Introducing optimization, solver, spreadsheet. Using a spreadsheet to solve a basic optimization problem. Steps for laying out the problem, identifying the constraints and using solver to find an optimal solution.

1. Introducing optimization
with Solver

2. In many situations, you want to find the best
way to do something. More formally, you
want to find the values of certain cells in a
worksheet that optimize (maximize or
minimize) a certain objective.
Spreadsheet Solver helps you answer
optimization problems such as the following
ones:

3. How can a large drug company
determine the monthly product mix
that maximizes corporate profitability
at its urban plant?
If Microsoft produces Xbox consoles at
three locations, how can it minimize
the cost of meeting demand for them?
What price for Xbox consoles and
games will maximize profit from Xbox
sales for Microsoft?

4.  Microsoft would like to undertake 20
strategic initiatives that will tie up money
and skilled programmers for the next five
years. It does not have enough resources
for all 20 projects; which ones should it
undertake?
 How do bookmakers find the best set of
ratings to set accurate point spreads for
NFL teams?
 How should I allocate my retirement
portfolio among high-tech stocks, value
stocks, bonds, cash, and gold?

5. An optimization model has three parts: the
target cell, the changing cells, and the
constraints.
The target cell represents the objective or
goal. You want to minimize or maximize the
amount in the target cell.
In the question about a drug company’s
product mix given earlier, the plant manager
would presumably want to maximize the
profitability of the plant during each month.

6. The cell that measures profitability would
be the target cell. The target cells for each
situation described at the beginning of the
chapter are listed in Table 1.

7. Changing cells are the worksheet cells that
you can change or adjust to optimize the
target cell.
In the drug company example, the plant
manager can adjust the amount produced for
each product during a month.
The cells in which these amounts are
recorded are the changing cells in this model.

8. Table 2 lists the appropriate changing cell
definitions for the models described at the
beginning of the chapter.
List of Changing Cell

9. Table 3 List of Constrains

10. To activate Solver, click the File
tab, choose Options, and then click
Add-Ins. In the Manage box at the
bottom of the dialog box, select
Excel Add-Ins and click Go. Select
the Solver Add-In check box in the
Add-Ins dialog box and click OK.
After Solver is activated, you can
run Solver by clicking Solver in the
Analysis group on the Data tab.

11. After you have input the target cell,
changing cells, and constraints, what
does Solver do? To answer this question,
you need some background in Solver
terminology. Any specification of the
changing cells that satisfies the model’s
constraints is a feasible solution. For
instance, any product mix that satisfies
the following three conditions would be
a feasible solution:

12. Does not use more raw material
or labor than is available.
Does not produce more of each
product than is demanded.
Does not produce a negative
amount of any product.

13. Essentially, Solver searches all feasible
solutions and finds the one that has the best
target cell value (the largest value for
maximum optimization, the smallest for
minimum optimization). Such a solution is
called an optimal solution.
-end-

14. Try this…

15. For each situation described, identify the
target cell, changing cells, and constraints:
1. I am borrowing PhP 100,000.00
for a 15-year mortgage. The annual
rate of interest is 8 percent. How
can I determine my monthly
mortgage payment?

16. For each situation described, identify the
target cell, changing cells, and constraints:
2. How should an auto company
allocate its advertising budget
between different advertising
formats?

17. For each situation described, identify the
target cell, changing cells, and constraints:
½ crosswise
 1. How should cities transport students to
more distant schools to obtain racial
balance?
 2. If a city has only one hospital, where
should it be located?
 3. How should a drug company allocate its
sales force’s efforts among its products?

18. For each situation described, identify the
target cell, changing cells, and constraints:
½ crosswise
 4. A drug company has allocated PhP2
billion to purchasing biotech companies.
Which companies should it buy?
 5. The tax rate charged to a drug company
depends on the country in which a product
is produced. How can a drug company
determine where each drug should be
made?