Introduction to management science 10e by bernard taylor chapter 01

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
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as
make
the
most
profit,
given the limited
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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:
(known values)

$20, $5, 4 lbs, 100 lbs

Formal Specification of Model:
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mple of Model Construction (3 of 3)
Model
Solve the constraint equation:
Solution:
4x = 100
(4x)/4 = (100)/4
x = 25 units
Substitute this value into the profit
function:
Z = $20x - $5x
= (20)(25) – (5)(25)
= $375
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(Produce 25 units, to yield a
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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.

TC c f  vcv



Profit (Z) - difference between total
revenue vp (p Z
=
unit
total cost,
vp price)
- c f - vcand
v
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:
vp  c  vc 0
f

v

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:

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Model Building:
Break-Even Analysis (6 of 9)

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Figure
1.2
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Model Building:
Break-Even Analysis (7 of 9)

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Figure
1.3
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Model Building:
Break-Even Analysis (8 of 9)

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Figure
1.4
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Model Building:
Break-Even Analysis (9 of 9)

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Figure
1.5
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Break-Even Analysis: Excel

Solution (1 of 5)

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Exhibit 1.1
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Break-Even Analysis: Excel QM
Solution (2 of 5)

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Exhibit

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Break-Even Analysis: Excel QM
Solution (3 of 5)

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Exhibit

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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

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Modeling
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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,
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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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