33th INFROMS Marketing Science Conference
Maintaining Market Share Growth: Optimal Budget
Allocation to Loyalty and Sales Promotion Programs
Hsiu-Yuan Tsao
Associate Professor
Department of Business Administration
Tamkang University
TAIWAN
ABSTRACT
• This study employs a first-order Markov-type market share
model to examine the differential unit cost of marginal effect
and the spending for promotion and loyalty programs on market
share.
• Sensitivity analysis with a spreadsheet is used to help
determine optimal budget allocations for both programs over a
multi-period during which the dual aim is to keep the overall
budget to a minimum and to maintain growth in market share.
•
We apply this approach to data from a 2009 consumer panel provided
by Taylor Nelson Sofres (TNS) Global Taiwan for the adult milk
product category, based on the given initial size of market share and
loyalty effect and on an estimation of the promotion effect, using
empirical data concerning the outlay budgeted for these two programs.
Markov Market Share Model
i  (1  i ) j
aij 
(1  i ) j
i
Loyalty Effect
j
Promotion Effect
j  i, i  1, 2,
,N
j  i, i  1, 2,
,N
the proportion of customers whose choice of
brand on the next occasion is simply to
purchase the same as before as a result of
their satisfaction
the proportion of customers whose
choice of purchase on the next occasion,
whether the same brand or not, is
affected by marketing mix activities
The brand share of the
th brand
at time is given by
N
y j ,t   j y j ,t 1   j ,t  1  i yi ,t 1
i 1
t  1, 2, , M
Estimation
• Effect of Loyalty Program
A share of the category requirement (SCR) is commonly used by
marketing practitioners to represent the loyalty statistic, namely
loyalty, in the marketing literature (Bhattacharya et al., 1993;
Ehrenberg et al., 2004),
• Effect of Promotion Program
the least squares method being used to estimate
the from these time series.
the promotion effect for each brand at
period is solved as follows:
 j ,t 
y j ,t   j y j ,t 1
N
 1    y
i 1
i
i ,t 1
The Objective Function
The objective for the focal brand is
to develop a budget allocation plan for
loyalty and promotion, while
minimizing the overall budget and
maintaining market growth rate (g).
T
  m 
MIN
t 1
1,t
wi j  wi  j  C j
 1,t 
s.t.
N
y j ,t   j ,t y j ,t 1   j ,t  1  i ,t yi ,t 1
i 1
y j ,t  (1  g ) y j ,t 1
N

i ,t
1
i ,t
1
i 1
N
y
i 1
0  yi ,t ;  i ,t ; i ,t ; g  1 i  1..N
m 1
(1) represent the unit cost (marginal
cost), to raise the level of the effect
of promotion and loyalty programming
t  1..T
(2) we propose a variable and
assume that given the same
level of marginal effect, the
spending on the promotion
w
program is
m  i
w i
times that spent on the loyalty
program (Blattberg & Deighton
1996).
(3) the market share growth rate
g
Method & Result
1.The data came from TNS global Taiwan and
covered the 12 months of 2009.
2. Excel Solver for nonlinear programming
solution and sensitivity analysis is used
to seek for the solution.
Table 1. Initial Market Share and Loyalty Effect
Adult Milk
Loyalty Effect
Market Share
(SCR)
Powder
KLIM
0.61
0.48
FERNLEAF
0.39
0.55
Ratio of
Ratio of
Total
Effect of
Budget
Effect for Budget
Promotion and
Allocation for Loyalty Programs
Promotion for Each Marke
Promotion and
and Loyalty Period t Share
3. the Objection Function : MIN (BUDGET) to
Promotion Loyalty
Promotion Loyalty
Loyalty
Program
MAINTAIN Market Share Growth Rate and
Program Program
Program Program
Program
N/A
N/A
0.61
N/A
N/A
0.55
N/A
4. Decision Variable is Budget Growth Rate for 1 N/A
Loyalty Program
1.28
0.62
2
0.86
0.14
6.40
0.66
0.51
3.80
1.22
0.62
3
0.86
0.14
6.11
0.66
0.54
3.87
1.17
0.63
4
0.85
0.15
5.84
0.67
0.58
3.94
1.12
0.63
5
0.85
0.15
5.58
0.68
0.61
4.02
1.07
0.64
6
0.84
0.16
5.34
0.69
0.65
4.11
1.02
0.65
7
0.84
0.16
5.11
0.70
0.69
4.20
0.98
0.65
8
0.83
0.17
4.91
0.71
0.73
4.30
0.94
0.66
9
0.83
0.17
4.72
0.73
0.77
4.41
0.91
0.67
10
0.82
0.18
4.56
0.75
0.82
4.55
0.89
0.67
11
0.82
0.18
4.46
0.77
0.87
4.73
0.90
0.68
12
0.82
0.18
4.52
0.83
0.92
5.07
Total Budget
(Periods)
46.99
Percentage of Budget
Allocation
manipulate the growth rate for the loyalty program and solve the
optimization model in a dual direction, increasing and decreasing the
growth rate by 0.01, plugging in the initial market share and initial
loyalty, and seeking an MIN(Total Budget)that maintains the market
share growth rate =1.01
m
Table 3. Budget Allocation with Differential
Unit Cost of Marginal Effect for Promotion
and Loyalty Programs
=5
=4
Promotio
Promotio
Budget
Loyalty
Loyalty
n
n
Allocatio
Program
Program
n
Program
Program
2 0.86
0.14
1
0
3 0.86
0.14
1
0
4 0.85
0.15
1
0
5 0.85
0.15
1
0
6 0.84
0.16
1
0
7 0.84
0.16
1
0
8 0.83
0.17
1
0
9 0.83
0.17
1
0
10 0.82
0.18
1
0
11 0.82
0.18
1
0
12 0.82
0.18
1
0
(Periods)
Total
Budget
46.98
38.88
Conclusion
• The primary contribution of this study has been to
provide the platform that uses the Markov market
share model and the method of sensitivity analysis
with spreadsheet to conduct an analysis that
illustrates the dynamic interaction between multiperiod brand shares and loyalty and promotion
effects.
• A second contribution has been that by
manipulating the parameter of the unit cost of
marginal effect for promotion and loyalty
programs (letting range from 5 to 1),
– we found that the greater the value of m , the
greater the total budget required to reach the
target market share.
Conclusion (Cont.)
•
Third, when the differential unit cost of the marginal effect for
promotion and loyalty programs is decreased to 4, please refer to
Table 3, for =4. The model and methodology proposed in our study
indicate this as the turning point at which firms should switch
budget spending away from loyalty and focus on the promotion
program alone.
•
This interesting result questions the rule that “the cost and
effect to acquire a new customer is larger than that to retain a
customer.” - in effect calling for halting budget allocation to the
loyalty program, instead of the favoured convention to increase it.
Future Research
• We might adopt the marginal diminishing return
for the unit cost and marginal effect for
promotion and loyalty program instead of linear
relationship
• We might try use the platform to examine and
seek to the optimal budget alloication for
maximizing the CLV(Customer Lifetime Value)
from the Macro perspective instead of micro
(individual) perspective as previous did.
Appreciate for your kind attention
And
Q&A