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Session 1a
Session 1a
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Overview
• Web Site Tour • Course Introduction
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2 Modules• Module I: Optimization• Module II: Spreadsheet Simulation
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What is Decision Modeling?
FormulationReal world
SystemDecision Model
Decision Modeling Process
Real World Conclusions Model
Conclusions
Deduction
Interpretation
Implementation
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What is Analytics?… besides bad English?
Decisions
Inferences
Data
Business
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Seven-step Process1.Definition2.Data Collection3.Formulation4.Model Verification5.Selection of an Alternative6.Presentation of Results7.Implementation
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Revised Process for This Course
0. Conclusions and Recommendations1. Managerial Definition2. Formulation3. Solution Methodology4. Discussion? Appendices?
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Software• Microsoft Excel
– Data Table– Goal Seek– Solver– Premium Solver, SolverTable– Analysis Toolpack– Charts and Graphs
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Software• The Decision Tools Suite
– @Risk– PrecisionTree– TopRank– BestFit– RiskView– StatPro
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Software• Other Software
– Crystal Ball– Extend– Sigma
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Descriptive Model• Approximates how a real system
works (or would work) given certain assumptions
• Does not give us the “right answer”
• Focus for Module 2
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Prescriptive Model
• Identifies the “right answer”• Focus of Module 1
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What is Optimization?• A model with a “best” solution• Strict mathematical definition of
“optimal”• Usually unrealistic assumptions• Useful for managerial intuition
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Elements of an Optimization Model
• Formulation– Decision Variables– Objective– Constraints
• Solution – Algorithm or Heuristic
• Interpretation
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Toomer Sporting Goods
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Managerial Problem Definition
Ishani Mukherjee must decide how many to produce of two products.
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Managerial Problem Definition
• 2-piece Yellow Jacket• 4-piece Sachin Special
Yellow Jacket Sachin Special Revenue ₹390 ₹442
Cost ₹273 ₹286 Profit ₹117 ₹156
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Formulationa) Define the choices to be made by the
manager (called decision variables).b) Find a mathematical expression for the
manager's goal (called the objective function).
c) Find expressions for the things that restrict the manager's range of choices (called constraints).
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Decision Variables
Variable Name Symbol Units Yellow Jacket X Cricket balls Sachin Special Y Cricket balls
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Objective FunctionA mathematical expression of the manager’s goal in terms of the decision variables.
Yellow Jacket (X) Sachin Special (Y) Revenue ₹390 ₹442
Cost ₹273 ₹286 Profit ₹117 ₹156
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What is the objective?
156Y117XProfit
Maximize or minimize?
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ConstraintsFind expressions for the things that restrict the manager's range of choices, in terms of the decision variables.
Amount Required Per Amount Resource Yellow Jacket Sachin Special Available Leather 4 oz 5 oz 6,000 oz Nylon 3 m 6 m 5,400 m Cork 2 oz 4 oz 4,000 oz Labor 2 min 2.5 min 3,500 min Stitching 1 min 2 min 2,000 min
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Leather Constraint
Each Yellow Jacket uses 4 ounces of leather and each Sachin Special uses 5 ounces.There are 6,000 ounces available.
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Leather Constraint
000,654 YX
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Nylon Constraint
Each Yellow Jacket uses 3 meters of nylon and each Sachin Special uses 6 meters.There are 5,400 meters available.
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Nylon Constraint
400,563 YX
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Cork Constraint
Each Yellow Jacket uses 2 ounces of cork and each Sachin Special uses 4 ounces.There are 4,000 ounces available.
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Cork Constraint
000,442 YX
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Labor Constraint
Each Yellow Jacket uses 2 minutes of general labor and each Sachin Special takes 2.5 minutes.There are 3,500 minutes available.
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Labor Constraint
500,35.22 YX
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Stitching Constraint
Each Yellow Jacket takes 1 minute of stitching time and each Sachin Special takes 1.6 minutes.There are 2,000 minutes available.
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Stitching Constraint
000,26.11 YX
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Nonegativity Constraints
0X0Y
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Solution MethodologyUse algebra to find the best solution.
(Simplex algorithm)
George B. Dantzig 1914 - 2005
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Point X Y A 0 0 B 0 900 C 1000 400 D 1500 0
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Point X Y Objective Function Profit A 0 0 117(0)+156(0) = ₹0 B 0 900 117(0)+156(900) = ₹140,400 C 1000 400 117(1,000)+156(400) = ₹179,400 D 1500 0 117(1,500)+156(0) = ₹175,500
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The Optimal Solution
• Make 1,000 Yellow Jackets and 400 Sachin Specials
• Earn ₹179,400
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