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Case Study 34
34
Decision Support System for Product Pricing
Decision Support System for Product Pricing
Problem Description
Pricing products is a challenging process that managers have to deal with quite often.
Different factors impact the price of a product. For example, costs and demand affect price.
Normally, the price we pay for a product is higher than the cost of manufacturing and
delivering the product. Formally, the price of a product is determined by demand and supply.
If the demand for a product is high and its supply is low, the customer would be willing to pay
a higher price. Pricing the products well is crucial for a company, as it directly affects the
profits. Higher prices imply higher profit margins. However, if the price of a product is too
high, it will negatively affect its demand, and as a result it will negatively affect profits of the
company.
The price of a product varies with time. Reasons for such a fluctuation could be changes in
the demand for the product, changes in the supply because of competition, and changes in
the production and delivery costs. The aim of this project is to build a decision support
system that will enable the companies to price their products considering important factors
such as demand and costs. Below we present a mathematical model that can be used to
price products.
Mathematical Model
We use the following notation:
I
total number of products
p1i
price of product i on-season
p2i
price of product i off-season
ci
cost of producing product i
m1
production capacity on-season
m2
production capacity off-season.
The decision variables are as follows:
d1i
on-season demand for product i
d2i
off-season demand for product i.
The demand functions on- and off-season are described below.
d1i  1i  1i * p1i   1i p2i
.
d 2i   2i   2i * p1i   2i p2i
Where, coefficients 1i, 2i present the demand for product i if the on- and off-season prices
were equal to zero; 1i, 2i present the change of demand with respect to one unit change of
the on-season price, and 1i, 2i present the change of demand with respect to one unit
change of the off-season price.
The following is a mathematical formulation of the problem:
Case Study 34
Decision Support System for Product Pricing
I
max :  d1i p1i  d 2i p 2i  ci (d1i  d 2i ) 
i 1
Subject to :
I
d
i 1
1i
 m1
(1)
2i
 m2
(2)
I
d
i 1
d1i   1i  1i * p1i   1i p 2i
for i  1,..., I ,
(3)
d 2i   2i   2i * p1i   2i p 2i
for i  1,..., I ,
(4)
d1i , p1i , d 2i , p 2i  0
for i  1,..., I .
(5)
The objective is to maximize profits. The first and second sets of constraints show that total
demand is bounded by production capacity limits. The third and fourth sets of constraints
present the demand function on- and off-season. The last set of constraints is the nonnegativity constraints.
Excel Spreadsheet
1.
Build a spreadsheet that presents historical data about demand and prices on- and offseason for all the products produced.
2.
Build a spreadsheet that presents the cost of producing the products.
User Interface
1.
Build a welcome form.
2.
Build a data analysis form. The following are suggestions to help you design this form:
3.
a.
Insert a text box where the user types in the total number of products considered.
b.
Insert a frame titled “Regression Analysis.” The frame includes a text box where the
user types in the location of Spreadsheet 1. Insert a command button that, when
clicked on, uses the regression analysis tools of Excel to identify the relationship
between prices and demand. The results from this analysis are used to identify
coefficients 1i, 2i, 1i, 2i, 1i and 2i (i = 1,…,I).
c.
Insert two text boxes where the user types in production capacity on- and offseason.
d.
Insert a command button that, when clicked on, solves the mathematical
formulation of the pricing problem using the Excel solver and opens Form 3,
described below.
Build a form to present the results of this study. In this form include two frames. The first
frame has a number of option buttons that enable the user to choose to open any of the
reports described below. The second frame, titled “Sensitivity Analysis,” has a number
of option buttons that enable the user to choose a parameter to perform a sensitivity
analysis. One can perform a sensitivity analysis with respect to production capacity,
demand, price, costs, etc.
Design a logo for this project. Insert this logo in the forms created above. Pick a background
color and a font color for the forms created. Include the following in the forms created: record
K T
K T
K T
k 1t 1
k 1t 1
k 1t 1
min :  ckt xkt   hkt I kt   Fkt z kt
Subject to :
K
 zkt  1
Case Study 34
Decision Support System for Product Pricing
navigation
operations
command buttons, and form operations
for t command
 1,..., T , buttons, record (1
)
command buttons as needed.
k 1
xkt  I k ,t 1  I kt  d kt
xkt  PktReports
z kt
xkt , I kt  0
z kt  {0,1}
for k  1,..., K ; t  1,..., T ,
(2)
for k  1,..., K ; t  1,..., T ,
(3)
1.
for kthe
 1optimal
,..., K ; tprice
 1,...,
, product.
(4)
Report
forTeach
2.
for k the
 1,...,
K ; t  profit
1,..., Tfound
.
(5from
)
Report
optimal
solving the mathematical formulation of the
problem.
3.
Report the results from the sensitivity analysis.
4.
Report the results from regression analysis. Report the values found for the coefficients
1i, 2i, 1i, 2i, 1i and 2i.
5.
Graph the relationship between on-season demand and on-season price for a particular
product.
6.
Graph the relationship between off-season demand and off-season price for a particular
product.
Reference
Montgomery, D.C., Runger, G.C., “Applied Statistics and Probability for Engineers,” 3rd Ed.,
John Wiley & Sons, 2003.
Winston, L.W., “Operations Research: Applications and Algorithms.” Duxbury Press, 3rd Ed.,
1994.