Chapter 1 Introduction to Business Analytics 23
ExAMPLE 1.8 A Sales-Promotion Decision Model
Advertising
Week Price ($) Coupon (0,1) ($)
1 6.99 0 0
2 6.99 0 150
3 6.99 1 0
4 6.99 1 150
5 6.49 0 0
6 6.49 0 150
7 6.49 1 0
8 6.49 1 150
9 7.59 0 0
10 7.59 0 150
11 7.59 1 0
12 7.59 1 150
13 5.49 0 0
14 5.49 0 150
15 5.49 1 0
16 5.49 1 150
In the grocery industry, managers typically need to
know how best to use pricing, coupons, and
advertising strategies to influence sales. Grocers
often study the relationship of sales volume to these
strategies by conducting controlled experiments to
identify the relationship between them and sales
volumes.1 That is, they implement different
combinations of pricing, coupons, and advertising,
observe the sales that result, and use analytics to
develop a predictive model of sales as a function of
these decision strategies.
For example, suppose that a grocer who operates
three stores in a small city varied the price, coupons
(yes = 1, no = 0), and advertising expenditures in a
local newspaper over a 16-week period and observed
the following sales:
1 Roger J. Calantone, Cornelia Droge, David S. Litvack, and C.
Anthony di Benedetto. “Flanking in a Price War,” Interfaces, 19, 2
(1989): 1–12.
To better understand the relationships among
price, coupons, and advertising, the grocer might
have developed the following model using business
analytics tools: sales = 500 − 0.05 × price + 30 ×
coupons + 0.08 × advertising + 0.25 × price ×
advertising
In this model, the decision variables are price,
coupons, and advertising. The values 500,−0.05, 30,
0.08, and 0.25 are effects of the input data to the
model that are estimated from the data obtained from
the experiment. They reflect the impact on sales of
changing the decision variables. For example, an
increase in price of $1 results in a 0.05-unit decrease
in weekly sales; using coupons results in a 30-unit
increase in weekly sales. In this example, there are no
uncontrollable input variables. The output of the
model is the sales units of the product. For example, if
the price is $6.99, no coupons are offered and no
advertising is done (the experiment corresponding to
week 1), the model estimates sales as
sales = 500 − 0.05 × $6.99 + 30 × 0 + 0.08 × 0
+ 0.25 × $6.99 × 0 = 500 units
We see that the actual sales in week 1 varied
between 481 and 510 in the three stores. Thus, this
model predicts a good estimate for sales; however, it
does not tell us anything about the potential variability
or prediction error. Nevertheless, the manager can use
this model to evaluate different pricing, promotion,
and advertising strategies, and help choose the best
strategy to maximize sales or profitability.