Transcript taylor_introms10_ppt_01.ppt

Management Science
Chapter 1
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Chapter Topics

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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The 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.

Management science, also known as operations
research, quantitative methods, etc., involves a
philosophy of problem solving in a logical manner.
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The Management Science Process
Figure 1.1
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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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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.
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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.
TC  c f  vc v
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Profit (Z) - difference between total revenue vp (p = unit
price) and total cost, i.e.
Z  vp - c
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f
- vc v
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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:
vp  c f  vc v  0
v ( p  cv )  c f
The break-even point
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v
cf
p  cv
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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: Excel Solution (1 of 5)
Exhibit 1.1
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Break-Even Analysis: Excel QM Solution (2 of 5)
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Exhibit 1.2
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Break-Even Analysis: Excel QM Solution (3 of 5)
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Exhibit 1.3
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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)
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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
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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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