Case Problem 1: Textbook Publishing
An integer programming model can be used advantageously to assist in developing
recommendations.
1 if book i is scheduled for publication
Let
xi =
{0 otherwise
The subscripts correspond to the books as follows:
i
1
2
3
4
5
6
7
8
9
10
Book
Business Calculus
Finite Math
General Statistics
Mathematical Statistics
Business Statistics
Finance
Financial Accounting
Managerial Accounting
English Literature
German
An integer programming model for maximizing projected sales (thousands of units) subject to the
restrictions mentioned is given.
Max
20x1 + 30x2 + 15x3 + 10x4 + 25x5 + 18x6 + 25x7 + 50x8 + 20x9 + 30x10 s.t.
30x1 + 16x2 + 24x3 + 20x4 + 10x5
40x1 + 24x2
+ 40x9
+ 24x7 + 28x8 + 34x9 + 50x10 ≤ 40 Susan
≤ 60 John
30x3 + 24x4 + 16x5 + 14x6 + 26x7 +
30x8 + 30x9 + 36x10 ≤ 40 Monica
x3 + x4 + x5
≤ 2 No. of Stat Books
x7 + x8 ≤ 1 Account Book
x1 +
x2
= 1 Math Book xi = 0, 1 for
all i
The optimal solution (x2 = x5 = x6 = 1) calls for publishing the finite math, the business statistics
and the finance books. Projected sales are 73,000 copies.
(1)
If Susan can be made available for another 12 days, the optimal solution is x2 = x8 = 1.
This calls
for publishing the finite math and managerial accounting texts for projected sales of 80,000 copies.
(2)
If Monica is also available for 10 more days, a big improvement can be made. The new
optimal solution calls for producing the finite math book, the business statistics book, and
the managerial accounting book. Projected sales are 105,000 copies.
(3)
The solution in (2) above does not include any new books. In the long run this would
appear to be a bad strategy for the company. A variety of modifications can be made to
the model to examine the short run impact of postponing a revision. For instance, a
constraint could be added to require publication of at least one new book.