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Management Science Modeling Lecture One. Introduction to Modeling (Chapter One). Chapter Topics. The Management Science Approach. The Management Science Process. Figure 1.1. Steps in the Management Science Process. Example of Model Construction (1 of 3). Information and Data:

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management science modeling lecture one

Management Science Modeling Lecture One

Introduction to Modeling

(Chapter One)

MS Modeling S 2010

chapter topics
Chapter Topics

MS Modeling S 2010

the management science process
The Management Science Process

Figure 1.1

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example of model construction 1 of 3
Example of Model Construction (1 of 3)
  • Information and Data:
  • Business firm makes and sells a steel product
  • Product costs $5 to produce
  • Product sells for $20
  • Product requires 4 pounds of steel to make
  • Firm has 100 pounds of steel
  • Business Problem:
  • Determine the number of units to produce to make the most profit, given the limited amount of steel available.

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Example of Model Construction (2 of 3)

Variables: X = # units to produce (decision variable)

Z = total profit (in $)

Model: Z = $20X - $5X (objective function)

4X = 100 lb of steel (resource constraint)

Parameters: $20, $5, 4 lbs, 100 lbs (known values)

Formal Specification of Model:

maximize Z = $20X - $5X

subject to 4X ≤ 100

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Example of Model Construction (3 of 3)

Model Solution:

Solve the constraint equation:

4x ≤ 100

(4x)/4 ≤ (100)/4

x ≤ 25 units

Substitute this value into the profit function:

Z = $20x - $5x

= (20)(25) – (5)(25)

= $375

(Produce 25 units, to yield a profit of $375)

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Model Building:

Break-Even Analysis (1 of 9)

  • Used to determine the number of units of a product to sell or produce that will equate total revenue with total cost.
  • The volume at which total revenue equals total cost is called the break-even point.
  • Profit at break-even point is zero.

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Model Building:Break-Even Analysis (2 of 9)

Model Components

  • Fixed Cost (cf) - costs that remain constant regardless of number of units produced.
  • Variable Cost (cv) - unit production cost of product.
  • Volume (v) – the number of units produced or sold
  • Total variable cost (vcv) - function of volume (v) and unit variable cost.

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Model Building:Break-Even Analysis (3 of 9)

Model Components

  • Total Cost (TC) - total fixed cost plus total variable cost.
  • Profit (Z) - difference between total revenue vp (p = unit price) and total cost, i.e.

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Model Building:Break-Even Analysis (4 of 9)

Computing the Break-Even Point

The break-even point is that volume at which total revenue equals total cost and profit is zero:

The break-even point

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Model Building:

Break-Even Analysis (5 of 9)

Example:Western Clothing Company

Fixed Costs: cf = $10000

Variable Costs: cv = $8 per pair

Price : p = $23 per pair

The Break-Even Point is:

v = (10,000)/(23 -8)

= 666.7 pairs

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Model Building:

Break-Even Analysis (6 of 9)

Figure 1.2

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Model Building:

Break-Even Analysis (7 of 9)

Figure 1.3

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Model Building:

Break-Even Analysis (8 of 9)

Figure 1.4

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Model Building:

Break-Even Analysis (9 of 9)

Figure 1.5

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Break-Even Analysis: QM Solution (4 of 5)

Exhibit 1.4

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Break-Even Analysis: QM Solution (5 of 5)

Exhibit 1.5

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Classification of Management Science Techniques

Figure 1.6 Modeling Techniques

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Characteristics of Modeling Techniques

  • Linear Mathematical Programming -clear objective; restrictions on resources and requirements; parameters known with certainty. (Chap 2-6, 9)
  • Probabilistic Techniques -results contain uncertainty. (Chap 11-13)
  • Network Techniques - model often formulated as diagram; deterministic or probabilistic. (Chap 7-8)
  • Other Techniques - variety of deterministic and probabilistic methods for specific types of problems including forecasting, inventory, simulation, multicriteria, etc. (Chap 10, 14-16)

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Business Use of Management Science

  • Some application areas:

- Project Planning

- Capital Budgeting

- Inventory Analysis

- Production Planning

- Scheduling

  • Interfaces - Applications journal published by Institute for Operations Research and Management Sciences (INFORMS)

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Decision Support Systems (DSS)

A decision support system is a computer-based system that helps decision makers address complex problems that cut across different parts of an organization and operations.

Features of Decision Support Systems

  • Interactive
  • Use databases & management science models
  • Address “what if” questions
  • Perform sensitivity analysis

Examples include:

ERP – Enterprise Resource Planning

OLAP – Online Analytical Processing

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Management Science Models

Decision Support Systems (2 of 2)

Figure 1.7 A Decision Support System

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assignment for chapter one
Assignment for Chapter One

Problems #4, 10, 12, 22, and 24

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