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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
Contents lists available at ScienceDirect
Information Sciences
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l oc a t e / i n s
mailto:[email protected]://www.sciencedirect.com/science/journal/00200255http://www.elsevier.com/locate/inshttp://www.elsevier.com/locate/inshttp://www.sciencedirect.com/science/journal/00200255mailto:[email protected]
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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.
44 T.-H. Hsu et al. / Information Sciences 179 (2009) 41–52
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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)
T.-H. Hsu et al. / Information Sciences 179 (2009) 41–52 45
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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.
46 T.-H. Hsu et al. / Information Sciences 179 (2009) 41–52
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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
2 81 E VH FH FH VH FH
3 90 E VH FH FH VH FH
Table 5
Catalog
Catalog/
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 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)
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 20 FH FH FH FH M M
Table 7
TV advertising
TV advertising/
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 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)
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 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
48 T.-H. Hsu et al. / Information Sciences 179 (2009) 41–52
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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)
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 0.4 FH FH FH FH H H
2 0.8 FH FH FH FH H H
3 1.0 FH FH FH FH H H
4 1.5 FH FH FH FH H H
Table 11
Internet advertising
Internet/
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 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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Store atmosphere 1 20 1 20
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Printer 4 14 2 9
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