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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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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
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
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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$2,B4:C4)
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A B C D E F G H IDecision Variables 6-oz 10-oz
6.4 4.29
Objective Function 500 450 5142.86
ConstraintsMolding Capacity 6 5 60 <= 60Demand for 6-oz 1 0 6.42857 <= 8Storage Space 10 20 150 <= 150
=SUMPRODUCT($B$2:$C$2,B4:C4)
=SUMPRODUCT($B$2:$C$2,B9:C9)
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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
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Communicating GraphicallyMalcolm's Glass Problem
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0 2 4 6 8 10
6-oz Glasses (100 cases)
10
-oz.
Gla
ss
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(1
00
ca
se
s)
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Enhancing ChartsMalcolm's Glass Problem
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0 2 4 6 8 10
6-oz Glasses (100 cases)
10
-oz.
Gla
ss
es
(1
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ca
se
s)
Optimal Solution
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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.