On the Optimal Allocation of Resources for a Marketing Campaign
Patrick Hosein
a
, Shiva Ramoudith
b
and Inzamam Rahaman
c
Department of Computing and Information Technology, The University of the West Indies, Trinidad and Tobago
Keywords:
Resource Allocation, Marketing, Optimization, Data Mining, Machine Learning.
Abstract:
Many companies and institutions, such as banks, typically have a wide range of products that they make
available to customers. However, such products must be marketed to their customers, especially when the
product is new. Phone calls, emails, postal mail, and online advertisements are among the ways companies
can market products to specific customers. However, the cost incurred during marketing increases with every
contact made. Phone calls are the most personal means of targeted marketing but also the most costly. In
telemarketing, a company can make multiple calls to a single customer with each call incurring a human
resource cost. Such calls may or may not be able to persuade a customer to subscribe to the service or product.
Some customers might subscribe after the first call. Some customers might require several calls to convince
them. Other customers might never be persuaded. In light of limited resources, to maximize return, a company
would need to determine which customers to contact and how many attempts to make for a customer. In this
paper, we present a mathematical model for this problem in which, given a marketing budget of calls, one can
determine a policy for selecting customers to target along with the optimal number of calls to use for each
selected customer. We illustrate our model using a Portuguese banking dataset and show that our model can
achieve significantly higher levels of success performance.
1 INTRODUCTION
Marketing is an essential aspect of modern business.
Businesses cannot earn revenue from a product if cus-
tomers are unaware of said product. There are many
media through which a business can market a prod-
uct. These include email campaigns, online adver-
tisements, social media advertisements, postal mail,
and phone calls. Regardless of the medium, a busi-
ness would want to minimize the cost of conducting a
marketing campaign while simultaneously maximiz-
ing its efficacy.
Some customers are more likely to purchase cer-
tain products over customers. Moreover, some mar-
keting media are more effective with different cus-
tomers. Making a sound judgement on an individual
customer is often impossible. For this reason, mar-
keting often uses features of customers to divide them
into customer segments (Loshin and Reifer, 2013).
By dividing customers into segments, we can derive
more refined marketing strategies that are more likely
to entice a particular segment. Furthermore, we can
a
https://orcid.org/0000-0003-1729-559X
b
https://orcid.org/0000-0001-9464-0954
c
https://orcid.org/0000-0002-3097-8355
decide if a specific segment is worth targeting.
Phone calls can serve as a useful, personal market-
ing tool and one potential benefit is that customers can
directly signal their intention to purchase or partake
in a product. Marketing conducted through the use of
phone calls is called telemarketing (Kotler and Keller,
2011). However, as noted by Roach (Roach, 2009),
not all segments might react favourably to phone-
based marketing campaigns. A corollary of this in-
sight is that not only would calls be wasted on cer-
tain segments (Mylonakis, 2008), but such calls can
also annoy members of different customer segments.
Such irritation can minimize a customer’s willing-
ness to consume more products in the future. Given
the above, it would be shrewd to design phone-based
marketing campaigns to target specific customer seg-
ments. The design of such marketing campaigns
ought to consider that the budget of contact attempts
that can be made is limited.
In this paper, we present a novel formulation of the
problem of designing a data-driven phone-based mar-
keting campaign. Given a budget of calls, our model
uses historical data to divide a customer base into cus-
tomer segments, and then using said segments and
their computed properties, allocates the number of
Hosein, P., Ramoudith, S. and Rahaman, I.
On the Optimal Allocation of Resources for a Marketing Campaign.
DOI: 10.5220/0010232001690176
In Proceedings of the 10th International Conference on Operations Research and Enterprise Systems (ICORES 2021), pages 169-176
ISBN: 978-989-758-485-5
Copyright
c
 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
169

calls to be assigned across customer segments to yield
the highest number of marketing successes. Note
that, in targeting a particular segment, we optimize
the maximum number of calls to be made for the seg-
ment so that sufficient calls are made to entice such
customers but not too many are made such that they
become frustrated. We validate our method using a
dataset used by Moro et al. (Moro et al., 2014) from
a Portuguese bank.
2 RELATED WORK
Several papers have examined the problem of design-
ing telemarketing campaigns using computational
techniques. Most papers in this space have looked
into using machine learning techniques to deciding
which customers a business ought to contact during
a telemarketing campaign.
Karim and Rahman (Karim and Rahman, 2013)
examined the problem from the perspective of binary
classification. Using Moro et al.’s (Moro et al., 2014)
dataset, they sought to use customer features to pre-
dict whether or not they would purchase the term de-
posit being marketed and compared the use of the
C4.5 Decision Tree algorithm against Naive Bayes
and found that the C4.5 Decision Tree algorithm pro-
duced more accurate results. However, Karim and
Rahman (Karim and Rahman, 2013) did not take into
account the number of calls made to customers.
Similarly, Lawi et al. (Lawi et al., 2017) also
approached the problem of determining which cus-
tomers to call by framing the problem as a binary clas-
sification problem. However, instead of decision trees
and Naive Bayes, Lawi et al. (Lawi et al., 2017) com-
pared SVMs against Ada-boosted SVMs. They per-
formed grid searches to determine the best combina-
tion of hyper-parameters for their models. Their Ada-
boosted SVMs performed better than regular SVMs.
Neural Network models have also been examined
and compared in some previous work. Puteri et al.
(Puteri et al., 2019) compared the use of radial ba-
sis functions (RBF) as activation functions against
Sigmoidal activation functions for determining cus-
tomers to call in the framework of binary classifica-
tion. Puteri et al. (Puteri et al., 2019) found that a
network with RBF activations in the hidden layer per-
formed better than Sigmoidal activations in the hidden
layer.
Aside from leveraging machine learning models
for bank telemarketing, Moro et al. (Moro et al.,
2015) also examined feature engineering in the con-
text of bank telemarketing. In particular, they used
sliding windows to compute measures of customer
lifetime value (LTV). Customer LTV is a proxy for a
customer’s value over time based on projected future
interactions (Dwyer, 1997). They were able to use
sensitivity analysis to derive explanations for which
LTV measures were most important and demonstrated
that LTV measures computed from historical data are
useful in predicting future behaviour, thereby obvi-
ating the need for acquiring more information about
customers.
Bertsimas and Mersereau (Bertsimas and
Mersereau, 2007) developed a dynamic programming
formulation for allocating messages to multiple
customer segments. In their paper, they also propose
a Lagrangian relaxation of their initial dynamic pro-
gramming problem and show that their Lagrangian
relaxation performs well in practice. They assumed
that customer segments are known and so do not
provide a procedure for the extraction of customer
segments from data.
3 MATHEMATICAL MODEL
We assume that we have a set of customers and each
customer has a set of features. We can make several
calls to a customer to convince them to purchase a
particular service or financial product (e.g., a loan).
The customer may, at some point, accept the product
in which case we do not call them again for the du-
ration of the campaign. After a specified number of
calls we remove the customer from the pool of poten-
tial customers.
We assume that customers with similar features
(classified as a customer segment) have the same
probability distribution for acceptance of the product.
Later we will demonstrate how this distribution can
be estimated. Our objective is to determine which
customers to target first and also how many times we
should contact them before giving up. Note that ex-
cessive calling can lead to customer irritation, and this
should be avoided. We first consider a mathemati-
cal formulation of the problem and later describe, us-
ing an example, the application of the formulation in
practice. Let us first consider a single customer seg-
ment, and later we will consider how to allocate calls
among customer segments.
Suppose that we have N customers each with fea-
tures identical to those in the concerned customer seg-
ment. Furthermore, assume that each of these cus-
tomers accepts the product with probability p
i
on the
ith call. If a maximum of k calls are made to each
customer then let s
k
denote the expected number of
successes and let c
k
denote the expected number of
calls made. The expected number of success is given
ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems
170

by
s
k
= N 1 −
k
∏
i=1
(1 − p
i
)
!
(1)
and the expected number of calls is given by
c
k
= N k
k
∏
j=1
(1 − p
j
) + p
1
+
k
∑
i=2
ip
i
i−1
∏
j=1
(1 − p
j
)
!
(2)
Next consider the function s
k
versus c
k
as k varies.
The gradient of this function at some k is given by
s
k+1
− s
k
c
k+1
− c
k
=
p
k+1
∏
k
j=1
(1 − p
j
)
∏
k
j=1
(1 − p
j
)
= p
k+1
(3)
Note that, in practice, p
k
decreases with increasing k
since a customer is less likely to purchase in succes-
sive attempts. Consider the piece-wise linear func-
tion with values at points (c
k
,s
k
). The gradients of
the successive linear components will be decreasing
and hence this is a piece-wise linear concave function.
Note that we assume here that, once we increase the
maximum number of calls for one customer in this
customer segment it is increased for all. This con-
vexity property is important since it now implies that
when we optimize over customer segments we will be
solving a convex optimization problem. Please note
as both s
k
and c
k
varies by N then the plot does not
change with N but the axes are scaled accordingly.
The objective of the problem is to determine how
many calls to assign to customers in each customer
segment. Let x
j
denote the number of calls that are
assigned to customer segment j. Let S
j
(x
j
) denote
the expected number of successes if x
j
calls are al-
located to customer segment j = 1. ..M. This is the
piece-wise linear, concave function that we derived
above scaled by the number of members in j. The
optimization problem becomes
V = max
~x
M
∑
j=1
S
j
(x
j
)
s.t.
M
∑
j=1
x
j
= T
~x ∈ {0, ... ,T }
M
(4)
Since S
j
is piece-linear and concave one can show
that a greedy approach can find a near-optimal so-
lution to this problem. Find the customer segment
with the largest initial gradient, assign as many calls
as needed to get to the next break-point, update the
gradient for that customer segment to that of the next
linear segment and repeat until all T calls have been
allocated. If the last assignment brings the total calls
for the customer segment to the next break-point, then
the solution is optimal, and so the solution is typically
quite close to being optimal. The pseudo-code pro-
vided in Figure 1 can be used to determine the optimal
allocation.
Require: T = Total number of calls to be allocated
Require: M = Total number of customer segments
Require: s
j
(k) = Expected #successes for a maxi-
mum of k calls
Require: c
j
(k) = Expected #calls for a maximum of
k calls
Require: N
j
= Number of customers in customer
segment j
Require: k
j
= 0 Initial maximum call value for cus-
tomer segment j
Require: g
j
(k
j
) = s
j
(1)/c
j
(1) set initial gradient for
customer segment j
while T > 0 do
j
∗
= argmax
j
{g
j
(k
j
)}
k
j
∗
← k
j
∗
+ 1
g
j
∗
=
s
j
∗
(k
j
∗
+1)−s
j
∗
(k
j
∗
)
c
j
∗
(k
j
∗
+1)−c
j
∗
(k
j
∗
)
T = T − N
j
∗
end while
for j = 1 : M do
x
j
= N
j
k
j
end for
return ~x
Figure 1: Call Allocation Optimization Pseudo-code.
Let us illustrate with a simple example. Assume
that we have two segments, j = 1,2. For the first cus-
tomer segment, suppose that the probability of suc-
cess for each of the first five call attempts is 0.10, 0.07,
0.02, 0.01 and 0, respectively. Hence 20% of cus-
tomers eventually accept, and the rest reject the offer.
For the second customer segment, we assume that the
corresponding probabilities are 0.06, 0.03, 0.02,0.01
and 0. The success versus call attempt plot is shown
in Figure 2.
Now suppose that we have 500 new customers
with 200 being in customer segment 1 (i.e., N = 200
for this customer segment) and 300 in customer seg-
ment 2. The initial gradients are 0.10 and 0.06, re-
spectively and hence the first set of customers are cho-
sen from customer segment 1. 200, one for each cus-
tomer in the customer segment are necessary to get to
the first break-point. The gradient for customer seg-
ment 1 drops to 0.07, so it is chosen again, but this
time 180 calls are needed to get to the next break-
point. At this break-point, the gradient drops to 0.02,
so customer segment 2 is chosen next and 300 calls
are required to get to the first break-point. Hence, if
On the Optimal Allocation of Resources for a Marketing Campaign
171

0 1 2 3 4
5
0.00
0.05
0.10
0.15
0.20
Total Calls (×N)
Total Successes (×N)
customer segment 1
customer segment 2
Figure 2: Variation of Successes with Calls.
we assumed a budget of 680 calls, then it is optimal to
call every customer in segment 1 no more than twice
and to call every customer in segment 2 once.
4 NUMERICAL RESULTS
In this section we provide numerical results to illus-
trate the benefit of the proposed approach in a real
environment. We first describe the dataset used and
then we provide details of our segment selection pro-
cess. Next, for each customer segment, we determine
the number of successes as a function of the number
of calls made to customers with features in the cus-
tomer segment. For some customers, after a few calls,
it might be best to give up on them (and avoid their re-
sentment), while for other customers it may take more
calls before they can be convinced. Finally, we illus-
trate its performance improvement.
4.1 Data Description
We used the Bank Marketing Dataset collected by
Moro et al. (Moro et al., 2014). The dataset is avail-
able on the UCI Machine Learning Repository. The
dataset contains customers from a Portuguese bank-
ing institution and the direct marketing campaigns
used to encourage them to subscribe to a term-deposit
product. The dataset contains 45211 records, each
representing a customer contacted during the market-
ing campaign. The chart in Figure 3 shows the fre-
quency of contacts for various call ranges. We con-
sider 99% of all calls made (we ignore customers
contacted greater than 34 times) to filter potentially
anomalous data points from our analysis. Table 3 lists
the features from the dataset considered for our anal-
ysis.
1 2 3 4 5 6 7 8 9
10
11-20 21-30 31-40
0
2,500
5,000
7,500
10,000
12,500
15,000
17,500
Figure 3: Number of Customers vs. Number of Calls made.
Table 1: Customer Features.
Attribute Values
Age Customer’s Age
Balance Customer’s Average Yearly
Balance (e)
Job Administrator, Blue-collar,
Entrepreneur, Housemaid,
Management, Retired, Self-
employed, Services, Student,
Technician, Unemployed or
Unknown
Marital Status Married, Single, Divorced or
Unknown
Education Primary, Secondary, Tertiary
Risk Yes, No or Unknown
Housing Loan Yes, No or Unknown
Personal Loan Yes, No or Unknown
Number of Calls 1-63
Success of Offer Yes or No
Given new customers and a budget of calls, our
objective is to determine which users to call and how
often they should be called. We use historical data
to determine customer segments, and for each cus-
tomer segment, we determine the number of calls
to assign to a customer in that segment. Therefore,
we first investigate how to derive customer segments
(feature selection), and then for each customer seg-
ment, we compute the success as a function of calls
made. Given a new set of customers, we can then de-
termine their customer segments, and based on this
classification, decide whom to call and the maximum
number of calls to be made to them.
ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems
172

4.2 Feature Selection
Given the chosen performance metric (success per
call rate), we can now use feature selection to de-
termine which features influence this metric. We se-
lected features that influenced the metric to determine
which customers to approach and the number of calls
to make to them. Note that we could use feature ex-
traction, but we chose feature selection to better un-
derstand which information of a customer is most im-
portant.
Given a new user, we can use their features to as-
sign them to the appropriate customer segment. Be-
fore doing this, we need to define the list of possi-
ble customer segments. Our approach starts by com-
puting the success rate of each value for a particu-
lar feature in isolation. Values were then aggregated
based on their success rates. For some features, we
used K-Means clustering to determine the aggrega-
tion of the values. We then use Silhouette analysis
(Rousseeuw, 1987) (with Euclidean distance) to de-
termine the optimal number of clusters. Using this
analysis, we obtained the optimal grouping of values
for a particular feature. Next, we give an example of
this approach with the job, marital status and educa-
tion features based on a random sample of users from
the dataset.
For each occupation, we averaged the success
per call rate of all customers with that job title.
These averages are provided in the bar chart in Fig-
ure 4 for each of the job titles and are used as in-
put for the clustering step. As mentioned before,
we used K-Means clustering and computed the Sil-
houette Score for all possible cluster numbers. In
this example, the highest Silhouette score corresponds
to 2 clusters, which is what we use. The two
clusters are [’unemployed’, ’admin.’, ’management’,
’self-employed’, ’technician’, ’unknown’, ’services’,
’housemaid’, ’blue-collar’, ’entrepreneur’] and [’stu-
dent’, ’retired’].
The success per call rate for the various values of
the marital feature are as follows: (Married, 0.037),
(Single, 0.059) and (Divorced, 0.048). We repeated
the process with these values in conjunction with
their success per call rates to determine the resulting
groups. They are as follows: [married, divorced] and
[single].
Regarding the education feature, our approach re-
vealed that two clusters were ideal: [primary, sec-
ondary] and [tertiary, unknown]. The success per call
rates for the various values of the education feature
are as follows: [(Primary, 0.032), (Secondary, 0.042),
(Unknown, 0.052), (Tertiary, 0.055)].
It would not be feasible to use the approach men-
Blue-collar
Entrepreneur
Housemaid
Unknown
Services
Technician
Self-employed
Administrator
Management
Unemployed
Retired
Student
0.02
0.04
0.06
0.08
0.10
0.12
Expected Success Rate
Figure 4: Average Success Rate for each Occupation.
tioned above with the age and balance features since
they are continuous. We chose to discretize each
feature by creating a set of contiguous intervals that
span the range of the feature’s values. We deter-
mined the possible intervals by utilizing a Decision
Tree algorithm since it is easy to interpret and it de-
termines the optimal splitting points that would de-
termine the contiguous intervals. We utilize the full
dataset (age/balance and success of offer features as
input) with the Decision Tree algorithm. We then
extract the splits at each level. This will be used as
the criteria for creating the intervals for the age and
balance features. We considered the following hyper-
parameters: max depth and criterion. We limited max
depth to a value of 5 since this has a direct impact on
the number of customer segments. There was no dif-
ference between either criterion (Gini Index and En-
tropy) based on our testing. We did not consider other
parameters for the Decision Tree since they play an
insignificant role when the tree is shallow along with
a sizeable dataset. We do not cluster the remaining
features since the number of values for those remain-
ing features were already small.
Table 2: Success Rates for Other Features.
Attribute Expected Success per Call Rate
Risk Yes (0.023), No (0.045)
Housing Loan Yes (0.061), No (0.031)
Personal Loan Yes (0.025), No (0.048)
On the Optimal Allocation of Resources for a Marketing Campaign
173

4.3 Optimal Allocation of Calls
We assume that we are given a set of features for each
customer i and that we have historical data on the
number of attempts made to each customer and the
outcome (success or failure) of each customer. Let v
i
denote the number of call attempts made to customer
i. Let q
i
= 1 if attempts to customer i are successful
(i.e, success was achieved on call v
i
) and q
i
= 0 other-
wise. We assume M customer segments and these are
indexed by j.
Note that one can reduce the number of calls made
by reducing the maximum allowed calls per customer,
thereby reducing the number of calls made. This re-
duction will lead to fewer successes, but the net result
might be a higher success per call rate. For the given
dataset, the maximum number of calls were already
chosen. However, we can deduce what would happen
if this maximum was reduced. If the maximum is less
than the number required to achieve success, then one
would be unsuccessful since the required number of
calls would not have been made. We use G
j
to repre-
sent the set of users who have the features specified by
customer segment j. Let us introduce the variable k
as the specified maximum number of calls. The num-
ber of successes achieved for a call maximum of k for
customer segment j is given by
s
k
( j) =
∑
i∈G
j
q
i
[min{1,max{0,k − v
i
+ 1}}] (5)
and the number of call attempts made is given by
c
k
( j) =
∑
i∈G
j
min{k, v
i
}] (6)
We use historical customer data to compute the func-
tion S
j
(x) for a given customer segment j. This is
a piece-wise linear function with endpoints given by
(0,0),(s
1
( j)c
1
( j)),(s
2
( j),c
2
( j)) etc.
Let us illustrate this function for one of the cus-
tomer segments (segment A in Table 3) obtained
through feature selection. This customer segment
contains 874 customers. In Figure 5 we plot (in blue)
the function S(x) based on the data. However we find
that the function is not exactly concave and hence in
order to apply the optimization approach previously
defined we replace the function S(x) with its Concave
Hull denoted by
˜
S(x). This hull is depicted in red.
Note that the difference in this case is quite small.
4.4 Performance Analysis
We use 5-Fold cross-validation to evaluate the pro-
posed method on the dataset in (Moro et al., 2014).
We use 80% of the customers (randomly chosen) for
training and the remaining 20% is used for testing.
0
500
1,000
1,500
2,000
2,500
0
20
40
Total Calls
Total Successes
S(x): based on Data
˜
S(x): Concave Hull
Figure 5: Successes as a function of calls made.
For each cross-validation fold, we use the training set
to infer the groupings of education, marital, and job
attributes. We form customer segments by all pos-
sible combinations of groupings across all features.
We then assign customers to customer segments given
their characteristics. We then apply the previously
defined methods and compare performance among
them. We repeat the process for each combination of
the various age/balance intervals. We found the opti-
mal intervals (based on our performance metric which
is described later on) for the age and balance features
respectively to be [(18, 25), (26, 59), (60, 87), (88,
93), (94, 100)] and [(-10000, 60), (61, 1578), (1579,
105000)].
Table 3 provides a breakdown of customer seg-
ments, randomly chosen, from best to worst, for one
of the cross-validation folds. This fold contains 960
customer segments in total, with 661 of them having
no customers. We recognize that customer segments
having low success per call rates are associated with
customers that have an existing loan. A possible rea-
son is that these customers do not have the financial
resources (low account balances) to support both the
loan and the term deposit. An exception to this obser-
vation is customer segment 2 where persons did have
an existing loan but still had the highest success rates.
A potential reason is that these customers have high
account balances. Customer segment 366 contains
customers who defaulted on a previous loan. As a re-
sult, this segment had the lowest success rates. These
customers are not ideal for targeting. In the dataset,
there were only 52 customers who subscribed to the
term deposit after defaulting on a loan.
Interestingly enough, 7 out of the top 10 customer
segments are associated with customers greater than
59 years old and they represented the minority pop-
ulation in the dataset. These customers could poten-
tially have savings that they are willing to invest in
the term deposit. Next, we rank customer segments
ICORES 2021 - 10th International Conference on Operations Research and Enterprise Systems
174

Table 3: Some Sample Customer Segments for One of the Cross Validation Folds (ranked by success rate).
CS Age Balance Education Status Job Risk Pers House Rate
A 26-59 -10000 - 60 (sec, prim) M (unemp, admin) no no no 0.0169
2 60-87 1579 - 105000 (sec, prim) M (student, retired) no yes no 1.0
16 18-25 61 - 1578 (sec, prim) (S,D) (student, retired) no no no 0.2425
46 18-25 -10000 - 60 (tert, unk) (S,D) Same as A no yes yes 0.1667
108 26-59 61 - 1578 (tert, unk) (S,D) Same as A no yes no 0.0507
366 26-59 -10000 - 60 (sec, prim) M (student, retired) yes no yes 0.0
by the average success per call rate, and, for a sub-
set of these segments, we plot, in Figure 6, the aver-
age success rate as a function of maximum number of
calls allowed. Once a call is successful then no more
calls are made (even though the maximum allowed for
that segment is continued to be increased in the plot).
For the high success rate segments success tends to be
achieved in the first call while for the others success
tends to come at a later call.
Figure 6: Success Rate vs. Call Limit for Various Segments.
We apply three methods to the test set for each
fold. The first method is the present mode of opera-
tion, which we call the Baseline (BL) method. Here
we assume that each call is provided to the customer
who has not yet accepted with the fewest contact at-
tempts made. Note that all customers are called once
and then, for those who did not accept, they are called
a second time, and this continues until the maximum
allowed number of calls is reached. For simplicity, we
only compute the cases where all customers who have
not accepted received the same number of calls, and
linearly interpolate between these points. Note that
this approach does not use any information from the
training set.
In the second approach, we order customer seg-
ments by their average success per call rate. We then
exhaustively call all customers in the highest success
rate customer segment, then the next highest, etc. In
this case, the average success rate of each customer
segment is computed from the training set and hence
this approach uses some information from the training
data to provide segment priority. We evaluate the suc-
cesses and calls each time a new customer segment is
added and plot these points but use a linear interpola-
tion between these points. This approach is called the
Greedy Customer Segment (GC) approach.
The final method is called the Gradient Ascent
(GA) approach. Here we apply the approach detailed
in Section 3 whereby we find the customer segment
with the largest gradient, call each customer in that
customer segment who can be called, update the gra-
dient for this segment and then repeat. In this case, we
incrementally choose customer segments that give the
best improvement in success per call and hence will
provide a near-optimal solution. The probability dis-
tribution for each customer segment is based on the
training set data, so here we extract even more details
from the training set.
We also determined an upper bound on perfor-
mance as follows. Suppose that we know the out-
comes for all customers(i.e. which customers sub-
scribed and the number of calls needed to get them
to subscribe). We can then allocate calls first to those
customers who we know will subscribe and, of these,
we start with those requiring the least number of calls.
This will provide the most successes for a given num-
ber of calls and hence is an upper bound which we
denote by (UB). Figure 7 shows a plot of successes
versus calls for a sample cross-validation fold. The
rest of the folds were very similar. As expected, for a
given number of calls, GC is better than BL, and GA
performs even better. Our implementation is publicly
available at (Ramoudith et al., 2020).
4.5 Performance Metric
Note that combining performance results across folds
is difficult as each test set contains a different number
of calls and successes. Instead, we compute the area
under the curve (AUC) for each method (BL, GC, and
GA) and use this as a measure of performance. Note
that a greater area under the curve indicates better per-
formance, with the Upper Bound having the greatest
area. Furthermore, since we are interested in the in-
crease in performance over the baseline, we use the
On the Optimal Allocation of Resources for a Marketing Campaign
175

Figure 7: Successes versus Calls for a Sample Fold.
ratio of the AUC for GC and the AUC for BL as the
performance metric for GC and similarly for GA. We
average these ratios over all of the folds to estimate
performance. When computed, these ratios were 1.34
for the GC approach and 1.38 for the GA approach.
Note that this ratio for the upper bound case, UB, is
approximately 2. Therefore, on average, we experi-
ence a call success rate gain of approximately 34%
for GC and 38% for GA when compared to the ap-
proach used by the Bank. We can translate this into
cost savings. Note that simply optimizing the allo-
cation of calls to segments based on the average suc-
cess rates provides most of the benefit. The Gradi-
ent Ascent algorithm provided a small additional in-
crease of 4% in performance but at the cost of addi-
tional complexity. When deployed, the approach will
work as follows. We will apply the method periodi-
cally (e.g., one week) to all eligible customers given
the available number of possible calls. One would
then contact the chosen customers based on their al-
lowed call limit. Every two months, one may also use
samples obtained over the prior two months to update
customer segments and parameter estimates.
We are currently conducting a thorough evalua-
tion of our methodology against machine learning ap-
proaches.
5 CONCLUSION
Our results indicate that implementing the proposed
method would increase the success of telemarketing
campaigns with a limited budget of calls. Addition-
ally, a firm can use the computed customer segments
to ameliorate other marketing decisions. In the fu-
ture, we will repeat the analysis using additional fea-
tures from the dataset and will also deploy a proto-
type to investigate our method’s performance in prac-
tice. Note that, as more customer outcomes are col-
lected, we can improve the accuracy of the estimated
probability distribution of each customer segment and
hence improve performance.
REFERENCES
Bertsimas, D. and Mersereau, A. J. (2007). A learning ap-
proach for interactive marketing to a customer seg-
ment. Operations Research, 55(6):1120–1135.
Dwyer, F. R. (1997). Customer lifetime valuation to support
marketing decision making. Journal of Direct Market-
ing, 11(4):6–13.
Karim, M. and Rahman, R. M. (2013). Decision tree and
naive bayes algorithm for classification and generation
of actionable knowledge for direct marketing. Journal
of Software Engineering and Applications, 6(4):196–
206.
Kotler, P. and Keller, K. (2011). A Framework for Market-
ing Management. Prentice Hall, Upper Saddle River,
NJ, 5th edition.
Lawi, A., Velayaty, A. A., and Zainuddin, Z. (2017). On
identifying potential direct marketing consumers us-
ing adaptive boosted support vector machine. In
2017 4th International Conference on Computer Ap-
plications and Information Processing Technology
(CAIPT), pages 1–4, Kuta Bali, Indonesia. IEEE.
Loshin, D. and Reifer, A. (2013). Using Information
to Develop a Culture of Customer Centricity: Cus-
tomer Centricity, Analytics, and Information Utiliza-
tion. Morgan Kaufmann Publishers Inc., San Fran-
cisco, CA, USA.
Moro, S., Cortez, P., and Rita, P. (2014). A data-driven
approach to predict the success of bank telemarketing.
Decision Support Systems, 62:22–31.
Moro, S., Cortez, P., and Rita, P. (2015). Using customer
lifetime value and neural networks to improve the
prediction of bank deposit subscription in telemarket-
ing campaigns. Neural Computing and Applications,
26(1):131–139.
Mylonakis, J. (2008). The influence of banking advertis-
ing on bank customers: an examination of greek bank
customers’ choices. Banks and Bank Systems, 3(4).
Puteri, A. N., Tahir, Z., et al. (2019). Comparison of poten-
tial telemarketing customers predictions with a data
mining approach using the mlpnn and rbfnn methods.
In 2019 International Conference on Information and
Communications Technology (ICOIACT), pages 383–
387, Yogyakarta, Indonesia. IEEE, IEEE.
Ramoudith, S., Rahaman, I., and Hosein, P. (2020). Bank
marketing approach - implementation. GitHub. https:
//github.com/shiv1994/BankMarketing.
Roach, G. (2009). Consumer perceptions of mobile phone
marketing: a direct marketing innovation. Direct mar-
keting: an international journal, 3(2):124–138.
Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to
the interpretation and validation of cluster analysis.
Journal of computational and applied mathematics,
20:53–65.
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