Session 1b

Decision Models -- Prof. Juran

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Overview

• Spreadsheet Conventions• Copying, Pasting, Reporting• Introduction to Solver

Decision Models -- Prof. Juran

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Spreadsheet Conventions

• Basic Idea: Customer-friendly• Easy to Read• Easy to Audit• Easy to Adapt

– “Parameterization”– “Dragability”

Decision Models -- Prof. Juran

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Spreadsheet Conventions

• Clear, logical layout• Separation across multiple sections

and/or worksheets• Clear headings for inputs, decision

variables, and outputs• Formatting for user clarity• Text boxes and cell comments

Decision Models -- Prof. Juran

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Written Reports

0. Conclusions and Recommendations– Done last, appears first

1. Managerial Problem Definition2. Formulation3. Solution Methodology4. Discussion? Appendices?

Decision Models -- Prof. Juran

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Written Reports

• Minimal Raw Spreadsheet Elements– i. e. none

• Graphical Communication – Equation Editor– Charts, Graphs– Spreadsheet Captures

Decision Models -- Prof. Juran

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Optimization Example:

Malcolm’s Glass Shop

Decision Models -- Prof. Juran

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Managerial Problem Definition

Malcolm owns a glass-molding machine capable of producing two products: six-ounce juice glasses and ten-ounce cocktail glasses. He needs to decide how many of each product he ought to make each week in order to make the greatest profit. He is limited by the production rate of the machine, demand for one of the products, and storage space.

Decision Models -- Prof. Juran

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Formulation

Decision variables: How many to produce of two products.

Objective: Maximize Profit.

Constraints:The molding machine can only produce so many glasses in a week. There is a market limit for 6-oz glasses.There is a limit on storage space.Malcolm can’t make negative amounts of either product.

Decision Models -- Prof. Juran

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Formulation

Maximize Profit from 6-oz glasses + Profit from 10-oz glasses

Subject to: Molding Machine capacity used for 6-oz + Molding Machine capacity used for 10-oz

<= Total Molding capacity

6-oz glasses produced <= Total Demand for 6-oz glasses

Storage Space used for 6-oz

+ Storage Space used for 10-oz <= Total Storage Space

6-oz glasses produced >= 0

10-oz glasses produced >= 0

Decision Models -- Prof. Juran

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Formulation

Decision Models -- Prof. Juran

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Formulation

Maximize: Z = 500X1 + 450X2

Subject to: 6 X1 + 5 X2 60 1 X1 + 0 X2 8 10 X1 + 20 X2 150 1 X1 + 0 X2 0 0 X1 + 1 X2 0

Decision Models -- Prof. Juran

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Solution Methodology

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A B C D E F G H IDecision Variables 6-oz 10-oz

1 1

Objective Function 500 450 950

ConstraintsMolding Capacity 6 5 11 <= 60Demand for 6-oz 1 0 1 <= 8Storage Space 10 20 30 <= 150

=SUMPRODUCT($B$2:$C$2,B9:C9)

=SUMPRODUCT($B$2:$C$2,B4:C4)

Decision Models -- Prof. Juran

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Solver Dialog Box

Decision Models -- Prof. Juran

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Decision Models -- Prof. Juran

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A B C D E F G H IDecision Variables 6-oz 10-oz

6.4 4.29

Objective Function 500 450 5142.86

ConstraintsMolding Capacity 6 5 60 <= 60Demand for 6-oz 1 0 6.42857 <= 8Storage Space 10 20 150 <= 150

=SUMPRODUCT($B$2:$C$2,B4:C4)

=SUMPRODUCT($B$2:$C$2,B9:C9)

Decision Models -- Prof. Juran

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Solver Answer Report123456789

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A B C D E F G HMicrosoft Excel 15.0 Answer ReportWorksheet: [01b-01-malc.xlsx]OptimizedReport Created: 9/3/2014 8:20:58 AMResult: Solver found a solution. All Constraints and optimality conditions are satisfied.Solver Engine

Engine: Simplex LPSolution Time: 0 Seconds.Iterations: 3 Subproblems: 0

Solver OptionsMax Time 100 sec, Iterations 100, Precision 0.000001Max Subproblems 5000, Max Integer Sols 5000, Integer Tolerance 5%, Assume NonNegative

Objective Cell (Max)Cell Name Original Value Final Value

$E$4 Objective Function 5142.857143 5142.857143

Variable CellsCell Name Original Value Final Value Integer

$B$2 6-oz 6.428571429 6.428571429 Contin$C$2 10-oz 4.285714286 4.285714286 Contin

ConstraintsCell Name Cell Value Formula Status Slack

$E$7 Molding Capacity 60 $E$7<=$G$7 Binding 0$E$8 Demand for 6-oz 6.428571429 $E$8<=$G$8 Not Binding 1.571428571$E$9 Storage Space 150 $E$9<=$G$9 Binding 0

Decision Models -- Prof. Juran

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Communicating GraphicallyMalcolm's Glass Problem

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6-oz Glasses (100 cases)

10

-oz.

Gla

ss

es

(1

00

ca

se

s)

Decision Models -- Prof. Juran

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Enhancing ChartsMalcolm's Glass Problem

0

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6

8

10

0 2 4 6 8 10

6-oz Glasses (100 cases)

10

-oz.

Gla

ss

es

(1

00

ca

se

s)

Optimal Solution

Decision Models -- Prof. Juran

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Enhancing Charts

Decision Models -- Prof. Juran

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Conclusions and Recommendations

• Make 642 cases of 6-oz glasses and 428 cases of 10-oz glasses.

• Earn $5,143 profit.

Decision Models -- Prof. Juran

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Summary

• Spreadsheet Conventions• Copying, Pasting, Reporting• Introduction to Solver