Problem 2 Page 199 Fruit Computer Company Team 9 Jin woo Choi Philip Liu Nallely Tagle Think Efficient Presentation Date November 15 th 2011 Table of Contents Problem Statement ID: 549212
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IE 416: Operations Research IProblem #2 Page 199 Fruit Computer Company
Team 9Jin woo ChoiPhilip LiuNallely Tagle
Think Efficient
®
Presentation Date: November 15
th
, 2011Slide2
Table of Contents
Problem StatementSummary of the ProblemFormulation of the ProblemSolution using WinQSB
- LP
Report to ManagerSolution using WinQSB
- GP
Report to Manager
Sensitivity Analysis - GPSlide3
Problem StatementProblem #2 Pg. 199Fruit 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
20
$400
2
50
35
15
$300
3
40
20
40
$250Slide4
Problem Summary Table
Table 2
Characteristics of a
Lot (100 Chips per lot)
Suppliers
Excellent
Good
Mediocre
Price Per
Lot
(100
Chips
)
Price per chip
Supplier 1
60
20
20
$400
$4.00
Supplier 2
50
35
15
$300
$3.00
Supplier 3
40
20
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 budgetSlide5
AssumptionIt was assumed that Fruit Computer Company has additional funds that can be allocated towards the annual budget if it is necessary.Slide6
Formulation of the ProblemDecision 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
goal
i
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.Slide7
Formulation of the Problem
Initial Constraints:1) At least 5,000 Excellent Chips from Suppliers 1, 2, 3: 60X
1 + 50X2 + 40X
3 ≥ 5,000 2) At least 3,000 Good Chips from Suppliers 1, 2, 3:
20X
1
+ 35X
2
+ 20X
3
≥ 3,000
3
) At least
1,000 Mediocre
Chips from
Suppliers 1
, 2, 3:
20X
1
+ 15X
2
+ 40X
3
≥
1,000
Slide8
Formulation of the ProblemInitial Constraints Continued:
4) Total cost of orders from Suppliers 1, 2, and 3 should not exceed Fruit’s budget of $28,000. 400X1 + 300X2 + 250X3 ≤ 28,000
5) Fruit does not ship any chips, it only receives: X
i, Si-, Si+ ≥ 0 Slide9
Formulation of the ProblemObjective Function:
Penalty cost for LPMin Z = 10S1- +6S2- + 4 S3
- + 1 S4+
For GP Order of importance: Budget (S4+) >> Excellent (S1-
) >> Good (S
2
-
) >> Mediocre (S
3
-
)
Min. Z1 = P1*
S
4
+
Min. Z2 = P2 *
S
1
-
Min. Z3 = P3 *
S
2
-
Min. Z4 = P4 *
S
3
-
Constraints with Deviational Variables:
1) 60X
1
+ 50X
2
+ 40X
3
+S
1
-
– S
1
+
=
5,000
2) 20X
1
+ 35X
2
+ 20X
3
+S
2
-
– S
2
+
= 3,000
3) 20X
1
+ 15X
2
+ 40X
3
+ S
3
-
– S
3
+
= 1,000
4) 400X
1
+ 300X
2
+250X
3
+ S
4
-
–S
4
+
= 28,000 Slide10
WinQSB for Linear Programming:InputSlide11
WinQSB for Linear Programming:OutputSlide12
Report to Manager(Summary Table)
Information
Fruit's Requirements
Deviation from RequirementsPenalty Cost
Quantity of excellent chips
≥ 5,000
Goal is met
$0.00
Quantity of good chips
≥ 3,000
Goal exceeded by 500
$0.00
Quantity of mediocre chips
≥ 1,000
Goal exceeded by 500
$0.00
Annual Budget
≤ $28,000
Goal exceeded by $2,000
$2,000.00
Total Penalty Cost
$2,000.00
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) = $30,000Slide13
Report to Manager - LPThe 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.Slide14
Preemptive Goal Programming
PriorityGoals
1st
The budget of $28,000 is not exceeded2
nd
At least 5,000 excellent chips are purchased
3
rd
At least 3,000 good chips are purchased
4
th
At least 1,000 mediocre chips are purchasedSlide15
WinQSB for Preemptive Goal Programming:InputSlide16
WinQSB for Preemptive Goal Programming:OutputSlide17
Report to Manager(Summary Table)
Supplier
Quantity of Lots
Quantity of excellent chipsQuantity of good chips
Quantity of mediocre Chips
Cost ($)
1
10
600
200
200
$4,000.00
2
80
4,000
2,800
1,200
$24,000.00
3
0
0
0
0
$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
$0.00Slide18
Report to ManagerFruit 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.) Slide19
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
Goals1st
At least 5,000 excellent chips are purchased
2
nd
At least 3,000 good chips are purchased
3
rd
At least 1,000 mediocre chips are purchased
4
th
The budget of $28,000 is not exceededSlide20
Scenario 2: Input (SA for Preemptive Goal Programming )Slide21
Scenario 2: Output(SA for Preemptive Goal Programming )Slide22
Scenario 3 (SA for Preemptive Goal Programming )
PriorityGoals
1
stAt least 1,000 mediocre chips are purchased
2
nd
At least 3,000 good chips are purchased
3
rd
At least 5,000 excellent chips are purchased
4
th
The budget of $28,000 is not exceededSlide23
Scenario 3: Input (SA for Preemptive Goal Programming )Slide24
Scenario 3: Output (SA for Preemptive Goal Programming )Slide25
Scenario 4 (SA for Preemptive Goal Programming )
PriorityGoals
1
stAt least 3,000 good chips are purchased
2
nd
At least 1,000 mediocre chips are purchased
3
rd
At least 5,000 excellent chips are purchased
4
th
The budget of $28,000 is not exceededSlide26
Scenario 4: Input (SA for Preemptive Goal Programming )Slide27
Scenario 4: Output (SA for Preemptive Goal Programming )Slide28
Scenario 5(SA for Preemptive Goal Programming )
PriorityGoals
1
stThe budget of $28,000 is not exceeded
2
nd
At least 1,000 mediocre chips are purchased
3
rd
At least 3,000 good chips are purchased
4
th
At least 5,000 excellent chips are purchasedSlide29
Scenario 5(SA for Preemptive Goal Programming )Slide30
Scenario 5 (SA for Preemptive Goal Programming)Slide31
Sensitivity Analysis Summary
Optimal Solution
Priority of Goals
Lots Purchased from Suppliers
Deviation
Highest
Second
Third
Lowest
1
2
3
Z
1
Z
2
Z
3
Z
4
Budget
Excellent
Good
Mediocre
10
80
0
0
-400
0
400
Excellent
Good
Mediocre
Budget
0
100
0
0
500
500
2000
Mediocre
Good
Excellent
Budget
10
80
0
400
0
-400
0
Good
Mediocre
Excellent
Budget
10
80
0
0
400
-400
0
Budget
Mediocre
Good
Excellent
10
80
0
0
400
0
-400Slide32
QUESTIONS?
COMMENTS?