IE 416: Operations Research IProblem #2 Page 199

Fruit Computer Company

Team 9Jin woo ChoiPhilip LiuNallely Tagle

Think Efficient®

Presentation Date: November 15th, 2011

Table of Contents

• Problem Statement• Summary of the Problem• Formulation of the Problem• Solution using WinQSB - LP• Report to Manager

• Solution using WinQSB - GP• Report to Manager

• Sensitivity Analysis - GP

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 MediocrePrice Per 100

Chips ($)

1 60 20 20 $400

2 50 35 15 $300

3 40 20 40 $250

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 budget

Assumption

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

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.

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

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.

400X1 + 300X2 + 250X3 ≤ 28,000

5) Fruit does not ship any chips, it only receives: Xi, Si

-, Si+ ≥ 0

Formulation of the Problem• Objective Function:• Penalty cost for LP

▫ Min Z = 10S1- +6S2

- + 4 S3- + 1 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) 400X1 + 300X2 +250X3 + S4- –S4

+ = 28,000

WinQSB for Linear Programming:Input

WinQSB for Linear Programming:Output

Report to Manager(Summary Table)

InformationFruit's

Requirements

Deviation from

Requirements

Penalty Cost

Quantity of excellent chips

≥ 5,000 Goal is met $0.00

Quantity of good chips

≥ 3,000Goal exceeded

by 500$0.00

Quantity of mediocre chips

≥ 1,000Goal exceeded

by 500$0.00

Annual Budget ≤ $28,000Goal 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) =

$30,000

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.

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

WinQSB for Preemptive Goal Programming:Input

WinQSB for Preemptive Goal Programming:Output

Report to Manager(Summary Table)

SupplierQuantity of

Lots

Quantity of excellent

chips

Quantity of good chips

Quantity of mediocre

ChipsCost ($)

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

chipsCost ($)

Goal 5,000 3,000 1,000 $0.00

Deviation from

Requirements

Goal is not met by 400

chipsGoal is met

Goal is exceeded by

400 chips$0.00

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.)

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

Scenario 2: Input (SA for Preemptive Goal Programming )

Scenario 2: Output(SA for Preemptive Goal Programming )

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

Scenario 3: Input (SA for Preemptive Goal Programming )

Scenario 3: Output (SA for Preemptive Goal Programming )

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

Scenario 4: Input (SA for Preemptive Goal Programming )

Scenario 4: Output (SA for Preemptive Goal Programming )

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

Scenario 5(SA for Preemptive Goal Programming )

Scenario 5 (SA for Preemptive Goal Programming)

Sensitivity Analysis Summary

Optimal Solution

Priority of GoalsLots Purchased from Suppliers

Deviation

Highest Second Third Lowest 1 2 3 Z1 Z2 Z3 Z4

Budget Excellent Good Mediocre 10 80 0 0 -400 0 400

Excellent GoodMediocr

eBudget 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 -400

QUESTIONS?

COMMENTS?