ch01management science
TRANSCRIPT
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Chapter 1- Management Science 1
Chapter 1- Management Science
Chapter Topics
• The Management Science Approach to Problem Solving
• Model Building: Break-Even Analysis
• Computer Solution
• Management Science Modeling Techniques
• Business Use of Management Science Techniques
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Chapter 1- Management Science 2
Management Science Approach
• Management science uses a scientific approach to solving management problems.
• It is used in a variety of organizations to solve many different types of problems.
• It encompasses a logical mathematical approach to problem solving.
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Chapter 1- Management Science 3
The Management Science Process
Figure 1.1 The Management Science Process
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Chapter 1- Management Science 4
Steps in the Management Science Process
• Observation - Identification of a problem that exists in the system or organization.
• Definition of the Problem - problem must be clearly and consistently defined showing its boundaries and interaction with the objectives of the organization.
• Model Construction - Development of the functional mathematical relationships that describe the decision variables, objective function and constraints of the problem.
• Model Solution - Models solved using management science techniques.
• Model Implementation - Actual use of the model or its solution.
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Chapter 1- Management Science 5
Example of Model Construction (1 of 2)Problem Definition
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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Chapter 1- Management Science 6
Example of Model Construction (2 of 2)Mathematical Model
Variables: x = number of units (decision variable)
Z = total profit
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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Chapter 1- Management Science 7
Model BuildingBreak-Even Analysis (1 of 7)
• Used to determine the number of units of a product to sell or produce (i.e. volume) 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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Chapter 1- Management Science 8
Model BuildingBreak-Even Analysis (2 of 7)
Model Components
Fixed costs (cf) - costs that remain constant regardless of number of units produced
Variable cost (cv) - unit cost of product
Total variable cost (vcv) - function of volume (v) and variable per-unit cost
Total cost (TC) - total fixed cost plus total variable cost
Profit(Z) - difference between total revenue vp (p=price) and total cost:
Z = vp - cf - vcv
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Chapter 1- Management Science 9
Model BuildingBreak-Even Analysis (3 of 7)
Computing the Break-Even Point
The break-even point is that volume at which total revenue equals total cost and profit is zero:
V = cf/(p-cv)
Example: Western Clothing Company
cf = $10000
cv = $8 per pair
p = $23 per pair
v = 666.7 pairs, break-even point
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Chapter 1- Management Science 10
Model BuildingBreak-Even Analysis (4 of 7)
Graphical Solution
Figure 1.2 Break-even model
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Chapter 1- Management Science 11
Model BuildingBreak-Even Analysis (5 of 7)
Sensitivity Analysis
Figure 1.3 Break-even model with a change in price
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Chapter 1- Management Science 12
Model BuildingBreak-Even Analysis (6 of 7)
Sensitivity Analysis (variable cost)
Figure 1.4Break-even model with a change in variable cost
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Chapter 1- Management Science 13
Model BuildingBreak-Even Analysis (7 of 7)Sensitivity Analysis (fixed cost)
Figure 1.5Break-even model with a change in fixed cost
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Chapter 1- Management Science 14
Computer Solution (1 of 5)
Excel Spreadsheets
Exhibit 1.1
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Chapter 1- Management Science 15
Computer Solution (2 of 5)Excel QM
Exhibit 1.2
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Chapter 1- Management Science 16
Computer Solution (3 of 5)Excel QM (continued)
Exhibit 1.3
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Chapter 1- Management Science 17
Computer Solution (4 of 5)QM for Windows
Exhibit 1.4
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Chapter 1- Management Science 18
Computer Solution (5 of 5)QM for Windows (continued)
Exhibit 1.5
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Chapter 1- Management Science 19
Management Science Modeling Techniques
Figure 1.6
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Chapter 1- Management Science 20
Characteristics of Modeling Techniques
• Linear mathematical programming: clear objective; restrictions on resources and requirements; parameters known with certainty.
• Probabilistic techniques: results contain uncertainty.
• Network techniques: model often formulated as diagram; deterministic or probabilistic.
• Forecasting and inventory analysis techniques: probabilistic and deterministic methods in demand forecasting and inventory control.
• Other techniques: variety of deterministic and probabilistic methods for specific types of problems.
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Chapter 1- Management Science 21
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