An optimal advertising media selection model for promotion of multiproducts in segmented market

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An optimal advertising media selectionmodel for promotion of multiproducts insegmented marketP. C. Jha a , Remica Aggarwal b , Anshu Gupta c & Sugandha Aggarwald

a Department of Operational Research , University of Delhi , Delhi ,110007 , India E-mail:b Department of Operational Research , University of Delhi , Delhi ,110007 , India E-mail:c Department of Operational Research , University of Delhi , Delhi ,110007 , India E-mail:d Department of Operational Research , University of Delhi , Delhi ,110007 , India E-mail:Published online: 14 Jun 2013.

To cite this article: P. C. Jha , Remica Aggarwal , Anshu Gupta & Sugandha Aggarwal (2012) Anoptimal advertising media selection model for promotion of multiproducts in segmented market,Journal of Statistics and Management Systems, 15:1, 61-80, DOI: 10.1080/09720510.2012.10701613

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* E-mail: [email protected]† E-mail: remica_or@rediff mail.com‡ E-mail: [email protected]§ E-mail: [email protected]

An optimal advertising media selection model for promotion of multi-products in segmented market

P. C. Jha *

Remica Aggarwal †

Anshu Gupta ‡

Sugandha Aggarwal §

Department of Operational ResearchUniversity of DelhiDelhi 110007, India

AbstractPromotion is a form of corporate communication that uses various methods to reach

a targeted audience with a certain message in order to achieve specifi c organizational objec-

tives. This promotional mix consists of a blend of advertising, personal selling, sales pro-

motion and public relations tools. An advertising decision is primarily infl uenced by the

choice of media, media budget etc. especially if the advertising is required to be done in

a segmented market. Therefore an optimal advertising media selection is a strategic factor

for the advertising of products in diff erent market segments as each segment is consumer

specifi c covering homogenous group of potential consumers with similar needs and wants.

In this paper media selection model is developed to facilitate the advertising media selection

process for multiple products that need to accommodate diff erent market segments. The

problem is solved through goal programming technique. A real life example from Indian

business industry has been taken to validate the results.

Keywords: advertising and media planning, media allocation, segmented market, goal programming.

1. Introduction

Marketing nowadays is typically seen as the task of creating, promot-

ing, and delivering goods and services to consumers and businesses.

Marketing decisions falls in to the four controllable categories of product,

Journal of Statistics & Management SystemsVol. 15 (2012), No. 1, pp. 61–80

© Taru Publications

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62 P. C. JHA, R. AGGARWAL, A. GUPTA AND S. AGGARWAL

price, place, promotion which together are known as 4P’s of marketing

mix. Advertising being the prime promotional mix is done to identify and

diff erentiate from other off erings, to communicate information about the

product, to induce consumers to try new products and to suggest reuse,

to stimulate the distribution of a product, to increase product use, to build

value, brand preference, and loyalty and to lower the overall cost of sales.

Media plays a crucial role in advertising through forming and refl ecting

public opinion, connecting the world to individuals and reproducing the

self-image of society. Advertising is done through diff erent forms of media

which are either in the print form or in electronic form. They are largely

responsible for structuring people’s daily lives and routines.

Planning for a suitable media is of prime concern for any marketing

manager. Media planning has two important aspects. First being the selec-

tion of advertising media, second being the development and allocation

of the suitable advertising budget. Choice of a right media mix involves

appropriate media that can target the right audience, message to be given

to the masses etc. The types of media, number of products to be adver-

tised, expected customer increase rate of the company’s major products,

the frequency of advertisements, etc. are various factors that determine

the allocation of the fi rms’ advertising budget. The amount of available

budget is limited and fi xed. So it is desired to spend the available budget

judiciously so as to obtain maximum exposure for all the products that

needs to be advertised in diff erent market segments. Market can be seg-

mented based on age and gender, race and nationality, education, occupa-

tion and income, marital status and living arrangements, activities and

interests, personality, preferences and opinion. So marketer of the product

divides the population of its potential adopters in to distinct groups of

consumers with common characteristics. This is done so that advertising

eff orts made by the fi rm target each segment of consumers distinctly. For

example, a fi rm can divide the potential market among kids, adults, aged

customers depending upon the kind of product it needs to advertise.

Most of the quantitative modelling tools that are available to solve

media planning problems are classifi ed as simulation, heuristic, or multi-

criteria decision-making models. These models use goal programming,

linear programming, analytical hierarchy process techniques etc. to obtain

satisfactory solution of the original problem. Few studies have explored

the confl icting media planning issues in terms of customer relationships,

advertising eff ects, and resource allocation. All these problems have con-

sidered all market segments alike. In reality each market segment is unique

and hence requires separate attention. In this paper we develop media

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OPTIMAL MEDIA SELECTION MODEL 63

selection model for multiple products in market with multiple segments.

A fi rm is considered which manufactures diff erent types of products

which can be catered to both industrial and domestic users. The products

considered are desktop, laptop, and printers/scanners. Since choice of

media depends on the kind of users, diff erent types of print media as well

as electronic media is considered for advertising. Magazines and newspa-

per form a part of print media whereas television and internet form a part

of electronic media. The aim is to determine the optimal number of ad-

vertisements in each media and allocate the advertising media budget to

selected media categories so as to maximize the total advertising reach to

customers for each product. The problem has been formulated as a multi-

objective programming problem and is solved through goal programming

technique. A real life example has been taken to validate the results.

The paper is organized as follows, literature review of various me-

dia allocation models have been given in section 2.1 Mathematical model

formulations for both the segments have been discussed in section 2.2

Solution methodology for the multi-objective programming problem has

been given in section 3. Case study has been discussed in section 4 to illus-

trate the solution methodology. Concluding remarks are made in section 5.

2. Model formulation

2.1. Literature review

Theoretical and empirical researches on advertising media selection

are extensive. Remarkable work in this direction was started by Charnes

et al. [2]. He introduced a GP model for media selection to address prob-

lems associated with the critical advertising measurement of frequency

and reach. Lee [9] considers a similar problem and use the goal program-

ming approach. The media selection models were also addressed using

MCDM modeling techniques. The study on improvements in media selec-

tion methods was based on generalized GP research by Kendall [6]. De

Kluyver [4] proposed the more realistic use of hard and soft constraints

for linear programming models used in media selection. Keown and Dun-

can [7] developed an integer GP model to solve media selection problems

and improve upon suboptimal results produced by linear programming

and non-integer GP models. The result provided examples of integer GP

formulations that overcome most of the limitations found in earlier linear

programming models. Hoff man et al. [5] identifi ed an approach to model-

ing the advertising planning process. They determined a test city’s critical

market characteristics that fi t most advantageously with the corporation’s

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marketing strategy. Lee and Kwak [10] has developed an information re-

source planning using an AHP based goal programming model. A linear

programming approach for determining optimal advertising policy by

Ching et al. [3] proposes advertising model which can capture the adver-

tising wear out phenomenon. The aim was to derive an optimal pulsa-

tion advertising strategy. The optimization problem was formulated as

linear programming problem. Their work was based on Mesak & Zhang

[11] who’ve derived optimal advertising pulsation policies through dy-

namic programming approach. Mihiotis and Tsakiris [12] reviewed the

recent study related to advertising planning. The study discussed the best

possible combination of placements of a commercial (channel, time, and

frequency) with the goal of the highest rating subject to constrained adver-

tising budgets. Kwak et al.[8] has presented a case study that resolve the

media selection process of dual market high technology products using a

mixed integer goal programming model .A chance constraints goal pro-

gramming model for the advertising planning problem by U.K. Bhattacha-

rya [1] presents a model which has been designed to decide the number

of advertisement in diff erent advertising media and the optimal allocation

of the budget assigned to the diff erent media. But these models ignore

the practical aspect of segmentation. In the following subsection, a model

has been developed which deals with determining the optimal number of

advertisements in each media and allocate the advertising media budget

to diff erent products in each segment, so as to maximize the customer

increase rate for each product.

2.2. Optimal media selection for multi product segmented market

Notations

,i m1 2f= segments

,j n1 2f= medium of advertising

, ,t T1 2 f= products

j :k media options of jth medium; jj ,k K1 2f=

:Zi expected advertising reach of ith segment

:fti expected advertising reach of tth product in ith segment

:rtij Expected customer increase rate of tth product in ith segment,

jth media

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:xijl decision variable corresponding number of advertisements in ith

segment, jth media; j

jK

x xk 1

j=

=ij ijkl /

:xjijk decision variable corresponding number of advertisements in ith

segment, jth media, kthj media option

:cjijk Unit cost of advertisement in ith segment, jth media, kth

j media

option

:ljijk Minimum number of advertisement in ith segment, jth media,

kthj media option

:ujijk Minimum number of advertisement in ith segment, jth media, kth

j

media option

:Bi Total advertising budget for ith segment

2.2.1. Problem formulation

The model formulation must provide a satisfying mix of advertis-

ing media expenditures that meet the maximization of advertising reach

objective for each type of product, while adhering to the limitations of

media resource availability in a segmented market. The problem of select-

ing appropriate media that will maximize the total advertising reach and

hence the expected customer increase rate for diff erent products that can

be marketed amongst diff erent segments using diff erent media can be for-

mulated as a mixed integer GP problem in the following general form as:

, , ..

, , ..

.

.

, , ..

f r x t T

f r x t T

f r x t T

1 2

1 2

1 2

Maximize

Z

Z

Z

j

n

j

n

j

n

1

1

1

1 1

2

t

t

m t tm

= = =

= = =

= = =

=

=

=

1

2

t

t

m

1

22

m j j

,

,

,

j

j

j

j

l

l

l

Z

[

\

]]]]]

]]]]]

_

`

a

bbbbb

bbbbb

/

/

/

(P1)

K

, ...B i mc x 1 2Subject to ijk ijkkj

n

11j j

j

j

6# ===

i//

j j

ij j

, ... ; , , .... ; , , ....

ijk

x l

x u

x

i m j n k K

0

1 2 1 2 1 2

& integers

ijk

ijk

k

j

j

j j6

$

#

$

= = =ijk

_

`

a

bb

bb

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Let the optimal value of Z i obtained on solving problem (P1) be Z *i .

Management sets its goals that needs to be achieve from all the products.

Since higher goals may not be met within the original budget hence even

the budget may be increased to meet higher goals. Incorporating the

required goals , the above problem can be written as the multi-objective

programming problem as

, , , ..

, , , ..

.

.

, , , ..

f x t T

f x t T

f x t T

r

r

r

1 2

1 2

1 2

Maximize

Z

Z

Z

'

j

n

t jj

n

j

tm jj

n

1

12

1

1

2

t

t

m t

= = =

= = =

= = =

=

=

=

t j

mj

i

22

m

11 l

l

Z

[

\

]]]]]

]]]]]

_

`

a

bbbbb

bbbbb

/

/

/

(P2)

j

, ...c x B i m1 2Subject to k

K

j

n

11j j

j

6# ===

iijkijk//

, , ...r x Z f t T1 2* *tij

j

n

16$ = =

=tiiijl/

, ... ; , , .... ; , , ....

x l

x u

x

i m j n k K

0

1 2 1 2 1 2

& integers

ijk

ijk

ijk

ijk

ijk

j

j

j j

j

j

j

6

$

#

$

= = =

_

`

a

bb

bb

This problem leads to an infeasible solution. In order to obtain a

feasible solution, goal programming approach may be used.

3. Solution methodology: Goal Programming

In a simpler version of goal programming, management set goals

and relative importance (weights) for diff erent objectives. Then an opti-

mal solution is defi ned as one that minimizes both positive and negative

deviations from set goals simultaneously or minimizes the amount by

which each goal can be violated. First we solve the problem using rigid

constraints only and then the goals of objectives are incorporated depend-

ing upon whether priorities or relative importance of diff erent objectives

are well defi ned or not.

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The problem (P2) can be solved in two stages as follows:

Stage 1

Minimize

j jj j

( , , ) ( )g n p x n p n p n pk

K

j

n

k

K

j

n

11 11

j j

= + + + + +== ==

i j ji ijk ijkijk ijk0l l^ ^h h// //

Subject to

j

j

ijk ijk , ,c x n p B i m1 2k

K

j

n

11

6 f+ - = ===

i i ij j//

u, ... ; , , .... ; , , ....

n p

n p

x l

xi m j n k K1 2 1 2 1 2

ijk

ijk

ijk ijk ijk

ijk ijk ijkj

j

j

jj j j

j j j

6+ -

+ -

=

== = =

l l3

egers&

,

,

int

, ... ; , , .... ; , , ....n p

n p

x

i m j n k K

0

0 1 2 1 2 1 2ijk

ijk

ijk

jj j

j j

j

j

6

$

$ = = =ijk

ijk

l l

_

`

a

bb

b

i,n p 0$i , ...i m1 26 =

Where j,n pijk ijkj

and j,n pijk ijkj

l l are the over and under-achievement (nega-

tive and positive deviational) variables of the goals for their respective

objective/constraints function. , ,n p xg0 ] g is goal objective function corre-

sponding to rigid constraints. Let , ,n p x0 0 0^ h be the optimal solution for

the problem (P3) and , ,g n p x0 0 00^ h be the objective function value then

fi nal problem can be formulated using the optimal solution of the problem

(P3) through the problem (P2).

Stage 2

Minimize

ti( , , )g n p x w n pt 1

3

= +=

titi^ h/

Subject to

j

ijk ijk ,c x n p B i m1 2k

K

j

n

11

j

6 f+ - = ===

ii ij j//

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, ... ; , , .... ; , , ....n p

n p u

x l

xi m j n k K1 2 1 2 1 2

ijk

ijk

ijk ijk ijk

ijk ijk ijkj

j

j

jj j j

j j j

6+ -

+ -

=

== = =

l l3

tij ij , ,r x n p f t T1 2j

n

16 f+ - = =

=i i tij j

*l/

egers&

, , ,

int, ; , , .... ; , , ....

n p n p

xi m j n k K

0

01 2 1 2 1 2

ijk ijk

ijkj

j j j j

jj 6 f$

$= = =

ijk ijkl l3

, , , ;,w n p t T w0 1 2 1,t T1

6 f$ = ==

ti ti ti ti/

, ,n p i m0 1 26 f$ =i i

( , , ) ( , , )g n p x g n p x0 0 0=0 0

(P3)

( , , )g n p x is objective function of the problem (P3) .Goal programming ap-

proach provides a compromise solution to the above problem.

4. Case problem

The company used for this case analysis is a leading computer fi rm,

producing and selling computers and its related accessories in both in-

dustrial as well as consumer market segments. The sources for the data

consist for historical advertising budget data in the fi rm. The name of the

company being studied is not released for confi dentiality. Three products

namely Desktops, Laptops, & Printers/scanners have been considered

which are being advertised through diff erent business publications, mag-

azines, newspapers, internet media, and spot television. Also there is a re-

striction on the minimum & maximum number of advertisements that can

be placed in a media. Preliminary media goal estimates has been assigned

using the method of expected customer increase rate of the company’s ma-

jor products. The main aim is to advertise in diff erent media so as to maxi-

mize the expected customer increase rate to the target segments within

its allowable budgets assigned for the diff erent media without violating

the maximum and minimum number of advertisements for various me-

dia. During research, experts were asked to give their views regarding the

relative importance of various constraint factors. Problem is formulated as

multi-objective programming problem. Expected customer increase rate &

advertising presence in diff erent publications have been provided in Table

4 & Table 5 of Appendix.

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Using the mentioned data, the linear programming problem to

maximize expected customer increase rate for industrial market subject to

the advertising cost budget constraint for three diff erent products (t = 1,2,3)

can be formulated as follows:

Maximize

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

Z

f x x x x x x x x

x x x x

f x x x x x x x x

x x x x

f x x x x x x x x

x x x x

4 3

4 4

7 5

2 6

10 5

3 2

1 =

= + + + + + + +

+ + + +

= + + + + + + +

+ + + +

= + + + + + + +

+ + + +

11 113 114 121 122 123 124

131 132 141 142

111 112 113 114 121 122 123 124

131 132 141 142

111 112 113 121 122 123 124

131 132 141 142

111 112

21

31 114

Z

[

\

]]]]

]]]]

_

`

a

bbbb

bbbb

Subject to

x x x x x x

x x x x x

x

290 320 360 350 250 310

220 210 600 540 490

410 3100000

113 121

#

+ + + + +

+ + + + +

+

111

124 131 132

142

112 114 122

123 141

; &S X 0X integers! $1 1 1

Where

, , , , , , , , , , ,X x x x x x x x x x x x x1 141 142= 111 112 113 114 123121 122 124 131 1326 @

; ; ; ; ; ;

; ; ; ; ;

; ; ; ; ; ;

; ; ; ; ;

; .

S

x x x x x x

x x x x x

x x x x x x

x x x x x

x x

18 12 6 6 52 52

300 300 1200 600 1800

2400 0

0 0 0 00 00

00 00

36 24 12 12 1 41 4 45 45 18 927 36

113 114 121

132 141

$ $ $ $ $ $

$ $ $ $ $

$ # # # # #

# # # # #

# #

=

131

122

142

1

111 112 122

123 124

142 111 112 113 114 121

123 124 131 132

141

R

T

SSSSSSS

V

X

WWWWWWW

(P4)

The optimal value of Z1 obtained on solving above problems be Z*1 . Then

21 31, ,Z f f f26545 33057 18280* *= = = =1 11* *7 A.

The management wants to set goals for a 5%, 5%, 10% increase in the

advertising reach for product 1, product 2 & product 3 respectively for

industrial users. These aspiration levels are set as objectives to be achieved

from diff erent products. Since the higher aspirations can not be achieved

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with the limited budget available hence an increased in the budget by 2%-

3% for both industrial users as well as domestic users is also suggested to

achieve the desired goals. With the increased aspiration levels and budget,

the above problem for industrial segment can be written as the multi-ob-

jective programming problem as

Maximize

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

( ) ( )

Z x x x x x x x x

x x x x x x x x

x x x x x x x x

x x x x x x x x

x x x x

4 3

4 4 7

5 2 6

10 5

3 2

1 = + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + +

111 112 113

111 112

111 112

114 121 122 123 124

131 132 141 142 113 114

121 122 123 124 131 132 141 142

113 114 121 122 123 124

131 132 141 142

Subject to (P5)

x x x x x x x

x x x x x

290 320 360 350 250 310 220

210 600 540 490 410 3200000

112

#

+ + + + + +

+ + + + +

111 113 114 121 122 123

124 131 132 141 142

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

x x x x x x x x

x x x x

x x x x x x x x

x x x x

x x x x x x x x

x x x x

4 3

4 4

7 5

2 6

10 5

3 2 20108

27873

34710

$

$

$

+ + + + + + +

+ + + +

+ + + + + + +

+ + + +

+ + + + + + +

+ + + +

131 142

132 142

111 112 113 114 121 122 123 124

132 141

111 112 113 114 121 122 123 124

131 141

111 112 113 114 121 122 123 124

131 132 141 142

; &XX S 0 integers1 1 1! $

Similarly for the consumer market segment, the linear programming

problem using the mentioned data to maximize the advertising reach sub-

ject to the advertising cost budget constraint can be formulated as follows:

Maximize

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

Z

f x x x x x x x x

x x x x

f x x x x x x x x

x x x x

f x x x x x x x x

x x x x

5 5

3 2

8 3

1 4

7 5

2 6

2

12 211 212 213 214 221 222 223 224

231 232 241 242

22 211 212 213 214 221 222 223 224

231 232 241 242

32 211 212 213 214 221 222 223 224

231 232 241 242

=

= + + + + + + +

+ + + +

= + + + + + + +

+ + + +

= + + + + + + +

+ + + +

Z

[

\

]]]]

]]]]

_

`

a

bbbb

bbbb

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Subject to

x x x x x x

x x x x x

280 320 370 330 260 250 220

210 620 600 400 460 3100000

211 212 213 214 221 222 223

231 232 241 242224 #

+ + + + + +

+ + + + +

; &X S 0X integers2 2 2! $

Where

, , , , , , , , , , ,X x x x x x x x x x x x x2 211 212 213 214 221 222 223 224 231 232 241 242= 6 @

; ; ; ; ; ;

; ; ; ; ;

; ; ; ; ;

; ; ; ; ;

;

S

x x x x x x

x x x x x

x

x x x x x

x x x x x

x x

18 12 6 6 52 52

300 300 1200 600 1800

2400

30 20 12 12 100

100 450 450 1800 900

2700 3500

214

224

242

$ $ $ $ $ $

$ $ $ $ $

$

# # # # #

# # # # #

# #

=2

213 214 221 222

224 231 232 241

242

211 213 221

222 223 232

241

211 212

223

212

231

R

T

SSSSSSSSS

V

X

WWWWWWWWW

(P6)

The optimal value of Z2 obtained on solving above problems be Z *2 . Then

22, ,Z f f f17545 21067 32633* * * *= = = =2 12 327 A.

Similarly setting 8%, 5%, 4% increase in the advertising reach for

product 1, product 2 & product 3 respectively for domestic users, the above

problem can be written as the multi-objective programming problem as

Maximize

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

( ) ( )

Z x x x x x x x x

x x x x x x x x

x x x x x x x x

x x x x x x x x

x x x x

5 5

3 2 8

3 1 4

7 5

2 6

2 211 213 214 221 222 223 224

231 232 241 242 211 212 213 214

221 222 223 224 231 232 241 242

211 212 213 214 221 222 223 224

231 232 241 242

= + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

+ + + +

212

(P7)

Subject to

x x x x x x x

x x x x x

280 320 370 330 260 300 220

210 620 600 400 460 3160000

211 212 213 214 221 222 223

224 231 232 241 242 #

+ + + + + +

+ + + + +

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( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

x x x x x x x x

x x x x

x x x x x x x x

x x x x

x x x x x x x x

x x x x

5 5

3 2 18949

8 3

1 4 22121

7 5

2 6 33939

221

211 212 213 214 221 222 223 224

231 232 241 242

211 212 213 214 222 223 224

231 232 241 242

211 212 213 214 222 223 224

231 232 241 242

$

$

$

+ + + + + + +

+ + + +

+ + + + + + +

+ + + +

+ + + + + + +

+ + + +

221

; &XX S 0 integers2 2! $2

Problems (P5) & (P7) when solved provide an infeasible solution. There-

fore in order to obtain a compromised feasible solution to the problems,

goal programming approach is used.

3. Solution Procedure: Goal Programming

For industrial users

Stage 1Maximize

( , , )g n p x n n n n n n n

n n n n

p p p p p p p p p

p p p

= + + + + + +

+ + + + +

+ + + + + + + +

+ + + +

111 112 113 114 121 122

124 132 141 142

132

123

114 121 122 123 124 131

142

111 112 113

141

0

Subject to

n p

x x x x x x

x x x x x x

290 320 360 350 250 310

220 210 600 540 490 410

3200000#+ -

+ + + + +

+ + + + + +

111

124 131123 132

112 113 114 121 122

141 142

1 1

;

; ;

;

p

n p

n

x

x

300

1800 2400

1200

- =

+ - =

+

; ; ;p p pn n nx x x900 2700 3600- = - = - =+ + +

; ;

; ;

;

;

; ;

; ;

; ;

;

;

;

;

p p

x n p p

p p

p p

p p

x n p p

p p

n p n n

n p n

n n

n n

n p n n

n p n

n n n p

x x x

x x

x x

x x

x x x

x x

x x x

12 6

6 52

300

600

24 12

12 104

450 450

18

52

36

104

1800

- = - =

- - = - =

- = - =

- = - =

= - = - =

+ - = - =

- = - =

+ - = + +

+ - = +

+ +

+ +

+ - + +

+ - = +

+ + + - =

111

111

113

121

123 12 131

113

121

123 12 131

111 112 112 112 113 113

114 114 122 122 122

123 123 12 12

132 132 132 1

111 112 112

114 122 122 122

123 123 12 12

132 132 132 1

141

141

111

114 121

131 131

141 141 142 142

112 113

114 114 121

131 131

141 141 142 142

121

111 113

121

4

4

4 4

4

4 4

4

2

2

l l l l l l

l l l l l l

l l l l l l

l l l l l l

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, ,& n pX 0 integers 0$ $1 1 1

j j

j j,

,

; , , , ; , , .. ; , , .. ;

, ; ,

pn

n p

i j k k

k k

0

0

1 1 2 3 4 1 2 4 1 2 4

1 2 1 21 2

3 4

6$

$

= = = =

= =ijk ijk

ijk ijkl l3 (P8)

Stage 2

Maximize

( , , )g n p x w n w n w n= + +21 21 3111 11 31

Subject to

n

x x x x x x

x x x x x x

290 320 360 350 250 310

220 210 600 540 490 410

3200000+ =

+ + + + +

+ + + + + +

111

124 131123 132

112 113 114 121 122

141 142

1

;

; ;

;

p

px

x

300

1800 2400

1200

- =

- =

; ; ;n n nx x x900 2700 3600= = =+ + +

; ;

; ;

;

;

; ;

; ;

; ;

;

;

;

;

;

p p

x p p

p p

p p

x n

p

p

n n n

n n

n n n

x x x

x x

x x

x x

x x x

x x

x x x

12 6

6 52

300

600

24 12

12 104

450 450

18

52

36

104

1800

- = - =

- = - =

- = - =

- = - =

= = =

+ = =

= =

- =

- =

+ + +

+ = +

+ + + =

111

111

113

121

123 12 131

113

121

123 12 131

111 112 112 113

114 122 122

123 12

132 132 1

112

114 122 122

123 12

132 132

141

141

114 121

131

141 142

112

114

131

141 142 142

111 113

121

4

4

4

4

4

2

l l l

l l l

l l l

l l l

( ) ( )

( ) ( )

x x x x x x x x

x x x x n p

4 3

4 4 27873

+ + + + + + +

+ + + + + - =11

112 113 11

131 132 141 142

111 121 122 123 124

11

4

21

( ) ( )

( ) ( )

x x x x x x x x

x x x x n p

7

2 6

5

34710

+ + + + + + +

+ + + + + - =

112 113 11

131 132 141 142 12

111 121 122 123 1244

j j

j j,

,

; , , , ; , , .. ; , , .. ;

, ; ,

pn

n p

i j k k

k k

0

0

1 1 2 3 4 1 2 4 1 2 4

1 2 1 21 2

3 4

6$

$

= = = =

= =ijk ijk

ijk ijkl l3 (P9)

, , , , , , ;, ,& n n n p p p w w wn pX 0 10 integers $$ + + =1 1 21 11 21 3131 111 11 21 31

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For domestic users

Stage 1

Maximize

( , , )g n p x n n n n n n n

n n n n n p

= + + + + + +

+ + + + + +231 242

211 212 213 214 221 222 223

224 232 241 2

0

Subject to

2n p

x x x x x x

x x x x x x

280 380 310 330 260 250

220 210 620 600 400 410

3160000+ -

+ + + + +

+ + + + + +

=

11

24

2

2 31 232 2

212 213 214

2232

22

41 242

221 2

2

;

; ;

;

p

px

x

300

1800 2400

1200

- =

- =

242

231

; ;n n nx x x900 2700 3 00= =+ + +2

; ;

; ;

;

;

; ;

; ;

; ;

;

;

;

;

;

p p

x p p

p p

p p

x n

p

p

n n n

n n

n n n

x x x

x x

x x

x x

x x x

x x

x x x

12 6

52 52

300

600

20 12

12 100

450 450

5

18

52

30

100

1800

231

224

- = - =

- = - =

- = - =

- = - =

= = =

+ = =

= =

=

+ =

- =

+ + +

+ = +

+ + + =

222 222

211

211 213

2

213

223 22

221

223

212 212 13

122 122

223 22

232

214 222 222

223 2

232 241

241

211 2

221 221

232 241 242

212

214

231 231

232 41 242 242

211 212 213

221

4 4

4

l l l

l l l

l l l

l l l

, ,& n pX 0 integers 0$ $2 2 2

j j

j j,

,

; , , , ; , , .. ; , , .. ;

, ; ,

pn

n p

i j k k

k k

0

0

2 1 2 3 4 1 2 4 1 2 4

1 2 1 21 2

3 4

6$

$

= = = =

= =ijk ijk

ijk ijkl l3 (P10)

Stage 2

Maximize

12( , , )g n p x w n w n w n= + + 32 322212 23

Subject to

2

2 2 2 2 2

2 2 22

n

x x x x x x

x x x x x x

280 320 370 330 260 300

220 210 620 600 400 460

3160000+ =

+ + + + +

+ + + + + +

211

2423 232

12 13 14 21 22

31 41 42

2

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;

; ;

;

p

px

x

300

1800 2400

1200

- =

- =

242

231

; ;n n nx x x900 2700 3 00= =+ + +2

; ;

; ;

;

;

; ;

; ;

; ;

;

;

;

;

;

p p

x p p

p p

p p

x n

p

p

n n n

n n

n n n

x x x

x x

x x

x x

x x x

x x

x x x

12 6

52

300

600

20 12

12 100

450 450

5

18

6 52

30

100

1800

231

- = - =

- = - =

- = - =

- = - =

= = =

+ = =

= =

=

+ =

- =

+ + +

+ = +

+ + + =

211

211 213

213

223 22

221

223

212 212 13

22

223 22

232

214 222 222

223 224 22

232 241

221 222 2

241

211 2

232 241 242

212

214

231 231

232 41 242 242

214 241

211 212 213

221

221

4 4

4

l l l

l l l

l l l

l l l

2

( ) ( )

( ) ( )

x x x x x x x x

x x x x n p

5 5

3 2 18949

+ + + + + + +

+ + + + + - =

212

2 12

213 214

232 41 42

211 221 222 223 224

231 12

2

( ) ( )

( ) ( )

x x x x x x x x

x x x x n p

8 3

1 4 22121

+ + + + + + +

+ + + + + - =

212 213 214

232 41 242 22

211 221 222 223 224

231 22

2

( ) ( )

( ) ( )

x x x x x x x x

x x x x n p

7 5

2 6 33939

+ + + + + + +

+ + + + + - =

212 213 214

232 41 242 23 3

211 221 222 223 224

231 2

j j

j j,

,

; , , , ; , , .. ; , , .. ;

, ; ,

pn

n p

i j k k

k k

0

0

2 1 2 3 4 1 2 4 1 2 4

1 2 1 21 2

3 4

6$

$

= = = =

= =ijk ijk

ijk ijkl l3 (P11)

32, , , , , ,, ,& n n n p pn p pX 00 integers $$2 2 22 322 12 12 22

w w w 1+ + +12 22 32

4. Numerical Illustration

Two diff erent print media (newspapers and magazines), T.V channels

& websites have been chosen for two types of users (industrial & domes-

tic). Also due weightages are given to diff erent products in each category

Table 1Expected vs Obtained Percentage increase in advertising reach

Product Industrial users Domestic users

Expected Obtained Expected Obtained

Desktops 5%-6% 4.6% 6%-8% 7.5%

Laptops 5%-6% 6% 5%-6% 4.6%

Printers/scanners 8%-10% 10% 4%-5% 4.2%

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Table 2Advertising reach & budget for diff erent products when equal

importance is attached to all the products

Industrial users Domestic users

. , . , .W W W33 33 33= = =2 31 . , . , .W W W33 33 33= = =2 31

Reach Budget Reach Budget

Desktops 27774 26291

Laptops 35082 3199980 32633 3099970

Printers 20118 17765

Table 3Allocation of advertisements to diff erent media when equal importance

is attached to all products

Segments Industrial users Domestic users

Publications Name Variable Frequency Variable Frequency

W1 = .33, W2 = .33, W1 = .33, W2 = .33,

W3 = .33 W3 = .33

Magazine Magazine 1 x111 36 x211 20

Magazine 2 x112 24 x212 12

Magazine 3 x113 12 x213 6

Magazine 4 x114 12 x214 6

Newspaper Newspaper 1 x121 104 x221 52

Newspaper 2 x122 70 x222 52

Newspaper 3 x123 450 x223 300

Newspaper 4 x124 450 x224 301

Television Channel 1 x131 1200 x231 1200

Channel 2 x132 600 x232 600

Website Website 1 x141 1800 x241 1800

Website 2 x142 2454 x242 2400

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of users and their respective individual reach & budgets have been shown

in Table 2. Comparison of expected vs. Obtained percentage increase in

advertising reach is given in Table 1.The total budget allocated initially

both for segment1& segment2 was Rs 31,00,000. With an increase in bud-

get of 2% & 3% for domestic users & industrial users respectively, alloca-

tion of advertisements to diff erent media are shown for the case when

equal weightages were assigned to diff erent products in Table 3. Problem

is solved using optimization software LINGO.

5. Conclusion and further interpretation

In this paper media selection model is developed for multiple prod-

ucts that need to accommodate diff erent market segments. The aim is to

maximize the total customer reach for all the products in multiple seg-

ments. The problem is solved through goal programming technique. A

real life example has been taken to validate the results.

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Tabl

e 4

Expe

cted

cus

tom

er in

crea

se ra

te (%

)

Pro

du

ct c

lass

In

du

stri

al

use

rs

Do

mes

tic

use

rs

M

ag

azin

e

New

spap

er

Inte

rnet

T

V

To

tal

M

ag

azin

e

New

spap

er

Inte

rnet

T

V

To

tal

Des

kto

ps

4

3

4

4

15

5

5

3

2

15

Lap

top

7

5

2

6

20

8

3

1

4

16

Pri

nte

rs/

Sca

nn

ers

10

5

3

2

19

7

5

2

6

20

App

endi

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Tabl

e 5

Adv

ertis

ing

pres

ence

in p

ublic

atio

ns fo

r diff

ere

nt s

egm

ents

S

egm

ents

In

du

stri

al

use

rs

Do

mes

tic

use

rs

Un

it c

ost

U

nit

co

stP

ub

lica

tio

ns

N

am

e V

ari

ab

le

Fre

qu

ency

ran

ge

(’

00)

Vari

ab

le

Fre

qu

ency

ran

ge

(’

00)

Mag

azin

e

Mag

azin

e 1

x111

(18,3

6)

290

X211

(18,3

0)

280

M

ag

azin

e 2

x112

(12,2

4)

320

x212

(12,2

0)

320

M

ag

azin

e 3

x113

(6,1

2)

360

x213

(6,1

2)

370

M

ag

azin

e 4

x114

(6,1

2)

350

x214

(6,1

2)

330

New

spap

er

New

spap

er 1

x

121

(52,1

04)

250

x221

(52,1

00)

260

N

ewsp

ap

er 2

x

122

(52,1

04)

310

x222

(52,1

00)

250

N

ewsp

ap

er 3

x

123

(300,4

50)

220

x223

(300,4

50)

220

N

ewsp

ap

er 4

x

124

(300,4

50)

210

x224

(300,4

50)

210

Tel

evis

ion

C

han

nel

1

x131

(1200,1

800)

600

x231

(1200,1

800)

620

C

han

nel

2

x131

(600,9

00)

540

x232

(600,9

00)

600

Web

site

W

ebsi

te 1

x

141

(1800,2

700)

490

x241

(1800,2

700)

400

W

ebsi

te 2

x

142

(2400,3

600)

410

x242

(2400,3

500)

460

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Received August, 2011

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An optimal advertising media selection model for promotion of multiproducts in segmented market

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