selection of the optimum promotion mix

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Selection of the optimum promotion mix by integrating a fuzzy

linguistic decision model with genetic algorithms

Tsuen-Ho Hsu a,*, Tsung-Nan Tsai b, Pei-Ling Chiang a

a Department of Marketing and Distribution Management, National Kaohsiung First University of Science and Technology, No. 2, Jhuoyue Road,

Nanzih District, Kaohsiung City 811, Taiwanb Department of Logistics Management, Shu-Te University, Kaohsiung 82445, Taiwan

a r t i c l e i n f o

Article history:

Received 5 September 2007

Received in revised form 2 September 2008

Accepted 11 September 2008

Keywords:

Integrated marketing communication

Promotion mix

Linguistic variable

Genetic algorithms

Decision-making

a b s t r a c t

Integrated marketing communication (IMC) is an important process by which a company

can influence a target market, improve the position of that company’s product/service in

the target market, and effectively build up its brand image. Sales promotion is an important

communication channel designed to influence the customer’s purchasing behavior in the

target market. There are many promotion tools available. Variations in business objectives

and budgetary limits make it impossible for a company to employ all these promotion tools

to convey sales messages to the customers. The selection of the best mix of promotion tools

involves subjective information processing, instead of a numerically expressed objective

decision-making process. In this research, we integrate a fuzzy linguistic decision model

with a genetic algorithm (GA) to extract the optimum promotion mix of a variety of tools

under satisfying expected marketing performance and budget limitations. The proposed

methodology shows satisfactory results in an empirical study in terms of estimating the

degree of satisfaction for achieving the business objectives, determining the optimum pro-motion mix, and minimizing expenditure on sales promotion activities.

2008 Elsevier Inc. All rights reserved.

1. Introduction

Traditional marketing studies show that the effects of promotion activities do not explicitly alter the consumer’s product

preference [6,30]. However, 60% of senior American marketing executives claim that the integrated marketing communica-

tion (IMC) is an important factor affecting the outcomes of marketing strategies [7] and can help a company to position their

products/services in touch with the target market, and effectively build up brand image [22]. Promotion activities form an

important channel for a company to communicate with potential customers, and ultimately influence customer purchasing

behavior in the target market. Recent studies have shown that the employment of promotion activities has had significantimpact on the underlying competitive market structure in many markets [11].

Research reveals that many companies use sales promotions to increase sales volume, strengthen consumer loyalty,

encourage customers to switch to their firm, and strengthen brand associations [1,22,24]. Most consumers expect to partic-

ipate in sales promotion activities and take advantage of products/services what they needed. Thus, the appropriate promo-

tion tools or the combination of such tools can considerably alter consumer purchasing behavior. However, the use of

promotion tools for sending messages and communicating with customers may not be completely effective or efficient.

In addition, for many companies, spending on sales promotions accounts for a major part of the marketing communication

expenditures.

0020-0255/$ - see front matter 2008 Elsevier Inc. All rights reserved.doi:10.1016/j.ins.2008.09.013

* Corresponding author. Tel.: +886 7 6011000x4217; fax: +886 7 6011043.

E-mail address: [email protected] (T.-H. Hsu).

Information Sciences 179 (2009) 41–52

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To maximize company profits by finding the best-selling strategy, the company needs to select the optimum promotion

mix to fulfill its business objectives within promotion budgetary limits [4,13]. To select promotion tools, it is essential for

marketing managers to understand the consequences of changes in promotion strategies. Specifically, managers would like

to know whether a promotion method will shift the pattern with their competition or not, they would like to understand the

impact of promotions on the market, and they would like to know how to manage or combine related promotion tools. In

other words, identifying both components, the promotion methods and promotion mix, based on consumer preference,

while satisfying the desired marketing performance and staying within in the planned budget is indeed necessary.

In the past, judgment-oriented or data-oriented methods have most often been used to determine the most appropriate

promotion tool mix [3,4,15]. However, these methods can neither show in advance the customer value of each promotion

mix nor take into account budget limitations for promotion activities. Additionally, the selection of a promotion mix usually

involves the processing of vague and uncertain information, instead of numerical expressions or objective decisions. To over-

come these problems, we develop a linguistic decision model capable of manipulating the uncertainty and vagueness linked

to the determination of the most advantageous promotion mix, since most of the methods for solving decision-making prob-

lems are with experts’ linguistic information which is represented as the linguistic variable [17]. Compared with traditional

numerical and subjective methods, the proposed model employs a linguistic weighted aggregation (LWA) operator [12,33] to

obtain the final degree of linguistic importance for each business objective, to estimate the degree of satisfaction for achiev-

ing business objectives, and to identify budget limits for each promotion mix. The genetics algorithm (GA) is a robust and

flexible method for a variety of optimization problems. The GA can cope with decision-making attribute interactions and

optimization problem to maximize the degree of satisfaction related to the achieving of business objectives, the fitness of

the business objective, and the fitness of the promotion mix.

2. Promotion mix management

Over the years, with the maturing of the retailing market, the number of competitors has been growing, and competition

in the market environment is becoming more rigorous. Sales promotion is a frequently used marketing strategy for a com-

pany to retain competitive advantage. The five major promotion tools often used in marketing are: advertising, personal

sales, sales promotions, direct marketing, and public relations [19]:

(i) Advertising : Advertising should be paid for, show the sponsor’s name, and allow for a non-personal presentation of

ideas, goods, or services. Messages are usually conveyed through television, internet, magazines and other media to

the target market [29]. When a company wants to disseminate new product information or build its own brand name,

television is probably the most powerful tool for commanding customer attention through images and sound [27];

however, when a company desires to send a sale message to regional customers, newspapers are a good choice.

(ii) Sales promotions: Sales promotions utilize diverse short-term techniques to induce customer awareness, with the goalof interesting customers to purchase products or services. For short-term retailing market, sales promotion is a pow-

erful tool, tempting customers to make impulse purchases. They tend to add an extra buying motive, encourage the

customer to buy other non-promoted products, and ultimately, reduce inventory level [14,21].

(iii) Direct marketing : In the direct marketing strategy, products/services are launched to the target market directly,

through which, there could be timely buying, selective contacts, savings of time, and an increase in convenience [26].

(iv) Personal selling : Personal selling is where the salespeople communicate with the customers in the target market. It has

the advantages of two-way communication, sending sale messages to the customers, and ultimately, decrease cus-

tomer resistance. In spite of these merits, the expenses involved in the personal selling technique are high. In addition,

personal selling has small message coverage, and sometimes, the sales message may be inconsistent [3].

(v) Public relations: Public relations can help a company build a communicable, understandable, acceptable, and cooper-

ative relationship with consumers. Generally, a company that is perceived as devoted to protecting the environment,

donating money to charitable organizations, obeying the law, or doing something good for the community, or utilizes

other public relations activities to enhance goodwill, tends to have a brand name that attracts new customers, andstrengthens customer loyalty, ultimately increasing profits [3].

The use of promotion tool combinations is usually based on marketing strategy. Using different promotion tools for deliv-

ering messages to customers can result in varied responses. For example, if a company desires to enhance its competitive

strength and short-term operating profits, price-oriented sales promotion is a good option [22]. If a company wants to

strengthen brand recognition, accelerate brand proliferation, and change consumer shopping patterns, advertising methods

can be adopted [22,25].

3. Genetic algorithms

GA is a robust parallel search technique, inspired by the mechanisms involved in natural selection and genetics in biolog-

ical systems [9]. GA differs from conventional search techniques which simultaneously evaluate many points rather than

searching in a point-to-point manner across the solution space, and it can deal with high-dimensional, multimodal and

42 T.-H. Hsu et al. / Information Sciences 179 (2009) 41–52


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complex problems and can accommodate itself to a changing situation. GA is more likely to converge towards a global solu-

tion [8,9].

Following the genetics terminology, each GA modeling parameter is a gene and the complete set of parameters is a chro-

mosome. The GA searching process begins with a set of candidates (initial population) based on a predefined number of

modeling variables. The different points in the search space are the different individuals of the population when using a

GA to solve the optimization problems [28]. A GA model usually has several generations and a constant population size

of parameter sets. The modeling parameter set is evaluated through an objective function to approach its fitness value.

The subsequent generations are then formed from the parent population using the modeling parameter sets having higher

fitness values. Offspring are successively bred through the processes of selection, crossover and mutation. The GA algorithm

can be expressed as the following pseudo-codes:

BEGIN GA

Randomly choose the initial population

Evaluate the fitness of each individual in the population

Do

1. Select the best-ranking individuals for reproduction

2. Produce a new generation using crossover and mutation to generate the offspring

3. Evaluate the individual fitness of the offspring

4. Replace the worst individuals in the population with the offspring

When the optimization criteria are met

Output the best solution

END GA

An initial population is chosen to generate the initial modeling parameter sets at the beginning of GA searching process. A

random method is frequently used to choose the initial population from which the modeling parameters are randomly gen-

erated without a priori knowledge for searching the optimum parameter set. A selection process determines the modeling

parameter sets in the current generation which will participate in producing new parameter sets for the next generation. The

parameter sets with the highest fitness value have the higher possibility of engaging in propagating new parameter sets.

The crossover operator can devise new offsprings by exchanging the chromosomes of the two parents. The three most fre-

quently used crossover approaches are: one-point crossover, two-point crossover and uniform crossover. Both one-point and

two-point crossover operators switch the chromosomes of the two parents at therandomly selected points of thetwo parents.

The uniform crossover operation depends on the random selection of individual genes from the two parents and not on the

parts of the chromosome. The mutation operator adds variability to the selected parents obtained from the crossover stage. Inthe binary coding scheme, mutation changes the encoded genes by changing 0s to 1s at randomly chosen locations on the

encoded chromosome. In this study, we employ the uniform crossover operation and binary coding in the mutation process.

In last decade, GA has received considerable interests in many fields. In business instances, GA has been used for sales

promotion design problems [13,25], multi-objective optimization problems [28], dynamic probability classification prob-

lems [23], distribution planning supply chain management [1], market segmentation methodology and management

[16,31], personnel assignment problems [32], optimization of new product positioning [10], and assessing the influence

and timing of pricing activities [18]. In this study, GA is applied to determine the optimum promotion mix with respect

to the degree of satisfaction in meeting business objectives, the fitness of the business objectives, and the budgetary limits.

4. Proposed methodology

Eliciting the optimum promotion mix is not straightforward. Firstly, we interviewed marketing experts working for

department store C in southern Taiwan. The purpose of the interviews was to acquire marketing knowledge, so as to under-

stand the essentials and the definitions of business objectives, the promotion tools, and the amount of investment required

for a promotion activity. Then, a linguistic decision model was formulated to determine the degree of satisfaction in terms of

achieving business objectives and the fit of the business objectives. The GA was found to outperform other methods (e.g.

simulated annealing for both constrained and unconstrained optimization problems) in terms of optimization performance

[20]. The GA optimization approach also effectively outperformed the hill climbing and simulated annealing approaches for a

complex system problem. Specifically, GA provided a lower cost solution with less variability in the results [5]. Accordingly,

the proposed GA algorithm is used to find the optimum promotion mix for the minimum expenditure, while satisfying ex-

pected marketing performance and budgetary limits, as illustrated in Fig. 1. For ease of reference, the notations used in this

and the remaining sections are listed below:

ok the kth business objective for a specific promotion program

o the set of business objectives selected for a specific promotion program

ak the linguistic weight of the kth business objective

T.-H. Hsu et al. / Information Sciences 179 (2009) 41–52 43


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n the number of promotion tools

nk the kth promotion tool

nhij the linguistic valuation of promotion tool h for business objective j making i insertion times

c hi the cost of i insertions of promotion tool h

T the promotion budget limitS h the investment amount for the hth promotion toolH h the number of insertions made for the promotion tool h

C hH h the investment level on the hth promotion tool with the H ht j the maximum level to achieve business objective j g j the maximum satisfaction degree of achieving business t j

T s the total cost of an adopted promotion mix

4.1. Research limitations and assumptions

This study is conducted based on the following assumptions:

(i) This research is limited to promotion activities for department stores located in southern Taiwan.

(ii) The marketing and promotion knowledge used by the department stores is derived from interviews with marketing

experts. Domain experts are supposed to provide sufficient knowledge and evidence to accommodate the marketing

trend.

(iii) The specific customer needs, company budget, and the business goals for a promotion activity acquired from the mar-

ket managers are assumed to be practical.

(iv) The study is limited to promotion tools normally employed by department store C, including advertising, personal

sales, sales promotion, direct marketing and public relations.

4.2. The definitions of business objectives and promotion mix

(i) The definition of business objectives: The business objectives, which include such items as increasing the sale volume,

attracting new customers, increasing market share, and strengthening brand loyalty, must be defined first. Suppose k

busi-

ness objectives are selected for a particular promotion program, formulated as follows:

Consultingwith experts

Derive the weights of promotion tools and

objectives

Randomly initializefirst population

Decode andevaluate the fitness

function

Selection

Crossover

Mutation

Set GAcondition

Satisfy“stop”

condition? Satisfaction degreeof achieving objective

Budget planning

Fitness of promotion mix

Overall evaluationof promotion mix

Linguistic decision model

Selecting the optimumpromotion mix

GA

s e ar c h

Fitness of objective

Yes

No

Fig. 1. The development flow for searching the optimum promotion mix.



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o ¼ ðo1; o2; . . . ; okÞ: ð1Þ

A company sometimes has several business objectives, although the importance of each objective may not be equal. The

nine linguistic weight labels (W ) in Eq. (2) are used to indicate the level of importance of each objective [13], followed by the

derived linguistic weights for k objectives, as shown in Eq. (3)

W ¼ fEssential; Very High; Fairly High;High;Moderate; Low; Fairly Low;Very Low;Unnecessaryg; ð2Þ

a ¼ ða1;a2; . . . ;akÞ; ai 2 W : ð3Þ

A triangular fuzzy number is designated within an interval (0,1) and denoted as (l/m, m/u) or (l, m, u) to represent the mem-bership degree. The parameters l, m, and u indicate the smallest possible value, the most promising value, and the largest

possible value. These three values are used to describe an event with a fuzzy condition. Thus, the linguistic labels illustrated

in Eq. (2) can be transformed into fuzzy numbers as listed in Table 1. The membership function is depicted in Fig. 2.

(ii) The definition of the promotion mix: To formulate a promotion mix, a company selects different promotion tools for

sharing messages with customers. A promotion mix consisting of different promotion tools can be defined as

n ¼ ðn1; n2; . . . ; nkÞ; ð4Þ

where n denotes the number of promotion tools.

After determining the promotion tools, the company is concerned with the degree of satisfaction for each business objec-

tive associated with the number of tools inserted (the number of times a promotion tool is applied). Eq. (5) can be used to

evaluate the degree of satisfaction for each business objective:

n1 ¼n

1

11 n1

12 n1

1k

.

.

.

.

.

.

.

.

.

n1m1 1 n1m1 2

nnmnk

0BB@

1CCA; n1ij 2 W ;

.

.

.

nh ¼

nh11 nh12 n

h1k

.

.

.

.

.

.

.

.

.

nhmn1 nhmn2

nhmnk

0BB@

1CCA; nhij 2 W ;

ð5Þ

where nhij is the linguistic value of the promotion tool h for objective j using i insertions; mi, . . . , mn represents the maximum

number of tool insertions.

Now, the company has to estimate the cost (investment) needed for each promotion tool. The more promotion tools used

by a company, the higher the marketing expenditure will be. Therefore, the company needs to appropriately control the

amount of investment for promotion, as illustrated in Eq. (6):

c 1 ¼ ðc 11; c 12; . . . ; c

1m1Þ;

.

.

.

c h ¼ ðc h1; c h2; . . . ; c

hmnÞ;

c hi 2 R; ð6Þ

where c hi represents the cost of i insertions of tool h.

A possible promotion mix (S ) is illustrated in Eq. (7)

S ¼ ðS 1; S 2; . . . ; S nÞ: ð7Þ

Finally, the total investment for initiating a promotion mix cannot exceed the company’s budgetary limit T 0; that is, it must

satisfy Eq. (8)

Table 1

The linguistic labels

Labels Linguistic terms Fuzzy number

E Essential (s8) (0.875, 1, 1)

VH Very High (s7) (0.75, 0.875, 1)

FH Fairly High (s6) (0.625, 0.75, 0.875)

H High (s5) (0.5,0.625, 0.75)

M Moderate (s4) (0.375, 0.5, 0.625)

L Low (s3) (0.25, 0.375, 0.5)

FL Fairly Low (s2) (0.125, 0.25, 0.375)

VL Very Low (s1) (0, 0.125,0.25)

U Unnecessary (s0) (0, 0, 0.125)


http://-/?-http://-/?-


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Xnh¼1

S h 6 T and C hHh ¼ S h; ð8Þ

where S h denotes the investment level for the kth promotion tool; H h is the number of tool insertion; C hHh is the cost of using

promotion tool h for h times of insertion.

4.3. The linguistic decision model

Linguistic terms are used in the decision model to indicate the degree of satisfaction for each business objective, and to

justify the cost of the promotion mix. This is followed by a GA searching process to extract the optimum promotion mix for a

variety of tool combinations. The procedure is described in details below:

(i) The degree of satisfaction for achieving business objectives: A company uses several promotion tools to achieve its business

objectives in the core market, but inserting different promotion tools into a promotion program can produce unequal effects,

or give consumers an inconsistent message. Therefore, the satisfaction degree for achieving business objectives must be eval-

uated first, and the maximum level of business objective achievement is identified as in Eq. (9):

t j ¼ MAXðn1H 1 j

;n2H 2 j; . . . ; nhH k j

Þ; j ¼ 1; . . . ; k; ð9Þ

where nhH h j

represents the degree of satisfaction achieved for the jth business objective using promotion tool h with insertion

H h.

(ii) The fitness of the business objective: To evaluate the fitness of the business objective, the maximum level of satisfaction

achieved for the business objective (t j) is compared with the importance of the business objective (a j), as in Eq. (10)

g j ¼ minða j; t jÞ; j ¼ 1; . . . ; k: ð10Þ

(iii) The fitness of the promotion mix: The linguistic ordered weighted averaging (LOWA) operator with the linguistic quan-

tifier ‘‘most” is used to evaluate the fitness of promotion mix. The fitness weights are obtained by using the fuzzy linguis-

tic quantifier Q [34,35]

Z s ¼ /Q ðminða1; t 1Þ; . . . ; minðak; t kÞÞ

¼ /Q ð g 1; g 2; . . . ; g kÞ;ð11Þ

where /Q is the LOWA operator.

4.4. The GA search process

Two decision-making rules are made and engaged in the GA search process for selecting an optimum promotion mix: (i)

the investment for a promotion mix; and (ii) the evaluation of the promotion mix.

(i) The investment for the promotion mix: A company usually specifies a certain budget for a promotion activity and gives

the constraint that the total cost (T s) for an adopted promotion mix cannot exceed the planned budget (T )

Xkh¼1

S h ¼ T s; and T s 6 T ; ð12Þ

where T is the budgeted limit.

(ii) The evaluation of the promotion mix:

The GA searching process determines the optimum promotion mix according to

the goal objective and the cost of every adopted promotion mix is illustrated in Eq. (13). The expression is justified to obtain

0.4 0.6 0.9

0.6

1

0.1 0.2 0.3 0.5 0.7 0.8 1

0.8

0.4

0.2

0

U VL FL L M H FH VH E

0

Fig. 2. The membership function.



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the maximum objective satisfaction and the minimum promotion cost. If promotion mixes S 1 and S 2 are the two candidate

promotion mixes, if the cost for S 1 is less than that of S 2, then S 1 is chosen.

Z s1 > Z s2 or Z s1 ¼ Z s2; and T s1


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5.3. Linguistic decision model

The degree of importance of each business objective is listed in Table 2 and the budget limit for each promotion tool is

illustrated in Table 3. The information in Tables 2 and 3 is used to generate three importance weights: (1) the maximum

Table 4

Prize

Prize/

insertion

Investment

(10,000)

Satisfaction degree of achieving business objectives

Enhancing sales

volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 72 E VH FH FH VH FH



Table 5

Catalog

Catalog/

insertion

Investment

(10,000)


Enhancing sales

volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 35 E E E M M E

2 39 M M M M M M

3 43 M M M M M M

4 54 VH H FH M M M

Table 6

Store atmosphere

Store

atmosphere/

insertion

Investment

(10,000)


Enhancing

sales volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 20 FH FH FH FH M M

Table 7

TV advertising

TV advertising/

insertion

Investment

(10,000)


Enhancing sales

volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 7.0 FH FH H M M M

2 9.0 M M M M M M

3 10.5 M M M M M M

4 15.0 H H M M M M

Table 8

Printer

Printer/

insertion

Investment

(10,000)


Enhancing sales

volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 7 VH VH VH H H H

2 9 H H H M M M

3 10 H H H M M M

4 14 VH VH VH H H H



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degree of satisfaction for achieving business objectives; (2) the fitness of the business objectives; and (3) the fitness of the

promotion mix.

(i) The maximum degree of satisfaction for achieving business objectives: We apply Eq. (9) on the information gathered from

Tables 4–11 to determine the maximum satisfaction level for achieving the business objectives. The analysis results are sum-

marized in Table 12 with the last row showing the maximum satisfaction level for each business objective.(ii) The fitness of the business objectives: The fitness of the business objectives are evaluated by Eq. (10). The results of

the comparison are illustrated in Table 13, where t j is the maximum satisfaction degree level for each business objective;a j isthe importance of each business objective; and g j represents the fitness of the business objective.

(iii) The fitness of the promotion mix: The communication effects of accomplishing business objectives for the selection of

promotion mix are evaluated by Eq. (11). The LOWA aggregation operator is used to derive the final fitness of the promotion

mix. The final fitness linguistic value is calculated to be FH (Fairly High) for this promotion mix (Eq. (14))

Z s ¼ /Q ðE; VH;VH; FL ;VL ; FHÞ ¼ FH; ð14Þ

where Z s denotes the fitness of the promotion mix.

Table 9

Public relation

Public relation/

insertion

Investment

(10,000)

Achieving business objectives

Enhancing sales

volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 3 M VH FH FH M M

Table 10

Radio advertising

Radio

advertising/

insertion

Investment

(10,000)


Enhancing

sales volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 0.4 FH FH FH FH H H




Table 11

Internet advertising

Internet/

insertion

Investment

(10,000)


Enhancing sales

volume

Attracting new

customers

Raising

market share

Strengthening

brand image

Reinforcing

brand loyalty

Increasing long-

term profit

1 2 H H FL FL FL FL

Table 12

The satisfaction degree of achieving business objectives

Tools Objectives

Enhancing sales

volume

Attracting new

customers

Raising market

share

Strengthening brand

image

Reinforcing brand

loyalty

Increasing long-term

profit

Prize E VH FH FH VH FH

Catalog VH H FH M M M

Store atmosphere FH FH FH FH M M

Television

commercials

H H M M M M

Printer VH VH VH H H H

Public relation M VH FH FH VH FH

Radio

commercials

FH FH FH FH H H

Internet H H FL FL FL FL

Maximum E VH VH FH VH FH



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5.4. The GA search process

A customized C++ program codes the GA search procedure that is used to determine the optimum promotion mix based

on the information accumulated from Tables 2–4. The 3 bit binary coding method is used to encode the promotion tools,

under the consideration of tool selection status and insertion(s), as shown in Fig. 3. The first bit of code indicates whether

a specific promotion tool is selected for the promotion mix or not. The last two bits represent the number of insertion for a

promotion tool.

5.5. Fitness function

The fitness of each promotion mix is obtained with equations Eqs. (9)–(11). They serve as fitness functions in the GA

searching process to determine the suitability of achieving the business objectives, the fitness of the business objective,

and the fitness of the promotion mix.

Proportion, rank, and tournament are the commonly used methods in GA selection process. In this work, the easily-under-

stood proportionate selection method (i.e., roulette wheel selection) is adopted. This method is utilized for the sake of dem-

onstrating the simplicity, higher convergence speed, and efficiency to achieve the close-to-optimal solution for multiple

decision attribute and cost estimation problems. The marketing personnel working for department store C have insufficient

knowledge of GA. Hence, in this study the roulette wheel selection method (Eq. (15) instead of other methods (e.g. the rank-

ing or tournament selection methods)) is used to generate the probability for performing a crossover operation. The larger

the area covered by a promotion mix, the higher the feasibility obtained to engage in the crossover process

P j ¼ f j

Pn j¼1 f j

; j ¼ 1;2; . . . ; n; ð15Þ

where f i denotes the fitness of the promotion mix j;Pn

j¼1 f j is the sum of the fitness of n promotion mixes.

Additionally, the mutation process is applied to expand the solution spaces and to avoid being quickly trapped in a local

optimum in the GA search process. The related GA parameters are summarized in Table 14. The optimum promotion mix and

the investment indicated after the GA search process are illustrated on the right part of Table 15. A ‘‘Very High” marketing

Table 13

The fitness of business objective

Weights Objectives

Enhancing sales

volume

Attracting new

customers

Raising market

share

Strengthening brand

image

Reinforcing brand

loyalty

Increasing long-term

profit

t j E VH VH FH VH FH

a j E VH E FL VL VH g j E VH VH FL VL FH

Promotion

tool #1

1 0 0

0: Not selected

1: Selected

Insertion(s):

00: one time

01: two times

10: three times

11: four times

Promotion

tool #2

Promotion

tool #3…

Promotion

tool # n

Fig. 3. The chromosome encoding method.

Table 14

The GA searching parameters

Parameters Settings

Number of generations 100

Number of individuals 24

Crossover rate 0.85

Mutation rate 0.08



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performance rating is obtained. The total investment for the promotion activity was US$ 1,560,000, a figure lower than ori-

ginal planned budget (US$ 2,000,000).

An examination of the results obtained from the traditional approach and the GA-based search ( Table 7) leads us to two

significant findings: (i) the number of insertions for each selected promotion tool obtained from the GA-based solution is

lower than that obtained from the traditional approach; and (ii) the GA-based solution requires less expenditure and gives

a higher objective significance than the traditional approach does. To improve a company’s market share, it is helpful to iden-

tify the frequency of tool usage. This depends on the initial plan and schedule for each promotion mix. After this the tools for

initiating the promotion activity are determined. In fact, in addition to the aforementioned elements, a company should pay

much attention to the combinational effects from the promotion mix.

6. Concluding remarks and suggestions

IMC is an important factor affecting the outcomes of marketing strategy, and can help a company to position its products/

services, reach its target market, and effectively build up brand image. Sales promotion is one IMC channel by which a com-

pany can communicate with customers, and ultimately influence customer purchasing behavior in the target market. A best-

selling strategy would identify both the best promotion methods and promotion mix, based on consumer preference, while

satisfying the expected marketing performance and the allocated budgetary limits. Furthermore, the communication effect

of each promotion tool alone and in combination should be simultaneously considered to draw an optimum promotion mix

solution. The procedure of selecting an optimum promotion mix is not straightforward and usually involves vague and

uncertain information processing rather than numerical expressions or objective decision-making. Marketing personnel tend

to count on working experience to select the most appropriate promotion tools and determine the best promotion mix to

obtain acceptable conditions. However, this can lead to less predictable results.

We proposed a linguistic decision model is used to minimize the uncertainty and vagueness linked with the degree of

importance of each business objective, estimate the degree of satisfaction for achieving business objectives, and identify

budget limitations for each promotion mix. Additionally, the GA is used to determine decision-making attribute interactions

and optimization problem, to maximize the degree of satisfaction for achieving business objectives, the fitness of the busi-

ness objective, and the fitness of the promotion mix for department store C, through an empirical implementation instead of

an example imitation. This proposed methodology can derive a close-to-optimal solution for the selection of promotion mix.

According to the comparison results obtained after the implementation phase, the proposed model is efficient and cost-effec-

tive for the entire promotion activity subject to the desired business objectives and the actual budget limitations planned by

departmental store C.

There are two issues related to future research opportunities. They are: (i) only domain experts who work for department

store C were interviewed. Gathering more information associated with sales promotion from different department stores

may be necessary to obtain an in-depth understanding of promotion mix management and marketing strategy; (ii) it may

be possible to apply other methodologies such as neural networks and genetic programming to minimize the expenditure

for a promotion activity and optimize promotion mix management.

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Table 15

The comparison of promotion mix selection

Promotion tool Traditional approach GA searching

Insertion Investment (10,000) Insertion Investment (10,000)

Prize 3 90 2 81

Catalog 4 54 1 35

Store atmosphere 1 20 1 20

TV commercials 4 15 1 7

Printer 4 14 2 9

Public relation 1 3 1 3

Radio commercials 4 2 3 1

Internet 1 2 0 0

Total budget 200 156

The linguistic value ( z s) Fairly High Very High



12/12

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