Transcript Management Science

Department of Business Administration
SPRING 2007-08
Management Science
by
Asst. Prof. Sami Fethi
© 2007 Pearson Education
Ch 1: Management Science
Outline: What You Will Learn . . .
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The Management Science Approach to Problem
Solving
Model Building : Break-Even Analysis
Computer Solution
Management Science Modeling Techniques
Business Usage of Management Science Techniques
Management Science Models in Decision Support
Systems
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Ch 1: Management Science
The Management Science Approach
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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.
 Management Science, also known as Operations
Research, Decision Sciences, etc., involves a
philosophy of problem solving in a logical manner.
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Ch 1: Management Science
The Management Science Process
Figure 1.1
The Management Science Process
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Ch 1: Management Science
Steps in the Management Science Process
Observation - Identification of a problem that exists (or may
occur soon) in a system or organization.
Definition of the Problem - problem must be clearly and
consistently defined, showing its boundaries and
interactions 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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Ch 1: Management Science
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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Ch 1: Management Science
Example of Model Construction (2 of 3)
Variables:
X = number of 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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Ch 1: Management Science
Example of Model Construction (3 of 3)
Model Solution
Consider the constraint equation:
4x = 100
or 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 8)
Ch 1: Management Science
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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Model Building:
Break-Even Analysis (2 of 8)
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Ch 1: Management Science
Model Components
Fixed Costs (cf) - costs that remain constant regardless
of number of units produced.
Variable Cost (cv) - unit production cost of product.
Total variable cost (vcv) - function of volume (v) and
unit variable cost.
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.
Z = vp - cf - vcv
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Ch 1: Management Science
Model Building:
Break-Even Analysis (3 of 8)
Computing the Break-Even Point
The break-even point is that volume at which total revenue
equals total cost and profit is zero:
vp - cf – vcv = 0
or v = cf/(p - cv)
(Break-Even Point)
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Model Building:
Break-Even Analysis (4 of 8)
Ch 1: Management Science
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) e.i., v = cf/(p - cv)
= 666.7 pairs
This gives the company a point of reference from which to
determine how many pairs of jeans it needs to produce and sell
in order to gain a profit.
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Ch 1: Management Science
Model Building: Break-Even Analysis (5 of 8)
Figure 1.2 Break-Even Model
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Ch 1: Management Science
Sensitivity Analysis
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If we develop a general relationship for determining the
break even volume, this enables us to see how the level of
profit or loss is directly affected by changes in volume.
 When we develop such a model, we assume that our
parameters fixed and variable costs and price are constant.
 In reality such parameter are frequently uncertain and can
rarely be assumed to be constant and changes in any of the
parameters can affect the model solution.
 Such changes on a management model is called sensitivity
analysis- observing how sensitive the model is to changes.
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Ch 1: Management Science
Model Building: Break-Even Analysis (6 of 8)
Figure 1.3
Sensitivity Analysis - Break-even Model with a Change in Price
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Ch 1: Management Science
Model Building: Break-Even Analysis (7 of 8)
Figure 1.4
Sensitivity Analysis - Break-Even Model with a Change in Variable Cost
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Ch 1: Management Science
Model Building: Break-Even Analysis (8 of 8)
Figure 1.5
Sensitivity Analysis - Break-Even Model with a Change in Fixed Cost
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Ch 1: Management Science
Break-Even Analysis: Excel Solution (1 of 5)
Exhibit 1.1
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Ch 1: Management Science
Break-Even Analysis: Excel QM Solution (2 of 5)
Exhibit 1.2
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Ch 1: Management Science
Break-Even Analysis: Excel QM Solution (3 of 5)
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Exhibit 1.3
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Ch 1: Management Science
Break-Even Analysis: QM Solution (4 of 5)
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Exhibit 1.4
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Ch 1: Management Science
Break-Even Analysis: QM Solution (5 of 5)
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Exhibit 1.5
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Ch 1: Management Science
Classification of Management Science Techniques
Figure 1.6
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Modeling Techniques
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Ch 1: Management Science
Characteristics of Modeling Techniques
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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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Ch 1: Management Science
Business Use of Management Science
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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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Management Science Models
Decision Support Systems (1 of 2)
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A decision support system (DSS) is a computer-based system
that helps decision makers address complex problems that cut
across different parts of an organization and operations.
A DSS is normally interactive, combining various databases and
different management science models and solution techniques
with a user interface that enables the decision maker to ask
questions and receive answers.
Online analytical processing system (OLAP), the analytical
hierarchy process (AHP), and enterprise resource planning
(ERP) are types of decision support systems.
Decision support systems are most useful in answering “whatif?” questions and performing sensitivity analysis.
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Management Science Models
Decision Support Systems (1 of 2)
Figure 1.7
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A Decision Support System
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Ch 1: Management Science
The End
Thanks
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