Media selection decision in social system: a fuzzy goal programming approach.

ABSTRACT

Media selection has been a perennial problem with any communication mix and this is more of a resource allocation exercise than anything else. Traditionally, the media researchers use the available forecasting model their long-term experience or intuition to select the media mix for any promotional campaign. This process may not be that scientific and effective all the time. Specifically, when the case considered here is social science based; that of a disintegrating cottage industry in the handloom sector of undivided Ganjam district of Orissa State in India and the available resources is too few. The handloom sector has got its rich cultural heritage and some cross-cultural products have been suggested as a solution to their existing problem. But none of the product design can ever be successful without an adequate positioning theme and promotion is the key ingredient in it. The current paper aims to design an optimal media plan for the cross-cultural product keeping the cultural background of the target consumer in mind. Obviously this involves managerial decision-making and any management decision-making can be viewed as a multi-criteria decision situation with multiple, conflicting and non-commensurable objectives seeking simultaneous solution. Various methodologies have been devised to solve this class of problems viz., vector maximization method, goal programming etc ... But, when the imprecision in the decision variables/ environment is more due to fuzziness than randomness; most of the existing methodologies fail to give satisfactory solutions. Hence, fuzzy sets and fuzzy logic are applied here, specifically with fuzzy goal programming, to provide an implementable solution procedure. Actually, the use of fuzzy goal programming has got added significance when culture is defined in a holistic manner in the consumer society for better differentiation, proper segmentation and effective positioning.

1. INTRODUCTION

Promotional media selection system is nothing but a communication mix so far as modern marketing is concerned. Developing a quality product as demanded by the market, pricing it attractively and making it accessible to the target customers, do not necessarily create a successful marketing system and it may so happen that most of the marketing objectives are not satisfied by it. Marketers need to effectively communicate about their product's status, benefits and attractive advantages over the competitors to the present and potential customers so as to develop a need, convert it to an obsessive positive predisposition and terminate it with sales. The art of generating requisite information and making it available to the right person at the right time in the right format is the key to finding right opportunities and optimally utilizing it to fulfill the marketing objectives. Hence, marketing would be successful only if the communication process between the producer and the consumer is most powerful, active and effective and this is because demand is created with information crossover and again, an inherent human need of cognitive knowledge accumulation is realized with the same information flow. Advertising, personal selling, sales promotion and publicity work as an integrated system of message outflow from producer to consumer as the reason for the development of any positive predisposition of the consumer and finally actual sales of the product i,e., consumer response and feedback on the brand from the market to the producer that act as the message inflow. All these, constitute the important marketing communication system where promotion is nothing but the consumer attitude formulating part of the marketing communication mix and through its various tools, it is aimed at any target segment to create a better response to the desired product.

Media for promotion are the various promotional tools like advertising, sales promotion, public relation and personal selling. These are various devices through which a promotional programme is implemented. The handloom market in the study area is pretty ill developed in terms of not only its traditional production and distribution process and lack of style and modern design, but also in terms of consumer awareness, public relations, advertising and sales promotion. The need of the hour is obviously a modern and developed production system with economy of scale in bulk production and consequently reduced cost of production, an advanced integrated distribution policy with maximum availability of goods to the ultimate consumer at the place of their requirements, and an attractive as well as acceptable (to both marketer and the consumer) pricing system which stands closer to penetration rather than skimming pricing. But the marketing objectives of sustenance, an appropriate income through adequate sales and a better market volume by optimum future growth in terms of consumers, customers, market, profit and return on investment can only be satisfied when the consumer's needs are analyzed, their wants are created, modified and personalized into a possession utility. This can be developed by an integrated promotional system, which obviously looks at cost only at the beginning, but gradually helps positioning the product in the target segment for a long-term achievement of the objectives.

The objectives of the promotional system are never single, but needs to be very unique and unidirectional. There are too many product lines to choose from, different types of promotional tools applicable, too many media vehicles viz., print-media, audio-visual-media, electronic-media, outdoor-media and sales promotional-media etc., to be selected and too many consumer categories based on geographic, demographic, psychographic or behavioral factors interacting and interfering. The basic objectives of a promotional system can be multifarious and multidimensional i.e., maximum reach, maximum frequency of reach, best scheduling, least cost, maximum consumer reliance on the media vehicles and promotional campaigns, minimum consumer dissonance and irritation and maximum convincing ability of the promotional mix so as to achieve the over all marketing objectives, viz., maximum sales, maximum return on investment, maximum future growth and minimum expenses etc.. Hence with so many inter-dependent intervening decision variables interacting, the decision model can only be multicriteria and with such a sensitive area like promotion which appeals directly to the inner self of a consumer (perception, personality, attitude, beliefs and values) to modulate him as per marketers' expectations, there is obviously a heavy influence of consumer's societal culture, marketer's organizational culture, individual's own associated culture and their inter-compatibility. Therefore, to design the optimal media selection system, one has to identify the various categories of consumers with due emphasis on the cultural variables, define their characteristics and then try to make a map with the product categories and the promotional vehicles within the associated resource constraints.

The present study is based on the handloom sector of undivided Ganjam district of Orissa state (India). The consistent failure of the traditional products of the handloom sector of this region in the current market scenario prompted the researchers to suggest a cross-cultural product-mix [Mishra (20000, Mangaraj et al. (2000)]. The precise background of the current study is based on the analysis that the handloom products of any region with all its embedded quality and design represent the culture of that region and culture of any region is truly reflected on the anatomy of the handloom product of the same region. So, each place provides a new culture and a new range of products. Their cultural mix can be created by picking up the best and most marketable designs from each type of product, cross-cultural product designs can be generated and their definite marketing activity can be ensured through an adequate marketing decision system for the resurrection of a dying species such as the handloom industry in Ganjam district. For example, in the industry, if only saree is considered, then its various aspects viz., border, body, colour, design etc., represent specific cultural bases of any specific region .Hence, sarees from different regions would display different border, body, design, colour etc. due to the embedded cultural differences amongst them. When border or body design of one region, (For example, Sambalpur) is imprinted upon the original saree (Berhampuri) of Ganjam, a cross-cultural product is created. While designing a promotional mix for this cross-cultural product, two target markets are considered viz., a traditional comparatively small location (Cuttack) and a relatively larger cosmopolitan location (Bhubaneswar) of Orissa state. But, a product is never launched alone, rather with a lot of other products of same or different brands, from the same or any other organization. Hence, it all depends upon how many products are launched into the market at a time and what is their combinational effect i.e., synergistic or self-eroding. Also ,the type of markets vary significantly with variety of consumer cultures based on geographic location, city type, climatic conditions or demographic factors such as occupation, education, income, family size and family life-cycle or psycho-cultural factors, such as, need-motivation, personality, perception, learning and behavioral factors such as product benefits, brand loyalty, usage pattern, market awareness and consumer attitude etc.. So, a combination of cross-cultural products and their effect along with the existence of various consumer cultures and their group effect lead to unmanageable number of parallel and cross cultural transactions. So, this evolving decision model needs to keep track of all these transactions and ensures the occurrence of an optimum combination of the most effective transactions. The tools to shape or reshape the transactions are the promotional media vehicles such as newspapers, magazines, radio, television, cinema halls, hoarding /posters/billboards, out-door promotions, personal selling, sales promotions and public relations etc.... These tools need to be selected on the basis of maximum exposure, minimum cost and maximum media reliability so as to develop the most effective cross-cultural transaction mix with the ultimate aim of satisfying overall marketing objectives.

2. METHODOLOGY

For the development of the optimal positioning model for a product mix, there can be multiple objectives regarding the product, price, distribution and promotion activities. However, in this paper only the media selection dimension of the promotion mix is considered. Hence, the research objectives become as follows:

--To identify the different consumer segments and define their characteristics

--To develop an optimal media selection decision model

Both the objectives involve two different research processes but, are dependent in the sense that the outcome of the first one becomes the input to the second.

2.1. IDENTIFICATION OF CONSUMER SEGMENTS

Segmentation--the process of dividing the target market into various homogenous groups is based on some predefined criteria and selecting the most suitable target segments for effective positioning strategy is as old and well established as the marketing stream itself [Kotler (1997)]. However, with plethora of methodologies available, the determination of a suitable method of segmentation becomes a challenge. This decision later on proves to be instrumental in identifying one's customers and developing appropriate strategies to achieve the preset objectives. Yankelovich (1964) proposes "once you discover the most useful ways of segmenting a market, you have produced the beginning of a sound marketing strategy". In his paper, he realizes the utility of segment brand mapping and stresses on the knowledge of how to segment, on successful achievement of objectives. Kotler(1997), Schiffman and Kanuk (1997) provide a good selection of criteria (bases) for segmentation viz., geographic, demographic, socio-cultural, behavioral, benefit bases usage based etc.. But these bases are by no means exhaustive; rather they are more suggestive. New requirements for more effective strategies to handle increasing complex market situations made management scientists develop and suggest newer and more radical bases for segmentation. Yankelovich (1964) suggests "Segmentation Analysis" to cut through the details and focus sharply on new opportunities . He denounces the exclusivity of traditional bases (geographic, demographic etc.) on being able to provide with significant knowledge to the marketer about his target consumers. He has taken the example of ten different categories of products and goes on to show the adequacy of a variety of bases in identifying the customer effectively (viz., value, susceptibility to change, purpose, aesthetic concepts, attributes, individual needs and self confidence etc.). Wendell Smith(1956) suggests "Segmentation is based upon development of demand side of the market and represents a rational and more precise adjustment of product and marketing efforts to consumer / user requirements". Haley(1968) analyzes the advantages and disadvantages of geographic, demographic and "heavy half" models and suggests benefit segmentation, which more of a causal factor for identifying the markets than descriptive factors. But, his categorization of benefit segments viz., "The status seekers, The swingers, The conservative, The rational man, The inner directed man and The Hedonist etc. depict more issues than only benefit seek; rather it shows the cause of the benefit so desired by the respective consumer groups. This can be more visualized as a personality and lifestyle based segmentation. Wolburg and Pokrywczynski (2001) in their paper of segmentation of "Generation Y" college students, analyze the worth of this segment at two different point of time and try to define the various dimensions of this segment. They look at the economic dimension, the generational influence within society and culture to understand the unique ideas about the lifestyle to which a given generation aspires (life stages, current conditions and cohort experiences etc.) and the psychological variables and self identity. They suggest the psychological variables to include personality traits (introversion, extroversion, dogmatism etc.), which affect the need, values and belief etc., which in turn influence the gratification sought by the consumers in the media. To take care of such factors and dimensions in segmentation of consumers, psychographic analysis is to be conducted. Psychographics is a way the marketers tie psychological traits to consumption and tries to quantify of consumer psychology [Heath(1995)]. According to Heath, psychographic studies usually employ lifestyle profiles (demographics, product / media use, psychographic / lifestyle items), personality traits, general life style segmentation and product specific segmentation. The advantage of such an approach is that it not only provides the psychological / lifestyle profile of the consumers, but also suggests their media consumption and purchasing habits. Consequently, later on, this helps in development of effective positioning strategies and effective achievement of marketing objectives [Gurevtich et al (1973), Smit et al(2000),Yuan et al (2000),Frank et al (1979)].Hence, it is more appropriate to identify the psychographic characteristics of the consumer, measure it and based on its score ,segment the consumer market. This process is called psychographic segmentation and A-I-O inventory is an accepted method for psychographic segmentation. Therefore, pilot survey, focus group and projective techniques can be used to determine the constituents of A-I-O inventory. Based on the above facts, the informaton requirements for segmenting the consumer market for handloom products in the study area were,

--Education, Occupation, Income

--Social status

--Personality characteristics

--Involvement in purchase decisions

--Type of purchase decisions

--Consistency and strength of attitude

--Usage pattern and brand loyalty

--Interests in various facets of life viz., reading, sports, celebrity worship, religion, culture etc.

--Opinions regarding anything under the sun viz., social, political, economic issues etc.

With the above information, A-I-O inventory was constructed with a likert type five-point degree of agreement scale. The scale construction was duly influenced by some existing culture monitoring devices viz., VALS instruments, Yanchelovich Moniter etc.. The sampling was stratified random based on social class with belongings being the indicator of social class. The administered questionnaire was subjected to Cluster Analysis which resulted in four distinct clusters of consumers, viz.,

a) Group-1 type

This type of consumers has affluent status. They normally reside in posh areas/better localities. They are highly educated, businessmen or high officials in Government or private sectors. They have high income and hence, higher standard of living with access to national and international markets. Normally, they are high-risk takers, extroverts, innovative swingers with low involvement in purchase related decisions and fluctuating attitudes. They go for frequent purchases with interest-based awareness about markets, but their usage rate (necessarily) of goods is normally pretty less. Hence, these actualizers are sophisticated, active and image conscious people with high esteem and abundant resources. They have wide range of interests starting from ethnic phenomenon to globalization and are concerned with social issues .They are open to change and are whimsical, convenience seekers with no specific brand loyalty .in general their lives are characterized by richness, diversity, and fine tastes in life.

b) Group-2 type

This type of consumers are from upper middle class. Normally, they are highly educated business people or professionals in various fields, with better income and having access to the national market. The middle age groups of this class are normally prime decision makers. These people are normally achievers who seek recognition. They are evaluative innovators, moderate risk takers; switching loyal or hardcore loyal with high involvement having rational decision making ability, cognitive attitudes, and significant learning behaviour. They have better awareness and are prestige, status and value conscious people having strong attachment to local culture.

c) Group-3 type

They are the lower-middle class people who normally have medium educational level and limited income. They are workers from Government or private sectors having access to local market only and they are normally driven by security and social needs. They are introvert or aggressive, low risk takers, opportunistic switchers and prestige conscious. Their purchase behaviour is normally active type with highly probing involvement and a lot of price sensitiveness. They expect maximum value for money, but on occasions they can be emotional and impulsive. They have got a lot to complain about everything in life.

d) Group-4 type

These consumers are middle class conservatives with rich background and traditional approach and belief to life. They are people with aristocracy, with property by inheritance and with their own business or government service. Hence, they are conventional people with proper education, better income, with concrete belief on their opinions and strong attachment to traditional institutions. These believers are matured, satisfied, comfortable and reflective people who value knowledge and responsibility; they possess moral codes, which are deeply rooted in their value system. They follow established routines and are not so open minded about new ideas and social changes.

2.2 MEDIA SELECTION DECISION

Apart from normal pilot survey and questionnaire insertion, focus group was also conducted and projective techniques were used. A lot of secondary data were analyzed and expert opinion was considered. Media selection / Media plan scheduling etc., generally begin with a subset of all possible media vehicles that are selected according to the correspondence between the profile of the advertising target and that of the media vehicle. If the two profiles differ too much, the media vehicle is eliminated from the plan [Sossors et. al. (1993), Winter(1980), Rossiter (1997)]. This retained set of media vehicles can be considered as a starting hypothesis and analyzed further with more quantitative results, which has been depicted in figure 1 [Frank et. al. (1997)].

[FIGURE 1 OMITTED]

The model above seems to be more of an intuitive approach with judgmental decision-making and economic value optimization with trial and error method. The CPM model along with the use of ADOPT / ADMOD only reduces the iterations in decision making; it does not make the process more scientific [Asker (1975, 1992), Reshelf et al (1985), Lancaster (1987)].

These approaches focus more on judgment for initial scanning of media vehicles and then reach, frequency, number and cost of insertion and marginal utility etc., to determine the media plan. This is quite contrary to the discussions presented above in terms of consumer psychographics and media acceptability [Smit et al (2000), Sissors et al (1971)].

It does not consider neither the competitive requirements of the market or the financial ability of the organization concerned. Of course, one can understand these differences could be due to the difference in market forces in a rural area, sick unit in developing economy and developed economy. Therefore, considering all these intricacies, this paper suggests an optimization based approach based on MCDM (Multi-Criteria Decision Making) The information regarding resources and constraints of the optimization model would be drawn from the consumer psychographic analysis thereby implying consumer oriented having economic dimension .The model tries to optimize multiple objectives with several resource constraints generating a media selection decision for the marketing of handloom products.

2.2.1 MULTI-CRITERIA DECISION MAKING

An objective is the reflection of the desire of the decision maker (DM) and generally indicates the direction in which he should strive to do better. For example, in the decision system, DM may desire to maximize the exposure, media reliability and at the same time, to minimize the total cost of advertising. This may be regarded as three objectives of the DM while taking any decision regarding media planning. The objective with an aspiration level expressed in terms of its attributes is called a goal. Achieving at least 70% of the media reliability capacity in the advertising decision system is a goal. If the full capacity of the advertising system is known, then 70% media reliability capacity can be transformed to the unit of measurement of the media reliability attribute. In mathematical form, it can be expressed as G (X) [??] g where g is equal to 70% of the total media reliability capacity. "Decision-Making with Multiple Objectives" makes a system more meaningful which has various real life applications [Benayoun (1971(b), Charnes et. al. (1961), Zeleny (1974(a),(b)].

But, in many real life cases, the DM is not able to assign a precise aspiration level to an objective. However, he is able to say the existence of this in terms of an imprecise interval around it, e.g., he is able to say that G (X) should be around g. An objective with such imprecise aspiration level is referred to as fuzzy goal [Zadeh (1965,1983)]. The mathematical expression for the above example is given by G (X) [greater than or equal to] g, where G (italics G) signifies the fuzzification of the goal G .As, in most of the real life cases, DMs assign aspiration levels to objectives and try to achieve these to the extent possible, assigning suitable aspiration levels [g.sub.i] to the objectives [G.sub.i] (X), i, the fuzzy goal version of the MCDM model can be stated as

(2.1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

According to Bellman and Zadeh [1970], a fuzzy decision is defined as the fuzzy set D, (say) of alternatives resulting from the intersection of the goals and constraints. The central idea behind fuzzy goal programming (FGP) mainly involves two aspects [Yager (1975), Zimmermann (1978,1983)] viz.,

--Ill-defined systems can be first modeled as fuzzy models, because, in most of the real world situations, the perception of the DM regarding goals in the DS is largely imprecise in nature.

--Since no solution procedure is available for fuzzy models, equivalent crisp models of the systems have to be designed using fuzzy set theory to facilitate their solutions by existing algorithms and computer codes [Gillet (1986)].

But, both the steps involve the cognitive factors of the DM, which is largely influenced by his environment. The decision he makes regarding the nature of aspiration levels of the objectives in the decision system(DS) are not only guided by the immediate factors governing the DS, but also depend strongly on a major component of DS, viz., the personality of the DM which is focused in terms of how he perceives the aspiration levels of the objectives in the DS [Urban et. al (1980)]. The concept behind this attempt stresses mostly the importance of the environmental factors as perceived by the DM in taking a rational decision in the DS rather than only seeing the system from within. Hence, in this approach, a dynamic interaction of the DM with the DS is always highlighted unlike the other approaches.

Now, the model (2.1) is a FGP model of a MCDS whose crisp substitute can be obtained by first identifying each fuzzy criterion "[G.sub.i] (x) [greater than or equal to] [g.sub.i]" as a fuzzy set [G.sub.i] defined over the set of feasible solutions (X 's) and then aggregating all these fuzzy sets [G.sub.i] to obtain a single fuzzy set of decision D . The membership function [[??].sub.D] (X) of D serves the purpose of an overall objective function and the X [??]S (the feasible solution space bounded by the rigid capacity constraints, if any, and non-negativity restrictions) which maximizes [[??].sub.D](X) is the satisficing decision as described by the DM. The crux of the decision process lies in defining decision function [[??].sub.D] (X) by aggregating the fuzzy set [G.sub.i] , for all i, using a suitable operator [Yager (1975), Zimmermann (1978,1983)] viz.,

Suppose for the above system, the DM specifies a boundary point [p.sub.i] < [g.sub.i] for the fuzzy goal "[G.sub.i] (X) [greater than or equal to] [g.sub.i]". Three cases arise:

i) Any alternative [x.sup.1] gives full satisfaction to the goal if ,"[G.sub.i] ([X.sup.1]) [??] [g.sub.i]";

ii) [X.sup.1] gives partial satisfaction ,if "[G.sub.i] ([X.sup.1]) [??] [g.sub.i]" is moderately violated, i.e., [p.sub.i] [??] [G.sub.i] ([X.sup.1]) [??] [g.sub.i] and

iii) [X.sup.1] gives no satisfaction at all if "[G.sub.i] ([X.sup.1]) [??] [g.sub.i]" is strongly violated, i.e., "[G.sub.i] ([X.sup.1]) [??] [p.sub.i]".

If no satisfaction and full satisfaction correspond to real numbers 0 and 1 respectively, then the levels giving partial satisfaction lying in the interval ([p.sub.i], [g.sub.i]) correspond to points in the open interval (0,1). Then the membership function of the ith fuzzy set [G.sub.i] may be defined linearly [Zimmermann (1976, 1978, 1983)] as follows:

(2.2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Here [??][G.sub.i](X) represents the degree of satisfaction of the DM for the fuzzy goal "[G.sub.i] (X) [greater than or equal to] [g.sub.i]. Here [??][G.sub.i](X) is linear in [G.sub.i](X) and therefore the marginal satisfaction of the DM is assumed to be constant. Various algorithms have already been developed and some of them are due to Hanna (1981(a), 1981(b)) Lena (1980), Narasimhan (1980.1981), Rubin & Narasimhan (1985), Sinha et. al. (1988, !989), Tiwari (1986). Application of such algorithms can be very well observed from Sinha et. al.(1988,1989),Mangaraj et. al. (2000), Mishra(2000) etc..In this paper an interactive algorithm based on the concept of Benayoun et.al. (1971(a)) has been presented for the media selection problem.

2.2.2. ALGORITHM

STEP I: Solve m linear programming problems of maximization type stated as :

Max [G.sub.i](X) : i = 1 ... m

subject to

[A.sub.j] (X) [??] [b.sub.j]

(2.3) X [member of] [I.sup.+]

Let [X.sup.i] be the optimum solution which maximizes the ith objective [G.sub.i](X) given [g.sub.ii] as its optimal value. The pay-offs on the other objectives at [X.sup.i] can be denoted by [g.sub.ji] signifying the value of jth objective [G.sub.i](X) of the optimal point [X.sup.i] of the ith objective.

STEP 2 : Construct a pay-off matrix G given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the matrix can be referred to as decision matrix. The k tuple ([g.sub.11],[g.sub.22], ... [g.sub.mm]) comprising the diagonal element of the matrix G is the ideal point in the m dimensional criterion space. Due to the conflicting nature of the objectives, this point usually does not lie in the feasible criterion space. Denote this point by [g.sup.*] = ([g.sup.*.sub.1],[g.sup.*.sub.2], ... [g.sup.*.sub.m]) after replacing [g.sub.ii] by [g.sup.*.sub.i]. The boundary point for the objective [G.sub.i](X) can be obtained by taking the minimum of all [g.sub.ij] for i [not equal to] j, i=1,.... m. Hence, for all [G.sub.i](X), their boundary point can be taken as [g.sub.i].

STEP 3 : This step is known as the decision making stage and involves the determination of a feasible point g' = ([g'.sub.1],[g'.sub.2] ... [g'.sub.m]) nearest to [g.sup.*] according to the choice of the DM. This will be accomplished by the following sub -steps.

SUBSTEP : I Determine X

Such that [G.sub.i] (X) [??] [g.sub.i.sup.*] : i=1,2, .......m

[A.sub.j] (X) [??] [b.sub.j] :j = 1, 2, .......k

(2.4) X [member of] [I.sup.+] ...

The fuzzy goal "[G.sub.i] (X) [??] [g.sub.i.sup.*]" can now be identified as [G.sub.i] defined over the set of feasible solutions with the membership function [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] [??][G.sub.i] defined linearly as follows.

(2.5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

SUBSTEP II : Combine entire fuzzy sets [G.sub.i] using minimum operator and solve the model as:

Maximize [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] ; i = 1 .. m

[A.sub.j]X[??][b.sub.j] ; j = 1 ... k

(2.6) [??], X [member of] [I.sup.+]

Let the solution of the model (2.6) be X = [X.sup.*] which yields [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for all i. If the decision yields satisfactorily for all membership values, then it is the final solution. Otherwise go to the next step. Here, it has to be noted that, I has is to be transformed as:

[??]=[[??].sub.1]/10+[[??].sub.2]/[10.sup.2]+[[??].sub.3] /[10.sup.3]+[[??].sub.4]/[10.sup.4]+[[??].sub.[??]]/[10.sup.5]

where [I.sub.i] [member of] [I.sup.+]

SUBSTEP III : The DM is asked whether he can make some concession in the level of any membership function, whose attainment in his opinions is more satisfactory to improve those which are less satisfactory. Suppose the DM is not satisfied with the solution X = [X.sup.*] and he can concede [??][[??].sub.h] amount from [[??].sub.h]. Then the following transformation can be made

[g.sub.i] [??] [G.sub.i]([X.sup.*]) and [g.sub.i.sup.*] [??] [g.sub.i.sup.*]. i [not equal to] h

Solve the equivalent problem

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

such that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

[G.sub.h](X)[??][[G.sub.h]([X.sup.*]-[??][[??].sub.h] ([g.sub.h.sup.*]-[g.sub.h])

[A.sub.j](X)[??][b.sub.j]

(2.7) [??], X [member of] [I.sup.+]

Repeat this step, till the DM becomes satisfied with the attainment level of all membership functions.

2.2.3. MULTI-CRITERIA MEDIA SELECTION DECISION MODEL

The decision variables, constants and symbols for the problem are as follows :

a) Decision Variables, Constants and Symbols

N : Newspaper medium

R : Radio medium

i : 1,2 for types of vehicles in each medium, viz., Newspaper-1, Newspaper-2 for newspaper medium and Radio advertisement 30 second or less and 60 second or more for radio medium respectively.

I : 1,2 for different consumer cultures developed by geographic segmentation of target market towards which the promotional campaign is aimed and where it is operational viz., region-1 and region-2 respectively.

k : 1,2,3,4 for different consumer segments determined by psychographic segmentation of the target market

M : Budgetary amount Y, [Y.sub.1], Z, [Z.sub.1] : Any media vehicle from N and R.

(i,k,l) :ith type of vehicle of promotional medium directed towards kth segment at lth area.

[E.sub.i.sup.kl] : Exposure for ith media vehicle within kth segment at lth area.

[C.sub.i.sup.kl] : Cost for ith media vehicle directed towards kth segment at lth area.

M[R.sub.i.sup.kl] : Media reliability for ith media vehicle directed towards kth segment at lth area.

N[X.sub.i.sup.kl] : ith type of vehicle of Newspaper medium directed towards kth segment at lth area.

R[X.sub.i.sup.kl] : ith type of vehicle of Radio medium directed towards kth segment at lth area.

The formulation of the system constraints and objectives is given below as :

2.2.4. SYSTEM CONSTRAINTS:

i) Budget Constraint:

In any organization, budget is the first and foremost deciding factor in any of its constructive activities. Had it not been so, all the organizations would have been producing, selling, expanding, diversifying all what so ever they want and reaping profit till they get satisfied. There would have been no necessity for planning, resource allocation and strategy formulation with situational analysis. This is because resources (of any type) are always limited and options for their utilization are too many. So, within available opportunities and constraints one needs to have the maximum utilization of available resources. In this case, considered here, the resources at the handloom sector of the study area are too scanty and profit is negative over the years. So, at such a time an effort is being made to provide a modern management system to this sinking unit and to use optimally the limited monetary resources in all the fronts, wherever it is needed on a priority basis for maximum effectiveness. Of course, at no point of time the cost of promotion would be zero as under no circumstance, either from marketing or non-marketing point of view, promotion can be totally scrapped. Hence, even though the cost is minimized, the total promotional effort is bounded by a budget considering the total resource available, significance of each cost incurring area (profit centers) and based on the important concept that let no area remain dry while other areas reap the harvest. Mathematically, the constraint can be written as :

(3.1) [summation over (i)] [summation over (k)] [summation over (l)] [C.sup.kl.sub.i] [??][N[X.sup.kl.sub.i] + R[X.sup.kl.sub.i][??] [less than or equal to] M

ii) Non-overlapping Constraint:

During promotional media planning, one cannot put simultaneously any number of advertisement copies in any medium. It needs a lot of media vehicle analysis, situational analysis and target segment culture analysis. May be a full page advertisement and a quarter page advertisement of the same product at two different pages in a newspaper significantly substantiates the appeal of the message or they may eat up each other's effectiveness considerably leading to unnecessary extra cost and reduced mass appeal. In a financially unstable company such as this case, each extra money spent is at the cost of some other utility and the reduction of market appeal for an innovative product is a crime. Hence, variables are constrained not to overlap each other destructively. Mathematically, the constraint can be represented as follows:

(3.2) [summation over (i)] N[X.sup.kl.sub.i] [less than or equal to] 1 [for all] k, l

(3.3) [summation over (i)] R[X.sup.kl.sub.i] [less than or equal to] 1 [for all] k, l

iii) Preferential Constraint :

Some media vehicles are preferred on specific occasions and on desired situations to their fellow partners. The simple reason behind this is that the media vehicle with more exposure in any specific locality or any particular target segment or the less cost of any specific media (say sales promotion, cinema hall or hoarding) at any specific region twists the choice in its favour. Normally, also more viewer ship like prime time or sports time, newspaper/magazines on their front page; hoarding with bigger size, attractive colour combination and at a big traffic center; cinema halls with a hit movie running or sampling or free gifts during festival occasions are all the time preferred to their counter parts. At some specific time, any specific medium also can have more value, belief and reliability so far as some specific consumer segments are concerned. Aristocrats may prefer print media to audiovisual medium where as middle class get more attracted by discounts, point-of-purchase or free gifts during festivals. Affluent class may derive their inspiration from cable network and teenagers may get influenced by visual media with attractive models. Hence, in the present case of handloom sector this model prefers some variables over the others considering target market, product lines and embedded resource situation. Mathematically, the media preference can be defined as:

(3.4) N[X.sub.p.sup.kl] [??] N[X.sub.w.sup.kl] for all k, l

where, p [??] w

As, this can be applied to each and every component of each and every media vehicle, the above relation may be generalized as

(3.5) Y[X.sub.p.sup.kl] [??] Z[X.sub.w.sup.kl] for all k,l

where the relation p [??] w holds good.

(3.6) Y[X.sup.kl.sub.p] + [Y.sub.1] [X.sup.kl.sub.p] [less than or equal to] Z[X.sup.kl.sub.p] + [Z.sub.1][X.sup.kl.sub.p]

iv) Competitor's Constraint:

Specifically in cloth and related products market, an entirely new method of promotion or distribution is a double edged sword i.e., it may pay off handsomely appealing the potential target segment from all sides or people may reject it outright because a lot of prestige and consumer psychology are involved in it. If it is rejected, then for the structurally and financially unstable handloom sector in the study area this will be a deathblow. Hence, neither the competitors can be overlooked nor they can be accepted totally. So, careful analysis needs to be done and certain media vehicles used by the competitors should be accepted. Mathematically, the situation can be put as:

Y[X.sub.i.sup.kl] + [Y.sub.1][X.sub.ij.sup.kl]

(3.7) Y[X.sub.i.sup.kl]. [??] 1 for each k,l

v) Geographical Constraint:

Various regions differ from each other not only in terms of its size, population, climate etc. but also in terms of the characteristics of its very own residents. People in each area show dynamically different perception, personality, attitude, price sensitivity and affinity towards any specific product. Consequently, different media for communication find suitability in different regions. This is simply because different regions involve divergent cost structure for promotional copy insertion in associated media vehicles. Also, the pricing structure and distribution channels network vary significantly through out the geographic distances due to the availability/ non-availability of desired resources at various localities. Hence, the model restricts certain media not to appear at specific areas or intentionally associates certain individual media vehicles or a combination of them to some desired areas. Mathematically, it can be put as:

(3.8) [summation over (i)] [summation over (k)] Y[X.sup.kl.sub.i] [greater than or equal to] 1 [for all] l

(3.9) [summation over (i)] [summation over (k)] Z[X.sup.kl.sub.i] [less than or equal to] 1 [for all] l

viii) Minimum Selectivity Constraint:

Sometimes, the whims of the marketer defy all logic and may be the situations also defy all rational thinking in behaving in a particular way. Under those circumstances some media vehicles are accepted without any further investigation. Also, some mass media have got universal appeal and are status symbols for the marketing, which may not be selected, in a scientific and innovative method of media selection. In such cases, the marketer wants those media to be selected even though they show some loss/misutilisation of resources in the process. Sometimes, the hunch or feeling of human beings out of intuition or experience does show its result in the long run which a feeling less computer can not identify. Hence, this constraint identifies all such "must selection" media vehicles and puts them under one roof. Mathematically, the individual or group selection, can be put as:

(3.10) Y[X.sup.kl.sub.i] [greater than or equal to] 1

2.2.5, SYSTEM OBJECTIVES

(1) Exposure Objective:

The effective utility of any media vehicle for any specific promotional programme is measured through exposure. Exposure is nothing but the total number of people effectively reached by any media vehicle in any specific period of time. Of course, it is very easy to find out this by determining the total coverage of any media vehicle. But any person being exposed to any specific media vehicle must accept the message and put it to long term memory with proper rehearsal so as to remember it on all occasions or on aided stimulation i,e., the message should be accurately perceived by the respondent who experiences the appeal by the media vehicle. So the message must pass through selective attention (out of the total number of messages which stand out from the rest or about which consumer has got genuine interest, get attention and enter into the short term memory of the consumer), selective distortion (the respondent tends to modify/amplify/rejects the message as per his own interest, opinion and attitude and then those distorted messages only go for rehearsal) and selective retention (putting the message to long term memory after adequate rehearsal and remember on instances). Neither all the internal mental processes can be controlled nor one can have any idea of the effectiveness of the advertising messages. But, repeated exposure of the message to the target audience and the increase in the overall readability percentage (all people do not read/identify 100% of the messages in any medium even after being exposed to it; so, readability is the percentage of the total messages read by the consumer) significantly influences the overall effective exposure. Increase in this exposure increase awareness among people about the organization and its product and there is a marked increase in information flow. Hence, there is a better chance of fulfilling business objective through promotional objective. Exposure can be defined as the product of coverage, frequency and readability. Mathematically, it can be put as

E = C * F * R,

where ; E,C,F,R represent exposure ,coverage, frequency, readability respectively

Also, the importance of exposure increases all the time in a sick handloom sector, which is trying to modify and develop itself with non-conventional innovations in product decision, and it wants to increase consumer awareness all the time with effective communication and for ultimate fulfillment of marketing objectives. Hence this objective of exposure is to be maximized. Mathematically it can be put as::

(3.11) Max [summation over (i)] [summation over (k)] [summation over (l)] [E.sup.kl.sub.i] [??]N[X.sup.kl.sub.i] + R[X.sup.kl.sub.i] [for all] i,k,l

ii) Cost Objective:

Cost is all the time, the most intriguing and eye catching factor in any business situation. Maximum utilization of least possible cost makes all the investment factors loose to revenue factors (considering a good sales) with profit, ample return on investment, long term sustenance and appropriate market share being the adequate indicators. So, all the participants in the marketing process get their due return, wish to invest more resources (physical, material and financial) and acquire an excellent work motivation. But promotion does not provide direct revenue in any case and consequently the most rational marketing man would always try to spend as less as possible on this front as one never knows which part really comes back to the investor. This matter grows more serious in a sinking unit where aids, loans and financial schemes become the crux of the sustenance and development. Innovation and refunding on product, price, place and promotion is inevitable to avoid cessation, but still it hurts to spend an extra penny. Each and every medium involves different costs of insertion and reinsertion of advertisement copy or implementation of sales promotional programmes leaving behind their preparation and development costs. Hence, all the time the cost has to be within a fixed budget and as minimum as possible for each and every cultural segment or geographic area but with maximum exposure and media reliability. So, the objective of cost is to be minimized and can be mathematically written as:

(3.12) Min [summation over (i)] [summation over (k)] [summation over (l)] [C.sup.kl.sub.i] [??]N[X.sup.kl.sub.i] + R[X.sup.kl.sub.i] [for all] i,k,l

iii) Media Reliability Objective:

Message in a medium is most effective when it is precise, unique, informative, alluring and the medium is reliable. All messages on all media do not have the same impact and it may not appeal equally to its target segment. Hence, the message with creditable exposure and least cost is efficient in satisfying its objectives in a reliable medium. Media readability may be defined as:

MR = P * N * A * D ,where,

MR : Media reliability

P : % of effective perception of the appeal

N : Latent need or need generating ability of the appeal

A : Ability of the appeal to develop an attitude of the mass to convert their need to effective purchasing.

D : Degree of post purchase dissonance i.e. the ability of the appeal to satisfy the consumer and force a repeat purchase. D varies between 0 and 1 based on consumer's degree of satisfaction i,e. D [??] [0,1],ranging from totally dissatisfied to fully satisfied and repeat purchase

Perception leads to selective retention of the message by the consumer and recalls it on instigation. This feeds on a latent need and develops an active need with strong drive to satisfy it. Adequate information and type of need creates an obsessive positive attitude, which leads to effective purchasing. But, one time purchase is not sufficient and a bad reputation for the company cannot be tolerated. Hence, the message in the media must attend to "purchased" people and reduce their dissatisfaction with proper logic of understanding as well as persuade them for a repeat purchase. This is what a media reliability is all about and in the situation of a retarded handloom sector, promotion with pinpoint accuracy and high media reliability is an absolute necessity for attracting, motivating and convincing consumers all the time. So, the objective of media reliability is to be maximized. Mathematically, the objective function can be written as :

(1.13) Max [summation over (i)] [summation over (k)] [summation over (l)] M[R.sup.kl.sub.i] [??]N[X.sup.kl.sup.i] + R[X.sup.kl.sub.i][??] [for all] i,k,l

2.2.6. (0,1) RESTRICTION:

Each decision variable has to take 0 or 1 as its solution.

Mathematically, it can be represented as N, R, [??] {0,1} for each i, k, l.

Based on the above procedure ,the following information were generated for the requirement of the decision model.

3. INFORMATION REQUIREMENTS FOR MEDIA SELECTION

-- Cost of advertisement insertion in different newspapers, viz., 'Samaj' and 'Sambad' in various styles and designs (i.e., full page, half page, quarter page, less than quarter page, top left, top right etc.), their total circulation and the type and the characteristic of people (consumers) purchasing it.

-- Circulation of the newspaper per district or locality.

-- Cost of advertisement insertion in radio based on timing of advertisement (prime time, normal time, sports or news time, after/before/within any specific programme) and time span of advertisement ([??]2 mts, [??] 1 mt, [??] 1.5 mts, [??] 0.5 mt. etc.), total no. of people listening to it, the type and the characteristic of people (consumers) using radio (may be time or programme bound).

-- Characteristic of the product proposed to be advertised.

-- Currently used promotion mix for various product lines (handloom sector and competing products)

-- The different consumer segments and their characteristics related to the product concerned.

-- Consumer's attitude per product/media vehicles and ability to create/reduce post purchase dissonance/product/media vehicle.

-- Likeness or dislike of people towards any specific medium/media mix when any specific product/product lines are advertised in it.

-- Preference of any media to others based on cost, consumer perception, media reliability, competitor comparison or consumer culture etc..

-- Competitor's (who are they) promotion mix, its advantages and disadvantages and expectation of the consumers from the new promotion mix (what would suit the proposed product line).

3.1. DATA COLLECTION METHOD

Majority of the data regarding type of advertisements in newspaper and radio media were available either by secondary means or through unstructured interviews with associated officials. Circulation figures were also available there. Common man (potential customers) were subjected to mainly structured disguised questionnaires having various measurement techniques and scales to measure media's readability, consumer's attitude towards product (current and proposed)/media and consumer's likeness or dislike ness towards any specific culture in any specific medium or media mix. The comparison among the various media vehicles was done using a semantic differential scale. The common media insertion practices available in the industry and the preferences were also determined using Likert type attitude scales.

3.2 SAMPLING PLAN

No sampling was required for data collection regarding the cost of various type of media, advertisement insertion costs and media circulation figures. All these area and associated people were fully covered. For consumer attitude survey, basically area sampling was used and then the sample frame was stratified based on income level, spending habits and benefits sought from various product lines. Four different combinations of bases (income, benefits, spending habits) were identified and information regarding them was used as identification data of the respondent. Even though, all these people were served the same questionnaire, the priority and value of their answers were different and hence different groups of data from various respondents were treated differently during analysis and interpretation. Approximately 5% of the sample frame was used as sample size with 95% confidence level.

4. ANALYSIS AND INTERPRETATION OF RESULTS

The multi-criteria interactive FGP algorithm, which has been presented in this paper, has been implemented for the marketing model and has been solved utilizing Lindo Software. The final result obtained has been presented in Table-1 which depicts the specific type of media vehicle with its associated dimensions targeted towards some particular customer segment in any specific region so as to develop a media vehicle mix with maximum promotional effectiveness.

The information regarding exposure, cost, media reliability of various media vehicles with their associated dimensions, the aimed target segments and application localities are also given in Table 1. The individual exposure maximization, cost minimization and media reliability maximization have been worked out. The maximum value for total exposure is determined to be 1025 lakh and the corresponding minimum value of total exposure in the presence of other two objectives is determined to be 310 lakh. Similarly, the minimum and maximum values for total cost are determined to be Rs.25.5 thousand and Rs.71.5 thousand respectively and the minimum and maximum values for total media reliability are 932.7 and 2519.3 respectively. After construction of membership functions as described earlier, the compromise solution set is obtained. The compromised total values for exposure, cost and media reliability are 730 lakhs, Rs. 44000/- and Rs. 1826.3 respectively. At this point it has been decided to reduce cost as much as possible because the test unit considered (i.e., handloom sector in Ganjam district) is sick; it is lacking infrastructure and suffering from acute resource problem. Consequently, the need of the hour is to provide maximum promotional coverage to improve the sagging demand situation. But, one has to reduce the cost of promotion within specific limits of exposure and media reliability. It was felt that exposure is a superior objective than media reliability under the current circumstances as it creates the awareness in the market and it provides a platform for initial launch.

Under this circumstances, one can think of improving the overall reliability of the media vehicle so that the promotional message has got a long term sustained impact on the market. Hence, a minimum acceptable value of exposure should decide the amount of reduction in cost. So exposure was traded off with a minimum value of 650 lakhs and the value for media reliability was kept in the interval (932.7, 1826.3) based on the survey and evaluation of current target market and their expected behaviour pattern. After re-reconstruction of membership functions for cost and media reliability, the final solution obtained has also been presented in Table 1. The associated final exposure, final cost and final media reliability values obtained are found to be 650 thousand, Rs.36500/-and 1401.1 respectively.

The individual values of the final outcome to this decision system are observed in zero-one mode i.e., rejection-selection format. Actually, the model accepts or rejects some specific media vehicles with all its associated dimensions, which are targeted towards some specific customer group in a specific region. Hence, at the beginning the characteristics and culture of the consumer (i.e. bases) in the four target groups selected and the specialties of the regions needs to be kept in mind before analyzing and interpreting the values of the final solution.

As newspaper- 2 is more costly, stylish, properly designed, innovative, supportive to good quality new products and as each day's newspaper gets published in the same evening, it has got faster and more appeal in the consumer group--1. One can go for a tailor made advertisement for affluent group with a lot of information to create a positive attitude in them. Naturally enough, it has got a little exposure in other classes of consumers and hence, it is wasteful to try and capture the market through this newspaper medium. Also, one can go for design of sarees or other handloom products and publish photo features of celebrities for better visual effects. The exposure and media reliability values are still higher in news paper-2 to make it a feasible attempt in region-2 inspire of a bit more cost. But, non-selection of newspaper--2 in region-2 (even though it has got more affluent and elite mass) draws its reason from the fact that less people in region-2 go for newspaper- 2 as more distance from the place of publication make it reach late to the consumers. Due to the amount of information and out-look, news paper 2 is a status symbol and image creator in a traditional locality like region--1 which may not be the case in region-2, because of the availability of lot many other avenues.

Newspaper--1, basically goes for upper-middle section in both the regions and conservatives in region--2. The reason could be that newspaper--1 is a standard cost descent information provider in a reasonably proper style and design. All these along with the long existence of newspaper--1 ,make it more believable to a rational mind as well as to a traditional conventionalist. The lesser cost of advertisement attracts more and more products for advertising, of almost all types and all ranges to newspaper--1. For the marketer, he can use it as a constant source of reminder to the customer apart from initial introduction and for the consumer it is an opportunity to choose from a number of alternatives where the source is also reliable and informative. Of course, two different types of advertisement copies would be needed for upper middle and conservative classes, but that again can be properly scheduled with simultaneous or alternative appearance. In any case newspaper - 2 is more aggressive and risk taking than newspaper--1 and so are their customers. It is also quite normal that high involvement and high risk taking in purchase decisions do not go side by side.

In region-1, radio caters to lower middle and conservative class of people. A 60-seconds advertisement for lower middle class of consumers means that in region-1, group--3 consumers generally seek their entertainment from radio programmes. In any case, stiff competition from television has made radio medium to improve its standard of programmes drastically and dramatically. For normal worker class people who have little education and little interest about any other matters in the world than their own affairs, radio becomes a low cost medium, which is entertaining, pleasantly informative and reliable. It can also be used at any point of time during any activity and even in work places. Hence, it is easier to target group-3 consumers through radio medium. Survey shows, it is very difficult to attract the attention of people in a relatively short period of time (30 sec). Even if, one can attract the attention, it is quite difficult to stand out from rest of others and enter into long-term memory with a positive predisposition because of the natural adaptability and lack of glamour of an only audio medium.

In region-2, advertisement of 60 sec. for radio is effective for group-1 and group-2 types of consumers. This looks quite normal with the latest developments in radio medium and the advent of new channels (like FM and others) with ultra modern technology which is now-a-days gaining a lot of appreciation and creating a significant influence on the audience. Teenagers and even people up to 40 years of ages or more than that in group-1 and group-2 type of consumers show a distinct interest to western music and its Indian counterparts. They normally ask for and enjoy a lot of film-based programmes while they also prefer the quality of music and the embedded messages with lot more awareness and better understanding.

These advertisements become more reliable and more interesting and hence, create susceptibility in group-1 and group-2 type of consumers. For the initial trial, 60-sec advertisement is obviously better than 30 sec. and also it provides more information so far as the product is concerned which is the need of group-1 and group-2 type of consumers. Radio advertisement of 30 sec. for lower middle class is basically due to lack of so much interest on their part in these specific programmes/channels in radio medium. Also, the advertisement is for reminding consumers rather than product introducing type. Gradually improving standard of living and purchase power means that group-3 consumers may become capable of purchasing T.V. and hence, impact of radio on them would be gradually less. But for the sake of old habits, already introduced products may be advertised in radio for reinforcement by going for 60 sec. advertisements.

In any case, the advertisements meant for any specific group for any specific regions, are also exposed to all other type of consumer groups in other regions, as the media used are mass media. So, that would obviously influence many other untargeted consumers into effective purchase.

TABLE 1 : DATA SHEET WITH RESULTS

Media Type                        Exposure    Cost    Media Reliability
                                  (Lakhs)     (Rs.)   a (Rs.)

[X.sub.1]                         50          5000     57.6
([R.sub.1][N.sub.1][C.sub.1])
[X.sub.2]                         70          5000     99
([R.sub.1][N.sub.1][C.sub.2])
[X.sub.3]                         30          5000    243
([R.sub.1][N.sub.1][C.sub.3])
[X.sub.4]                         75          5000    205.8
([R.sub.1][N.sub.1][C.sub.4])
[X.sub.5]                         65          7000     84
([R.sub.1][N.sub.2][C.sub.1])
[X.sub.6]                         40          7000    128.7
([R.sub.1][N.sub.2][C.sub.2])
[X.sub.7]                         80          7000    207.9
([R.sub.1][N.sub.2][C.sub.3])
[X.sub.8]                         70          7000    205.8
([R.sub.2][N.sub.2][C.sub.4])
[X.sub.9]                         30          5500     50
([R.sub.2][N.sub.1][C.sub.1])
[X.sub.10]                        50          5500    129.8
([R.sub.2][N.sub.1][C.sub.2])
[X.sub.11]                        45          5500    235
([R.sub.2][N.sub.1][C.sub.3])
[X.sub.12]                        60          5500    210
([R.sub.2][N.sub.1][C.sub.4])
[X.sub.13]                        20          7000     90
([R.sub.2][N.sub.2][C.sub.1])
[X.sub.14]                        60          7000    150
([R.sub.2][N.sub.2][C.sub.2])
[X.sub.15]                        75          7000    195
([R.sub.2][N.sub.2][C.sub.3])
[X.sub.16]                        65          7000    220
([R.sub.2][N.sub.2][C.sub.4])
[X.sub.17]                        115         3000    107.8
([R.sub.1][N.sub.60][C.sub.1])
[X.sub.18]                        75          3000    128.7
([R.sub.1][N.sub.60][C.sub.2])
[X.sub.19]                        15          3000    157.5
([R.sub.1][N.sub.60][C.sub.3])
[X.sub.20]                        80          3000    176.4
([R.sub.1][N.sub.60][C.sub.4])
[X.sub.21]                        100         1500     70
([R.sub.1][N.sub.30][C.sub.1])
[X.sub.22]                        75          1500    117.9
([R.sub.1][N.sub.30][C.sub.2])
[X.sub.23]                        15          1500     85
([R.sub.1][N.sub.30][C.sub.3])
[X.sub.24]                        75          1500    176.4
([R.sub.1][N.sub.30][C.sub.4])
[X.sub.25]                        30          3000     99
([R.sub.2][N.sub.60][C.sub.1])
[X.sub.26]                        60          3000    120
([R.sub.2][N.sub.60][C.sub.2])
[X.sub.27]                        75          3000    170
([R.sub.2][N.sub.60][C.sub.3])
[X.sub.28]                        60          3000    180
([R.sub.2][N.sub.60][C.sub.4])
[X.sub.29]                        25          1500     80
([R.sub.2][N.sub.30][C.sub.1])
[X.sub.30]                        50          1500    110
([R.sub.2][N.sub.30][C.sub.2])
[X.sub.31]                        75          1500    203.4
([R.sub.2][N.sub.30][C.sub.3])
[X.sub.32]                        60          1500    180
([R.sub.2][N.sub.30][C.sub.4])

Media Type                        Compromise      Final
                                  Solution        Solution

[X.sub.1]                         0               0
([R.sub.1][N.sub.1][C.sub.1])
[X.sub.2]                         0               1
([R.sub.1][N.sub.1][C.sub.2])
[X.sub.3]                         0               0
([R.sub.1][N.sub.1][C.sub.3])
[X.sub.4]                         1               0
([R.sub.1][N.sub.1][C.sub.4])
[X.sub.5]                         1               0
([R.sub.1][N.sub.2][C.sub.1])
[X.sub.6]                         1               0
([R.sub.1][N.sub.2][C.sub.2])
[X.sub.7]                         0               1
([R.sub.1][N.sub.2][C.sub.3])
[X.sub.8]                         0               0
([R.sub.2][N.sub.2][C.sub.4])
[X.sub.9]                         0               1
([R.sub.2][N.sub.1][C.sub.1])
[X.sub.10]                        0               0
([R.sub.2][N.sub.1][C.sub.2])
[X.sub.11]                        1               0
([R.sub.2][N.sub.1][C.sub.3])
[X.sub.12]                        0               1
([R.sub.2][N.sub.1][C.sub.4])
[X.sub.13]                        0               0
([R.sub.2][N.sub.2][C.sub.1])
[X.sub.14]                        0               0
([R.sub.2][N.sub.2][C.sub.2])
[X.sub.15]                        0               0
([R.sub.2][N.sub.2][C.sub.3])
[X.sub.16]                        0               0
([R.sub.2][N.sub.2][C.sub.4])
[X.sub.17]                        1               1
([R.sub.1][N.sub.60][C.sub.1])
[X.sub.18]                        1               0
([R.sub.1][N.sub.60][C.sub.2])
[X.sub.19]                        1               0
([R.sub.1][N.sub.60][C.sub.3])
[X.sub.20]                        0               0
([R.sub.1][N.sub.60][C.sub.4])
[X.sub.21]                        0               0
([R.sub.1][N.sub.30][C.sub.1])
[X.sub.22]                        0               0
([R.sub.1][N.sub.30][C.sub.2])
[X.sub.23]                        0               0
([R.sub.1][N.sub.30][C.sub.3])
[X.sub.24]                        1               1
([R.sub.1][N.sub.30][C.sub.4])
[X.sub.25]                        1               0
([R.sub.2][N.sub.60][C.sub.1])
[X.sub.26]                        1               1
([R.sub.2][N.sub.60][C.sub.2])
[X.sub.27]                        0               1
([R.sub.2][N.sub.60][C.sub.3])
[X.sub.28]                        0               0
([R.sub.2][N.sub.60][C.sub.4])
[X.sub.29]                        0               1
([R.sub.2][N.sub.30][C.sub.1])
[X.sub.30]                        0               0
([R.sub.2][N.sub.30][C.sub.2])
[X.sub.31]                        1               0
([R.sub.2][N.sub.30][C.sub.3])
[X.sub.32]                        1               1
([R.sub.2][N.sub.30][C.sub.4])

Key to Table 1

[X.sub.N] : Variables considered for modeling
[C.sub.n] : Consumer segment 1; 'n = 1,2,3,4
[R.sub.n] : Region n; n = 1,2
[N.sub.n] : Newspaper n; n = 1,2
[R.sub.60] : Radio advertisement for 60 seconds or more
[R.sub.30] : Radio advertisement for 30 seconds or less

REFERENCES

Aaker D., ADMOD: An Advertising Decision Model, JMR, 12,1 (1975), pp 37-45.

Aaker D., The CPM Rule: An Alternative Approach to Media Planning", Canadian Journal of Marketing Research, 11,(1992), pp 47-54.

Bellman, R. E. and Zadeh, L. A., Decision-Making in a Fuzzy Environment, Management Sci., 17 (1970) 141-164.

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Dr. Ashis Mishra earned his Ph.D. at Utkal University, Bhubaneswar, India, in 2000. Currently he is an assistant professor in marketing at XLRI Jamshedpur, one of the premier Business Schools in the Asia-Pacific region. His research interests include consumer research, modeling in marketing and retail research. He has published ten research papers in the above mentioned areas in journals.

Dr. B. K. Mangaraj is a Professor at Utkal University, Bhubaneswar (India). He holds a M.S. in Mathematics and Ph.D. in operations research, both from Indian Institute of Technology, Kharagpur (India) in 1983 and 1989 respectively. In the year 2002, he was awarded D.Sc. in Development Anthropology from Utkal University for his work "Cultural Information Management of Endogenous Development in a Simple Societal System". His research interests include Fuzzy Logic, Multi-Objective Optimization and application of these techniques to management and development problems. He has published over thirty five research papers in these areas in journals.

Dr. Upali Aparajita is a Reader at Utkal University, Bhubaneswar (India). She earned her masters degree in social anthropology in 1985, and a doctorate degree in developmental anthropology in 1991, both from Utkal University. Her research interest is primarily on development issues in traditional societies and has published over twenty-five research papers in various areas of management and development highlighting cultural dimension in the development process.