1. Using Binary Integer Programming to Deal with Yes-or-No Decisions
Chapter 7: Hillier and Hillier

2. Agenda Case Study: California Manufacturing Company
Wyndor Case Revisited
Variation of Wyndor’s Problem

3. Applications of Binary Variables
Binary variables only allow two choices
This makes them suited for problems that are characterized by variables that can take on only two possibilities.
Examples:
Do a project or not do a project?
To hire or not to hire?
To build or not to build?
To Sell or not to sell?

4. Case Study: California Manufacturing Company (CMC)
The California Manufacturing Company is a company with factories and warehouses throughout California.
It is currently considering whether to build a new factory in Los Angeles and/or San Francisco.
Management is also considering building one new warehouse where a new factory has been recently built.
Should the CMC build factories and/or warehouses in Los Angeles and/or San Francisco?

5. Capital Needed (Millions)
Case Study: CMC Cont.
Binary Decision
Decision Variable
NPV (Millions)
Capital Needed (Millions)
Build a factory in Los Angeles
FLA $8 $6
Build a factory in San Francisco
FSF 5 3
Build a warehouse in Los Angeles
WLA 6
Build a warehouse in San Francisco
WSF 4 2
Building Money Available:
$10 million

6. Case Study: CMC Cont.
FLA, FSF, WLA,WSF are all binary variables which take on the value of 1 if the specific item is done and zero if it is not done.
We also need to make sure that at most one warehouse is built and it is built where a factory is built.

7. Mathematical Model for CMC

8. Wyndor Case Revisited Two new products have been developed:
An 8-foot glass door
A 4x6 foot glass window
Wyndor has three production plants
Production of the door utilizes Plants 1 and 3
Production of the window utilizes Plants 2 and 3
Objective is to find the optimal mix of these two new products.

9. Wyndor Case Revisited Cont.
Production Time Used for Each Unit Produced
Plant
Doors
Windows
Available Per Week 1
1 hour
0 hour
4 hour 2
2 hour
12 hour 3
3 hour
18 hour
Unit Profit
$300
$500

10. Wyndor Case Revisited Cont.

11. Changing Wyndor to Account for Setup Costs
Suppose that two changes are made to the original Wyndor problem:
If Wyndor chooses to produce doors, it must pay a one time set-up cost of $700, while if Wyndor produces windows it must pay a set-up cost of $1,300.
We want to restrict the doors and windows to be integer values.

12. Graphical Solution to Original Wyndor Problem
Figure 9.6 This graph summarizes the application of the graphical method to the original Wyndor problem.

13. Feasible Solutions for Wyndor with Setup Costs
Figure 9.7 The dots are the feasible solutions for variation 1 of the Wyndor problem. Also shown is the calculation of the total net profit P (in dollars) for each corner point from the net profits given in Table 9.4.

14. Wyndor’s Mathematical Model With Set-Up Costs

15. Changing Wyndor to Account for Mutually Exclusive Products
Suppose Wyndor decides that it only wants to produce doors or windows rather than both.
This implies that either doors have to be zero or windows have to be zero.

16. Wyndor’s Mathematical Model With Mutually Exclusive Products

17. Changing Wyndor to Account for Either-Or Constraints
Suppose the company is trying to decide whether to build a new up-to-date plant that will be used to replace plant 3.
This implies that Wyndor wants to examine the profitably of using plant 4 versus plant 3.

18. Wyndor’s Data with Either/Or Constraint
Production Time Used for Each Unit Produced
Plant
Doors
Windows
Available Per Week 1
1 hour
0 hour
4 hour 2
2 hour
12 hour 3
3 hour
18 hour 4
2 hours
4 hours
28 hours
Unit Profit
$300
$500

19. Graphical Solution with Plant 3 or Plant 4
Figure These two graphs for variation 3 of the Wyndor problem with either-or constraints show the linear programming problem and its optimal solution that would result if the plant chosen to help produce the two new products were (a) plant 3 or (b) plant 4.

20. Wyndor’s Mathematical Model With Either/Or Constraint