Introduction to Management Science
by Bernard W. Taylor III
Chapter 1
Management Science
Chapter 1- Management Science 1
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
Chapter 1- Management Science 2
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, Decision Sciences, etc., involves a philosophy
of problem solving in a logical manner.
Chapter 1- Management Science 3
The Management Science Process
Figure 1.1
The Management Science Process
Chapter 1- Management Science 4
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.
Chapter 1- Management Science 5
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.
Chapter 1- Management Science 6
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
Chapter 1- Management Science 7
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)
Chapter 1- Management Science 8
Model Building:
Break-Even Analysis (1 of 8)
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.
Chapter 1- Management Science 9
Model Building:
Break-Even Analysis (2 of 8)
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
Chapter 1- Management Science 10
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)
Chapter 1- Management Science 11
Model Building:
Break-Even Analysis (4 of 8)
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
Chapter 1- Management Science 12
Model Building: Break-Even Analysis (5 of 8)
Graphical Solution
Figure 1.2 Break-Even Model
Chapter 1- Management Science 13
Model Building: Break-Even Analysis (6 of 8)
Figure 1.3
Sensitivity Analysis - Break-even Model with a Change in Price
Chapter 1- Management Science 14
Model Building: Break-Even Analysis (7 of 8)
Figure 1.4
Sensitivity Analysis - Break-Even Model with a Change in Variable Cost
Chapter 1- Management Science 15
Model Building: Break-Even Analysis (8 of 8)
Figure 1.5
Sensitivity Analysis - Break-Even Model with a Change in Fixed Cost
Chapter 1- Management Science 16
Classification of Management Science Techniques
Figure 1.6 Modeling Techniques
Chapter 1- Management Science 17
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.
Chapter 1- Management Science 18
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)
Chapter 1- Management Science 19
Management Science Models
Decision Support Systems (1 of 2)
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
“what-if?” questions and performing sensitivity analysis.
Chapter 1- Management Science 20
Management Science Models
Decision Support Systems (2 of 2)
Figure 1.7 A Decision Support System
Chapter 1- Management Science 21
End of Chapter
Chapter 1- Management Science 22
