DIFFERENT STRATEGIES FOR RESOLVING PRICE DISCOUNT
COLLISIONS
Henrik Stormer
University of Fribourg
Department for Informatics
Bd de Perolles 90
CH-1700 Fribourg
Keywords:
Prices, discount collision, dTree, graphical discount modelling.
Abstract:
Managing Discounts is an essential task for all business applications. Discounts are used for turning prospects
to new customers and for customer retention. However, if more than one discount type can be applied, a
collision may arise. An example is a promotional discount and a discount for a customer. The system has to
decide which discount should be applied, eventually also combinations are possible. A bad collision strategy
can lead to annoyed customers as they do not get the price that they think is correct.
This paper examines three different business applications designed for small and medium sized companies and
shows the applied strategies for resolving discount collisions. Afterwards, a n ew way of defining discounts,
called discount tree (dTree) is introduced. It is shown that with dTrees, collisions can be detected directly
when the discounts are defined. A detected collision can then resolved by the administrator.
1 INTRODUCTION
One of the most important decision making factors
when buying a good or service is the price (Gijs-
brechts, 1993). Therefore, a major task for shops
or companies that sell goods or services is to find
a price for a customer. Electronic business offers
new chances to improve this task because prices can
be changed instantaneously on the internet (Jap and
Naik, 2004).
A price can be defined as the value agreed upon
by the the buyer and the supplier in exchange (Nagle
and Holden, 2002). In this paper, we will calculate
the price of a product (we will use the term product to
specify a good or service) by utilizing a standard price
and a discount. A discount should motivate the user
to buy the product directly. Additionally, a discount
can encourage a customer to buy more and therefore
rise the sales volume of the seller.
It is difficult to find a good base price and a discount
for products and customers. There exist a number of
different strategies (Inoue et al., 2001). Throughout
this paper, we will assume that a strategy has been
chosen and that a discount has to be applied in a con-
crete business application. A problem arises, if more
than one discount is defined for the same product and
customer. The business application has to find one
(or a combination) discount. This is called a discount
collision.
Discounts are defined by a number of parameters
(compare to (Kelkar et al., 2002)):
Customer: If the discount is calculated for the cus-
tomer an individual price is generated. Typically,
this kind of discount is either used for high priced
products or for products where the price is nego-
tiated. Sometimes, a discount can be calculated
automatically when the customer is classified in a
special customer segment.
Quantity: Discounts that depend on the quantity are
common (often called scale price). The economic
reason is that the marginal costs are decreasing. A
typical discount on quantity is defined in a table,
where for each quantity interval a discount is as-
signed.
Time: A time interval can be used to specify the va-
lidity of a discount, this is sometimes called pro-
motional. A discount is given for a product only
for a period of time, for example one week.
Region: Sometimes, different discounts are applied
when the product is sold in different regions. The
reason is the buying power that usually varies from
region to region.
Other Products: Some vendors package products to
449
Stormer H. (2006).
DIFFERENT STRATEGIES FOR RESOLVING PRICE DISCOUNT COLLISIONS.
In Proceedings of the Eighth International Conference on Enterprise Information Systems - ISAS, pages 449-452
DOI: 10.5220/0002445904490452
Copyright
c
 SciTePress

bundles (Bakos and Brynjolfsson, 1999; Bakos and
Brynjolfsson, 2000). If a customer buys such a
bundle, he gets a discount compared to the sum of
the individual prices.
Most important, typical discounts are defined by us-
ing a combination of the parameters above. A com-
bination of parameters typically lead to the following
different discounts:
customer discount: This discount is based on the
customer parameter. It is often possible to extend it
by defining a time interval and a scale price.
promotional discount: A promotional discount is
based on the time paramter. Like the customer dis-
count, this can be extended by defining defining a
scale price.
standard discount: Usually, this discount can only
be defined by a scale price.
bundle discount: This discount is applied by choos-
ing different products and giving this bundle a spe-
cial price. Afterwards, the bundle is internally
managed as a single product (and therefore, all dis-
counts above can be used).
To make defining discounts easier, some systems
offer extended approaches:
price lists: A price list defines list prices for a num-
ber of products. Typically, systems offer a way to
define price lists for different customer segments.
This approach is a simpler way for specifying cus-
tomer discounts.
product groups: Some systems offer a way to group
products, for example by arranging them into cate-
gories. Using this approach, a discount is not only
applied for one product but for a product group.
Whenever multiple discounts are defined for a
product, a discount collision can arise. An example
could be customer Smith who wants to buy 5 products
X. The standard price for product X is $10. Therefore,
without a discount Smith has to pay $50. Let’s as-
sume that promotional discount using the scale price
parameter is defined for product X:
Quantity Price
1-3 no discount
4-6 -$2 per item
With this scale price, Smith has to pay only $40.
Let’s also assume that Smith has a customer dis-
count for product X of $9 per item. Then, with this
discount, he has to pay $45. The collision arises be-
tween the discount of the customer and the promo-
tional discount. There are now three different possib-
lities:
• The customer has to pay $40 because of the promo-
tional discount.
• The customer has to pay $45 because of his cus-
tomer discount.
• The customer has to pay $35. The customer dis-
count defines a price per item of $9 and the scale
price of the promotional discount gives $2 off.
2 MODELLING DISCOUNTS
GRAPHICALLY
This section shows a new way of defining discounts
using a graphical tree, called the dTree (discount tree).
Please note that the tree is only used for illustration
and graphical modelling purposes, the calculation is
done more efficiently (cf 2.3).
2.1 The dTree Composition
This section shows the basic idea behind dTree. A
discount is usually defined for one product (it is pos-
sible to extend this to product groups). Therefore, the
root of the dTree is the product X for which a dis-
count should be defined. For each supported discount
parameter, the dTree defines one level. The nodes of
the tree consists of elements. An element is an atomic
definition of a discount parameter. All elements of
one layer define the complete discount parameter set.
The root node is product X. Level 1 of the tree is the
customer parameter. An atomic element in this level
is one customer, ie Customer A. For each customer, an
element is created. This is usually a finite set. Level 2
of the tree is the quantity parameter. For each possi-
ble quantity (1, 2, 3,. . . ), one element is created. This
set is infinite because a customer can buy whatever
quanitity he wants to buy of product X. Level 3 of the
tree shows the time. An element of this parameter is
one day (ie 21. May 1999). This is also an infinite set.
To make the example easier, all infinite sets are re-
stricted to finite ones by defining upper (and lower)
bounds. The quanitity is restricted to 3 (a customer
cannot buy more than three product X at once). The
time is restricted from the 21.05.99 to 23.05.99 (it is
not possible to define discounts with time restrictions
for other days). It is also assumed that our shop has
only three customers (A,B,C). Then a discount can be
defined by connecting one element of each layer. This
is a path in the tree from the root to the leaf. A pos-
sible path is Product X, Customer B, 1, 23.05, shown
in figure 1(a).
A path in the tree defines exactly one discount.
Therefore, a discount value can be assigned (for ex-
ample 10% off). The path of figure one describes the
discount: Customer B gets 10% off of Product X if he
buys exactly 1 product X at 23. May.
The main advantage of the paths are that it is very
easy to define when a collision occurs:
ICEIS 2006 - INFORMATION SYSTEMS ANALYSIS AND SPECIFICATION
450

Figure 1: Different illustrations of the dTree.
Theorem 1. A discount collision between two dis-
counts A and B occurs exactly when they both have
the same path.
Assume that two paths are not equal but a collision
occurs. This would be a contradiction of the atomic
elements definition. The next section will show how
we can group elements for making discount defini-
tions simpler.
2.2 Element Groups
Right now, it is cumbersome to define discounts be-
cause all parameters have to be defined exactly. Ad-
ditionally, it is often the case that only a subset of the
parameters should be defined. For example, promo-
tional discounts are usually not customer dependent.
Therefore, we introduce the idea of element groups.
In a first step, we sort the elements of each layer. The
quantity is sorted ascending (1,2,3,. . . ). The same is
done for the time (23.05, 24.05, 25.05,. . . ). The cus-
tomer could be sorted using different attributes, de-
pending on how customer groups (or customer seg-
ments) are defined. An element quantity group could
be 1 to 3, written as [1,3]. An element group can
now be seen as a combination of paths. Suppose that
the example of figure 1(a) should not be restricted to
quantity 1 but for quantities [1,3], resulting in a path
Product X, Customer B, [1,3], 23.05. Then, the tree
can be seen as in figure 1(b) where the quantity group
is defined. What exactly does an element group de-
fine?
Theorem 2. An element group definition [a
1
, a
k
]
that is used in a path p = e
1
, e
2
, e
i
, [a
1
, a
k
], e
i+2
, e
n
is only a short description for defining paths for all
elements inside the group definition [a
1
, a
k
]:
p
1
= e
1
, e
2
, e
i
, a
1
, e
i+2
, e
n
p
2
= e
1
, e
2
, e
i
, a
2
, e
i+2
, e
n
.
.
.
p
k
= e
1
, e
2
, e
i
, a
k
, e
i+2
, e
n
This can be seen directly because of the combina-
tion of elements to groups. The example of figure 1(b)
can be transformed to the three paths (cf. figure 1(c)):
Product X, Customer B, 1, 23.05
Product X, Customer B, 2, 23.05
Product X, Customer B, 3, 23.05
With element groups, it is easy to define discounts that
are not restricted to a discount parameter. If, for ex-
ample, a promotional discount should be created that
is not restricted to a customer, it is defined for all
customers by using the element group [Customer A,
Customer Z] (assume that Customer A is the first and
Customer Z the last customer of our sorted customer
set. We define the star symbol (*) as a short for all
elements: [*].
2.3 Calculating Discount Collisions
Efficiently
As we noted earlier, the tree is only used for illustra-
tion purposes. It is expensive to add all the paths to
the tree. And it is also not necessary:
Theorem 3. If two paths p
1
= a
1
, . . . , a
n
and p
2
=
b
1
, . . . , b
n
possibly containing element groups are to
be checked for a collision, on each layer i three dif-
ferent cases can occur:
1. a
i
and b
i
are both no element group.
DIFFERENT STRATEGIES FOR RESOLVING PRICE DISCOUNT COLLISIONS
451

2. One of the elements, either a
i
or b
i
is an element
group. We assume that a
i
is the group (if not, we
swap a
i
and b
i
).
3. a
i
and b
i
are both element groups.
A collision occurs when for all layers n with 1 ≤ i ≤
n the following tests do not return no collsion:
Case 1: if a
i
and b
i
are not equal return no collsion.
Case 2: if b
i
is not an element of a
i
return no coll-
sion.
Case 3: if a
i
and b
i
do not overlap return no coll-
sion.
The theorem follows from theorem 1 and 2. Theo-
rem 1 says that we have a collision exactly when the
path is equal. Therefore, if, in case 1, the two ele-
ments are not equal, there is no collision. Theorem 2
says that an element group can be transformed into a
number of paths. For case 2, if the element b
i
is not
inside the element group, the paths do not share and
therefore we have no collision. The same is true for
case three.
3 DISCUSSION AND OUTLOOK
This paper has shown different ways of defining dis-
counts used in popular business software systems to-
day. It was shown that the automatic calculation of
discounts is difficult and can lead to annoyed cus-
tomers. Afterwards, the paper presented the dTree to
define discounts graphically. It was shown that with
dTrees, discounts can be defined more easily and for
all collisions, the administrator can choose one path.
The dTree is not restricted to the parameters used as
an example in this paper, although they are the most
popular. It could be extended by using other parame-
ters, for example the shipping region (compare to sec-
tion 1). Another interesting extension is to show the
dTree also to the customers to make the calculation of
discounts more transparent.
To further prove the concept, the dTree approach
is currently implemented in the eSarine business ap-
plication system (Werro et al., 2004). eSarine is open
source and can be used to manage, offer and sell prod-
ucts on the internet.
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