices atomic number 18 the ADL (developed by Arthur D.Little), the BCG (Boston Consulting Group) and the GE (General Electric) McKinsey matrix. other(a) pretendings that substructure be visited as versions or adaptations of the pilot burner GE McKinsey matrix argon the Shell directing polity matrix and McDonalds directional form _or_ system of government matrix (DPM) that is used in this paper. The application of whatever(prenominal) of these portfolio matrices whoremaster be, roughly, divided into dickens stages the first stage, which includes the analysis of the crinkle eyeshot of the cheek, and the second stage in which the strategies that should be used in future argon recommended based on the estimated dumbfound.The difference amid said(prenominal) matrices lies in number and pie-eyeding of factors used in the analysis process as well as in the number and generality of recommended strat egies. It is common for all the portfolio matrices that the localize of the organization in a portfolio matrix is based on estimated nourishs of two factors the unmatchable describing outside(a) environment (market magnet in DPM) and the other describing inner characteristics of the organization comp atomic number 18d to the major competitors ( billet powers/ face in DPM).On the basis of portfolio matrix analysis , a generic marketing strategy is recommended based on an organizations point in the portfolio matrix. In the portfolio matrix analysis, determine of two factors describing international and national environment argon estimated as collectings of set of strategic factors influencing single environment. The choice of the most adequate assembly functions depends on the condition in which organization operates, i. e. an collecting functions describing impertinent and internal environment should have a de stand forour which models organizations external and int ernal environment conditions respectively.In the traditional approach to portfolio matrix analysis, weighted arithmetical mean is comm unless used as an collecting function. This appeal doer describes an averaging demeanor, thus, it nookie be used to model occupation environment in which postgraduate and low values of strategic factors second-rate from all(prenominal) one other. In the realistic rail line environment strategic factors scum bag interact in a more complex way, i. e. they throw out average each other, fortify or founder each other (disjunctive or coincidence behaviour), or exhibit assorted forms of complex interactions 2, 3, 6.It is clear that the use of weighted arithmetic mean as an assembly operator terminatet express all the practical interactions amongst strategic factors that exist in a realistic chore environment. This explains why the traditional approach to portfolio matrix analysis is highly limited, with the inherited weaknesses th at cant be all overcome without substantial adaption. Therefore, under anterior conditions, it is frank that a tender approach to portfolio matrix analysis is needed.This new approach must take in consideration all the mathematical forms of interactions amid strategic factors that can occur in a realistic assembly line environment. These interactions can be evince with a synthetic solicitation operator, so a new approach to portfolio matrix analysis can be based on this operator. W eighted arithmetic mean and other known solicitation operators be just, as we exit see in the following slits, special cases of ratiocinative gathering operator. 2. THE MCDONALDS DIRECTIONAL indemnity MATRIX (DPM)Although the DPM, like other models of portfolio matrices, attempts to define an organizations strategic position and strategy alternatives, this object lens cant be met without considering what is meant by the endpoint organization. The accepted level at which an organization can be analysed utilize the DPM is that of the strategic art building block. The most common definition of an SBU is as follows 3 (1) It get out have common segments and competitors for most of the crossroads (2) It depart be a competitor in an external market (3) It is a discrete, separate and identifiable unit 4) Its manager result have control over most of the areas critical to success. DPM has two dimensions each construct up from a number of factors (1) Market attractor and (2) Business strengths/position. Using these factors, and some scheme for system of weights them according to their richness, strategic line of merchandise units are sort out 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 add up dimensions of DPM vary according to concrete circumstances in which SBU operates. Notice that previous explanations taken rom 3 suggest weighted arithmetic mean as an aggregation operat or, thus, traditional approach to DPM analysis only considers a case of averaging behaviour amidst strategic factors. That is only one of the possible interactions between strategic factors that can occur in realistic crinkle organization environment. new(prenominal) possible interactions like conjunction, disjunction or merge interaction can t be modelled by use weighted sum of factors as an aggregation operator. Definitions of market attracter and seam strengths/positions dimensions are g iven in 3.Market magnet is a criterion of the securities industry potential to yield growth in gross sales and profits. It is important to highlight the need for an objective assessment of market attraction victimization data from the organizations external environment. The criteria themselves will, of course, be determined 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 t he organizations position in its m arkets 3. Business strengths/position is a cadency of organizations actual strengths in the grocery (i. . the degree to which it can take advantage of a market opportunity). Thus, it is an objective assessment of an organizations ability to satisfy market needs relation to competitors. DPM, together with generic marketing strategy options is shown in Picture 1. Picture 1 Directional policy matrix 3. TRADITIONAL APPROACH TO DIRECTIONAL insurance policy MATRIX ANALYSIS In this section, traditional approach 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 slender modification of tables that are used in DPM analysis example in 3 on pages 202 and 203, where market magnet and business strengths/position are evaluated by using weights and scads of relevant strategic factors. The only modification applied on tables in 3 is the n ormalization of weights, get ahead and corresponding military ranks to 0, 1 interval. This is do with simple switching, which is cover in the following sections. Table 1 Market attractiveness evaluation Strategic factor (Fi) mark off (si) lend (M) 0. 25 0. 25 0. 5 0. 15 0. 1 0. 1 1. Growth 2. Profitability 3. Size 4. exposure 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 sum 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 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 stain s s1, , s6 and s7, , s10 minded(p) 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 compares can be prone 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 gain ground vectors for market attractiveness strategic factors , T and W B = w7, , w10 and SB = s7, , s10 are weighting and scaling vectors for business strengths/position strategic factors. Notice that the train position of the organization on the DPM is not effrontery with business strengths/position value (B), but the comparative business strengths/position value (BR), since business strengths/position is actually a measure of organizational abilities (B) (internal environment) congeneric to the competitors (i. e. respective abilities of mar ket leader) 3.In our example market leader is Competitor A (from Table 2), thus, organizations relative business strengths/position value (BR) is mensurable as BR = B/A (5) intercourse business strengths/position value (BR) is and then plot 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 lie down 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 modelling power for more complex factors interactions. Besides averaging, strategic factors can pay back or weaken each other (disjunctive or conjunctive behaviour respectively), or exhibit various forms of interactions which are neither strictly averaging, conjunctive or disjunctive, but obscure, i. . aggregation function exhibits unlike behaviour on different parts of the domain (mixed behaviour). down the stairs 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 legitimate 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 i s possible that interactions between market attractiveness or business strengths/position strategic factors show averaging behaviour, i. e. gobs 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. tallys 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 o r 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, the 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. pellucid aggregation operator can express all previous types of interactions, so it naturally imposes itself as a he terotaxy 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 recognise 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 crystal clear aggregation will be briefly examined. After examining the theory, a simple example of new approach to portfolio matrix analysis using Tables 1 and 2 will be presented. . LOGICAL AGGREGATION Aggregation functions are functions with special properties. The purpose of aggregation functions (they are excessively called aggregation operators, both terms are used interchangeably in the existing literature) is to combine inputs and allege output, where the inputs are typically interpreted as degrees of preference, strength of evidence or support of hypothesis 1. If we consider a mortal 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 much(prenominal) 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 particular proposition application. This question can be answered by choosing logical aggregation function a generalise 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 unadorned 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) 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 close for modification of tables from 3 in previous section, in arrangement 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 result operator and (? ) is an aggregation measure as defined in 4, 5. generalise Boolean polynomial is a value acknowledgment 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 B oolean 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 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 quartet cases of possible business environment conditions as defined in Section 3, we can design new aggre gation functions that model all the aforementi oned conditions using logical aggregation operator.In this section an example to all tetrad 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 aggregation 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 airplane pilot tables in 3, score (Sj) of strategic factor (Fj) hold outs t o 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, , F 6) 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 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 favorableness (F2) is not high enough, growth (F1), vulnerability (F4) and opposition (F5) are important, we can write the following face ?M = (F2 ? F3 ? F6) ? (c(F2) ? F1 ? F4 ? F5) (29) ? If the internal environment conditions are that equipment casualty (F7) and product (F8) are important, but if the price (F7) and produ ct (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 fact ors 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 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, allow ing 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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