Session 1a. Decision Models -- Prof. Juran2 Overview Web Site Tour Course Introduction.

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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Seven-step Process

1.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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Formulation

a) 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 Function

A 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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Constraints

Find 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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Nonnegativity Constraints

Each Yellow Jacket takes 1 minute of leather and each Sachin Special takes 1.6 minutes.

There are 2,000 minutes available.

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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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