1. Team 9 Jin woo Choi Philip Liu Nallely Tagle
IE 416: Operations Research I Problem #2 Page 199 Fruit Computer Company
Think Efficient®
Team 9
Jin woo Choi
Philip Liu
Nallely Tagle
Presentation Date: November 15th, 2011

2. Table of Contents Problem Statement Summary of the Problem
Formulation of the Problem
Solution using WinQSB - LP
Report to Manager
Solution using WinQSB - GP
Sensitivity Analysis - GP

3. Characteristics of a Lot of 100 Chips
Problem Statement
Problem #2 Pg. 199
Fruit Computer Company
Fruit Computer Company is ready to make its annual purchase of computer chips from suppliers 1, 2, and 3.
Characteristics of a Lot of 100 Chips
Supplier
Excellent
Good
Mediocre
Price Per 100 Chips ($) 1 60 20
$400 2 50 35 15
$300 3 40
$250

4. Problem Summary Table Suppliers Excellent Good Mediocre Price Per Lot
Characteristics of a Lot (100 Chips per lot)
Suppliers
Excellent
Good
Mediocre
Price Per Lot
(100 Chips )
Price per chip
Supplier 1 60 20
$400
$4.00
Supplier 2 50 35 15
$300
$3.00
Supplier 3 40
$250
$2.50
Total
≥ 5,000
≥ 3,000
≥ 1,000
≤ $28,000
Price of Special Order per Chip
(Penalty Cost)
$10/chip
$6/chip
$4/chip
$1 for every dollar over budget

5. Assumption
It was assumed that Fruit Computer Company has additional funds that can be allocated towards the annual budget if it is necessary.

6. Formulation of the Problem
Decision Variables
Let Xi : number of lots provided by Supplieri (where i = 1, 2, and 3)
Deviational Variables:
Si- : amount that goali is under (goal is not achieved and where i = 1, 2, 3, and 4)
Si+ : amount that goali is over (goal has been passed and where i = 1, 2, 3, and 4)
Note: Goals refer to maintaining the budget and achieving the desired demand of excellent, good, and mediocre chips.

7. Formulation of the Problem
Initial Constraints:
1) At least 5,000 Excellent Chips from Suppliers 1, 2, 3:
60X1 + 50X2 + 40X3 ≥ 5,000
2) At least 3,000 Good Chips from Suppliers 1, 2, 3:
20X1 + 35X2 + 20X3 ≥ 3,000
3) At least 1,000 Mediocre Chips from Suppliers 1, 2, 3:
20X1 + 15X2 + 40X3 ≥ 1,000

8. Formulation of the Problem
Initial Constraints Continued:
4) Total cost of orders from Suppliers 1, 2, and 3 should not exceed Fruit’s budget of $28,000.
400X X X3 ≤ 28,000
5) Fruit does not ship any chips, it only receives:
Xi, Si-, Si+ ≥ 0

9. Formulation of the Problem
Objective Function:
Penalty cost for LP
Min Z = 10S1- +6S S S4+
For GP
Order of importance: Budget (S4+) >> Excellent (S1-) >> Good (S2-) >> Mediocre (S3-)
Min. Z1 = P1* S4+
Min. Z2 = P2 * S1-
Min. Z3 = P3 * S2-
Min. Z4 = P4 * S3-
Constraints with Deviational Variables:
1) 60X1 + 50X2 + 40X3 +S1- – S1+ = 5,000
2) 20X1 + 35X2 + 20X3 +S2- – S2+ = 3,000
3) 20X1 + 15X2 + 40X3 + S3- – S3+ = 1,000
4) 400X X2 +250X3 + S4- –S4+ = 28,000

10. WinQSB for Linear Programming: Input

11. WinQSB for Linear Programming: Output

12. Report to Manager (Summary Table)
Information
Fruit's Requirements
Deviation from Requirements
Penalty Cost
Quantity of excellent chips
≥ 5,000
Goal is met
$0.00
Quantity of good chips
≥ 3,000
Goal exceeded by 500
Quantity of mediocre chips
≥ 1,000
Annual Budget
≤ $28,000
Goal exceeded by $2,000
$2,000.00
Total Penalty Cost
Information
Results
Purchase from Supplier
Supplier 2
Quantity of Lots Purchased
100 lots at $300 per lot
Quantity of Each Chip Obtained
5,000 excellent chips, 3,500 good chips, and 1,500 mediocre chips
Total Cost
(100 lots) * ($300/lot) = $30,000

13. Report to Manager - LP
The current budget of $28,000 will have to be raised to $30,000 to accommodate this purchase order.
To minimize the penalty cost , purchase 100 lots of chips from Supplier 2.
The company will have 5,000 excellent chips, 3,500 good chips and 1,500 mediocre chips.
The reason for ordering extra chips: No penalty cost for having overstock.

14. Preemptive Goal Programming
Priority
Goals
1st
The budget of $28,000 is not exceeded
2nd
At least 5,000 excellent chips are purchased
3rd
At least 3,000 good chips are purchased
4th
At least 1,000 mediocre chips are purchased

15. WinQSB for Preemptive Goal Programming: Input

16. WinQSB for Preemptive Goal Programming: Output

17. Report to Manager (Summary Table)
Supplier
Quantity of Lots
Quantity of excellent chips
Quantity of good chips
Quantity of mediocre Chips
Cost ($) 1 10
600
200
$4,000.00 2 80
4,000
2,800
1,200
$24,000.00 3
$0.00
Total
N/A
4,600
3,000
1,400
$28,000.00
Quantity of excellent chips
Quantity of good chips
Quantity of mediocre chips
Cost ($)
Goal
5,000
3,000
1,000
$0.00
Deviation from Requirements
Goal is not met by 400 chips
Goal is met
Goal is exceeded by 400 chips

18. Report to Manager
Fruit will be able to achieve only three of the specified four goals (the goal of excellent chip will not be met).
The goal for excellent chips will be short by 400 chips.
The goal for mediocre chips will be exceeded by 400 chips.
If Fruit decides to fulfill all goals, the company should buy 100 lots of chips from Supplier 2. (Explained in the Report to Manager for Linear Programming.)

19. Scenario 2 (SA for Preemptive Goal Programming )
Sensitivity analysis was performed for the equation by changing the priority levels of the goals.
Scenario 2
Priority
Goals
1st
At least 5,000 excellent chips are purchased
2nd
At least 3,000 good chips are purchased
3rd
At least 1,000 mediocre chips are purchased
4th
The budget of $28,000 is not exceeded

20. Scenario 2: Input (SA for Preemptive Goal Programming )

21. Scenario 2: Output (SA for Preemptive Goal Programming )

22. Scenario 3 (SA for Preemptive Goal Programming )
Priority
Goals
1st
At least 1,000 mediocre chips are purchased
2nd
At least 3,000 good chips are purchased
3rd
At least 5,000 excellent chips are purchased
4th
The budget of $28,000 is not exceeded

23. Scenario 3: Input (SA for Preemptive Goal Programming )

24. Scenario 3: Output (SA for Preemptive Goal Programming )

25. Scenario 4 (SA for Preemptive Goal Programming )
Priority
Goals
1st
At least 3,000 good chips are purchased
2nd
At least 1,000 mediocre chips are purchased
3rd
At least 5,000 excellent chips are purchased
4th
The budget of $28,000 is not exceeded

26. Scenario 4: Input (SA for Preemptive Goal Programming )

27. Scenario 4: Output (SA for Preemptive Goal Programming )

28. Scenario 5 (SA for Preemptive Goal Programming )
Priority
Goals
1st
The budget of $28,000 is not exceeded
2nd
At least 1,000 mediocre chips are purchased
3rd
At least 3,000 good chips are purchased
4th
At least 5,000 excellent chips are purchased

29. Scenario 5 (SA for Preemptive Goal Programming )

30. Scenario 5 (SA for Preemptive Goal Programming)

31. Sensitivity Analysis Summary
Optimal Solution
Priority of Goals
Lots Purchased from Suppliers
Deviation
Highest
Second
Third
Lowest 1 2 3 Z1 Z2 Z3 Z4
Budget
Excellent
Good
Mediocre 10 80
-400
400
100
500
2000

32. QUESTIONS? COMMENTS?