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

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

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

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

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) 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

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) 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

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 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

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