- MNG 2201 –
MANAGEMENT SCIENCE
Troy J Wishart
ASSUME THE POSITION
MANAGEMENT SCIENCE
Lecture
Times
 Mondays 5:15 – 7:10
 Wednesdays 8:15 – 9:10
Tutorial
Times – 5 hours
MANAGEMENT SCIENCE
Lecture
Notes
 Main Text - Taylor, W.B. (2007) Introduction to
Management Science. 9th edition. Pearson Prentice
Hall.
 Power Point Presentations
 Can be downloaded from:
www.troywishart.wordpress.com
We Believe that
Death and Life is in the
Power of the Tongue…
I am getting an
‘A’ in this Course
INTRODUCTION TO
MANAGEMENT SCIENCE
Lecture 1
DEFINITION
Management
Science (MS), an
approach to managerial decision
making that is based on the scientific
method and makes extensive use of
quantitative analysis.
DEFINITION
A
Scientific Approach to solving
management problems
Help managers make better decisions.
Known as Operations Research (OR)
Both terms are used interchangeably.
HISTORY
The
Scientific
Management
Revolution began in the early 1900s,
Initiated by
It
Frederic W. Taylor,
provided the foundation for MS/OR.
HISTORY
Both
originated during the World War
II period.
Operations
Research Teams were
formed to deal with Strategic And
Tactical Problems faced by the
military.
HISTORY
These
teams, which often consisted of
people with Diverse Specialties
 (e.g. Mathematicians, Engineers, And
Behavioural Scientists),
After
the war, - continued their
research on quantitative approaches
to decision making.
PROBLEM SOLVING
Problem
Solving can be defined as the
process of identifying a difference
between some actual and some
desired state of affairs and then taking
action to resolve the difference.
PROBLEM SOLVING
Steps to Problem Solving…
1. Identify and Define the Problem
2. Determine the set of alternative
solutions
3. Determine the criterion or criteria
that will be used to evaluate the
alternatives
4. Evaluate the alternatives
PROBLEM SOLVING
Steps to Problem Solving…
5. Choose an alternative
6. Implement the selected alternative
7. Evaluate the results, and determine
if a satisfactory solution had been
obtained.
DECISION MAKING
Decision
Making is the term generally
associated with the first five steps of
the problem-solving process.
 Decision making ends with the choosing
of an alternative, which is the act of
making a decision.
PROBLEM& SOLVING
DECISION MAKING
PROBLEM SOLVING
&
DECISION MAKING
Example – Step 1 & 2
 Problem:
Graduated & looking for a job satisfying career
 Alternatives: Job Offers..
 Company located in Rochester, New York
 Company located in Dallas, Texas
 Company located in Greensboro, North
Carolina.
 Company located in Pittsburgh, Pennsylvania
PROBLEM SOLVING
&
DECISION MAKING
 Step
3 - determine the Criterion or Criteria to
evaluate alternatives
 Single Criterion Decision Problems -
Problems in which the objective is to
find the best solution with respect to
one criterion
 Multi-criteria Decision Problems –
Problems that involve more than one
criterion.
PROBLEM SOLVING
&
DECISION MAKING
Example – Criterion Criteria
Single Criterion - “Best” criterion is
the starting salary of the each job .
Multi-Criteria - Location of Job &
potential for advancement
PROBLEM SOLVING
&
DECISION MAKING
Example – Step 4 Evaluation
Alternatives
Starting
Salary
Potential for
Advancement
Job
Location
Rochester
$28,500
Average
Fair
Dallas
$26,000
Excellent
Average
Greensboro
$26,000
Good
Excellent
Pittsburg
$26,000
Average
Good
PROBLEM SOLVING
&
DECISION MAKING
Example – Step 5 – Choose
It is now time to make a choice among
the alternatives – Decision.
Alternative 3 seems the best and is
therefore referred to as the decision
This completes the decision making
process.
PROBLEM SOLVING
&
DECISION MAKING
Define
Problem
Identify the
Alternatives
Determine
the Criteria
Problem Solving
Evaluate the
Alternatives
Choose an
Alternative
Implement
the Decision
Evaluate the
Results
Decision Making
QUANTITATIVE ANALYSIS
&
DECISION MAKING
QUANTITATIVE ANALYSIS
&
DECISION MAKING
The decision-making process
may take on two basic forms:
1.Quantitative
2.Qualitative.
QUANTITATIVE ANALYSIS
&
DECISION MAKING
Qualitative
Analysis - based primarily
on the manager’s judgement and
experience;
It includes the manager’s intuitive
“feel” for the problem
It is more an Art than a Science.
It used when the problem is
Relatively Simple.
QUANTITATIVE ANALYSIS
&
DECISION MAKING
 Quantitative
Analysis is used if the
problem is sufficiently complex.
 Analyst
will:
 Concentrate on the quantitative facts
or data associated with the problem
 Develop mathematical expressions  that describe the objectives, constraints, and other relationships
that exist in the problem
 Make a recommendation using one or
more quantitative methods,.
QUANTITATIVE ANALYSIS
The
&
DECISION MAKING
manager must be:
 Knowledgeable of both in qualitative
and
quantitative
decision-making
sources of recommendations
 Able to ultimately combine the two
sources and to make the best possible
decision.
QUANTITATIVE ANALYSIS
&
DECISION MAKING
Reasons why the quantitative approach
might be used in decision making:
1. The Problem is Complex
 The manager cannot develop a good
solution without the aid of quantitative
analysis.
2.
The Problem is Very Important
 (e.g. a great deal of money is involved), and
the manager desires a thorough analysis
before attempting to make a decision.
QUANTITATIVE ANALYSIS
&
DECISION MAKING
Reasons why the quantitative approach
might be used in decision making:
3. The Problem is New,
 The manager has no previous experience to
draw on.
4.
The Problem is Repetitive,
 the manager saves time and effort by
relying on quantitative procedures to make
routine decision recommendations.
QUANTITATIVE ANALYSIS
&
DECISION MAKING
Qualitative
Analysis
QUANTITATIVE ANALYSIS
&
DECISION MAKING
Quantitative
Analysis
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 Models
are representations of real objects or
situation. The various forms are:
1. Iconic Models – physical replicas of real
objects.
 E.g. scale model of an airplane or a child’s toy
truck.
2.
Analog Models – Models that are physical
in form but do not have the same physical
appearance as the object being modeled.
 E.g. the speedometer & thermometer
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
3.
Mathematical Models – a model that
represents a problem by a system of
symbols
and
mathematical
relationships or expressions.
 It is a critical part of quantitative
approach to decision making.
E.g. A profit function for the sale of a product
$10: - P = 10x
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
Purpose of Models
 It enables us to make inferences about
the real situation by studying and
analyzing the model. Example…
 An iconic model of a new airplane can tested
in a wind tunnel,
 A mathematical model can be used to
calculate profit with specified quantity of a
product.
 P = 10x for 3 units - P = 10(3) = $30
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
Advantages of Models
1. Requires less time and is less expensive
than experimenting with the real object
or situation.
It reduces the risk associated with
experimenting with the real situation,
2.

E.g. A Large Investment.
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 However,
the value of model-based
conclusions is dependent on how well the
model represents the real situation.
 The
Problem Definition phase leads to a:
 Specific Objective, such as Maximization of
Profit or Minimization of Cost,
 Restrictions or Constraints, such as Production
Capacities.
QUANTITATIVE ANALYSIS
 The
&
MODEL DEVELOPMENT
success of a mathematical model and
quantitative approach will depend heavily
on accurately expressing :
 The Objective and Constraints in terms of a
mathematical equations or relationships.
A
Mathematical Expression that describes
a problem’s objective is referred to as the
Objective Function,
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 Example
- P = 10x.
 A production capacity constraint could be
that 5 hours are required to produce each
unit and there are only 40 hours available
per week.
 Let x indicate the number of units
produced each week so that: 5x≤40.
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
A
complete mathematical model for this
production problem is
 Maximize
P = 10x Objective Function
 Subject to (s.t.)

5x≤40
Constraints

x≥0

This model is an example of linear programming
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 Models
can contain environmental factors
that are Controllable or Uncontrollable:
 Controllable Inputs – Inputs that are
controlled or determined by the
decision maker – e.g. Quantity x.
 Controllable inputs are the decision
alternatives specified by a manager and are
also referred to as Decision variables.
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 Uncontrollable
Inputs – Environmental
factors which can affect both the
objective function and the constraints.
 E.g. Profit per unit $10, 5 hours and production
capacity -40hrs per week.
 Uncontrollable inputs can either be known
exactly or be uncertain and subject to
variation.
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 Deterministic
Model If all uncontrollable
inputs to a model are known and cannot
vary, e.g. Corporate Income Tax.
 The distinguishing feature of a deterministic
model is that the uncontrollable inputs are
known in advance.
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
 Stochastic
or Probabilistic Model, If any of
the uncontrollable inputs are uncertain or
subject to variation e.g. Demand.
 The distinguishing feature of a stochastic
model is that the value of the output cannot
be determined even if the value of the
controllable input is known, because the
specific values of the uncontrollable inputs
are unknown. In this respect, stochastic
models are often more difficult to analyze.
QUANTITATIVE ANALYSIS
&
MODEL DEVELOPMENT
Flowchart showing the process of transforming (Production) Model Inputs into Output
QUANTITATIVE
ANALYSIS
DATA PREPARATION
DATA PREPARATION
 Data
in this sense refer to the values of
the uncontrollable inputs to the model.
 All uncontrollable inputs must be specified before
analyzing model and recommend decision/solution.
 E.g. $10 per unit, 5 hours per unit for production time, and 40 hours
for production capacity.
 Analysts combines model development and data
preparation into one step if the model is relatively
small and the uncontrollable inputs are few.
DATA PREPARATION
 If
the uncontrollable inputs or data is
unavailable the analyst will usually develop a
General Notation:
c = profit per unit
a = production time in hours per unit
b = production capacity in hours
 As such the following general model is developed:
Max cx
s.t.
ax ≤ b
x ≥0
QUANTITATIVE
ANALYSIS
MODEL SOLUTION
MODEL SOLUTION
The
analyst will attempt to identify the
values of the decision variables that
provide the “best” output for the
model.
This
is referred to as the Optimal
Solution for the model.
MODEL SOLUTION
 To
determine the best value of x:
 Trial-and-Error approach where the model is
used to test and evaluate various decision
alternatives.
 Infeasible - If a particular decision
alternative does not satisfy one or more of
the model constraints.
 Feasible If all constraints are satisfied, it
becomes a candidate for the “best”
solution or recommended decision.
MODEL SOLUTION
 The
disadvantage of the trial-and-error
approach is that it may not necessarily and
being inefficient in terms of requiring
numerous calculations if many decision
alternatives are tried.
MODEL SOLUTION
Decision Alternative
(Production Quantity) x
0
3
4
6
8
10
12
Projected
Profit
0
20
40
60
80
100
120
Total Hours of
Production
0
10
20
30
40
50
60
Feasible Solution?
(Capacity = 40)
Yes
Yes
Yes
Yes
Yes
No
No
QUANTITATIVE
ANALYSIS
REPORT GENERATION
REPORT GENERATION
An
important part of the quantitative
analysis process.

It is essential that the results of the
model appear in a managerial report
The
Report should be easily
understood by the decision maker.
REPORT GENERATION
The
report should include:
 The recommended decision
 Other pertinent information about
the model results that can help to
the decision maker.
QUANTITATIVE
ANALYSIS
IMPLEMENTATION
IMPLEMENTATION
It
is the responsibility of the manager
to integrate the quantitative solution
with qualitative considerations.
The
manager
should
oversee
implementation
and
follow-up
evaluation of the decision.
IMPLEMENTATION
User
Involvement is one of the most
effective ways to ensure a successful
implementation.
If
the user feels he/she has been
involved they are much more likely to
enthusiastically
implement
the
results.
MODELS OF COST,
REVENUE, AND PROFIT
MODELS OF COST,
REVENUE, AND PROFIT
Volume
Models are some of the most
basic quantitative models
 E.g those involving the relationship
between a volume variable-such as
production volume or sales volume-and
cost, revenue, or profit.
MODELS OF COST,
REVENUE, AND PROFIT
Financial
planning,
production planning,
sales quotas, and other
areas
of
decision
making can benefit
from
such
cost,
revenue and profit
models.
COST AND
VOLUME MODELS
COST AND VOLUME MODELS
The
cost
of
manufacturing or
producing
a
particular product is
a function of the
volume produced.
COST AND VOLUME MODELS
This
cost can usually be defined as a
sum of two costs:
Fixed Cost – the portion of the total
cost that does not depend on the
production volume.
Variable Cost – the portion of the
total cost that is dependent on and
varies with the production volume.
COST AND VOLUME MODELS
 Example,
the setup cost for a production line is
$3,000 (fixed cost), variable labour and
material costs are $2 for each unit produced.
 The cost-volume model for producing (x) units
would be written as

C(x) = 3000+2x
 Where

x = production volume in units

C(x) = total cost of producing x units
COST AND VOLUME MODELS
 Marginal
Cost is the rate
of change of the total cost
with respect to volume.
 It
is the cost increase
associated with a one-unit
increase in the production
volume. E.g. $2 as per model.
REVENUE AND
VOLUME MODELS
REVENUE AND VOLUME MODELS
Projected
Revenue associated with
selling a specified number of units
can be determined through a model
relationship between revenue and
volume.
REVENUE AND VOLUME MODELS
For
instance if the product above sells
for $5 per unit then:
R(x) = 5x
Where
x = sales volume in units
R(x) = total revenue associated with selling x units
REVENUE AND VOLUME MODELS
 Marginal
Revenue
is
defined as the rate of
change of total revenue
with respect to sales
volume.
 It is the increase in total
revenue resulting from
one-unit increase in sales
volume. E.g. $5
PROFIT VOLUME MODELS
Profit
is one of the
most
important
criteria for managerial
decision making.
PROFIT AND
VOLUME MODELS
PROFIT AND VOLUME MODELS
If
only what is produce what is sold,
the production volume and sales
volume will be equal.
As such a profit-volume model can be
developed to determine profit
associated
with
a
specified
production-sales volume.
PROFIT AND VOLUME MODELS
Since
the total profit is total revenue
minus total cost, the following model
is associated with producing and
selling (x) units:
P(x) = R(x) – C(x)
= 5x – (3000 + 2x) = -3000 + 3x
BREAK-EVEN
ANALYSIS
BREAK-EVEN ANALYSIS
The
volume that
results
in
total
revenue
equaling
total cost (providing
$0 profit) is called
the
break-even
point.
BREAK-EVEN ANALYSIS
If
the break-even point is known a
manager can quickly infer :
 That a volume above the break-even
point will result in profit,
 While volume below the point will result
in loss.
BREAK-EVEN ANALYSIS
 The
break-even point can be found by
setting the profit expression equal to zero
and soling for the production volume.
P(x) = -3000 + 3x = 0
3x = 3000
X = 1000
 Production and sales of the product must be at least
1000 units before a profit can be expected
MANAGEMENT SCIENCE
TECHNIQUES
MANAGEMENT SCIENCE TECHNIQUES
Linear
Programming –
 is a problem-solving approach
 has been developed for situations
involving maximizing or minimizing
linear function
 subject to linear constraints that limit
the degree to which the objective can be
pursued.
MANAGEMENT SCIENCE TECHNIQUES
Integers
Linear Programming –
 is an approach used for problems that
can be set up as linear programs
 with the additional requirement that
some or all of the decision
recommendations be integer values.
MANAGEMENT SCIENCE TECHNIQUES
Network
Models – A network is a
graphical description of a problem
consisting of circles called nodes that are
interconnected by lines called arcs.
 Solves managerial problems such as
transportation system design, information
system design, and project scheduling.
MANAGEMENT SCIENCE TECHNIQUES
Project
Management: PERT/CPM –
The PERT (Program Evaluation and
Review Technique) and CPM (Critical
Path Method) techniques help
managers carry out their project
scheduling responsibilities.
MANAGEMENT SCIENCE TECHNIQUES
 Inventory Models –
 are used by managers faced with the
dual
problem
of
maintaining
sufficient inventories to meet
demand for goods
 and, at the same time, incurring the
lowest possible inventory holding
costs.
MANAGEMENT SCIENCE TECHNIQUES
Waiting-Line
or Queuing Models –
 have been developed to help managers
understand
 and make better decisions concerning
the operation of systems involving
waiting lines.
MANAGEMENT SCIENCE TECHNIQUES
Computer
Simulation –
 is a technique used to model the
operation of a system over time.
 This technique employs a computer
program to model the operation of
systems involving waiting lines.
MANAGEMENT SCIENCE TECHNIQUES
Decision
Analysis –
 can be used to determine optimal
strategies in situations involving several
decisions alternatives
 and an uncertain or risk filled pattern of
events.
MANAGEMENT SCIENCE TECHNIQUES
Goal
Programming –
 is a technique for solving multi-criteria
decision problems, usually within the
framework of linear programming.
MANAGEMENT SCIENCE TECHNIQUES
Analytic
Hierarchy Process –
 A multi-criteria decision making
technique that permits the inclusion of
subjective factors in arriving at a
recommended decision.
MANAGEMENT SCIENCE TECHNIQUES
Forecasting
–
 forecasting methods are techniques that
can be used to predict future aspects of
a business operation.
MANAGEMENT SCIENCE TECHNIQUES
Markov-Process
Models –
 Markov-process models are useful in
studying the evolution of certain
systems over repeated trials.
 For example, Markov have been used to describe
the probability that a machine that is functioning
in one period will continue to function or break
down in another period.
MANAGEMENT SCIENCE TECHNIQUES
Dynamic
Programming –
 is an approach that allows us to break
up a large problem in such a fashion
that once all the smaller problems have
been solved, we are left with an optimal
solution to the large problem.
MANAGEMENT SCIENCE TECHNIQUES
Calculus-Based
Procedures –
 are used to solve problems that involve
a nonlinear objective function and/or
constraints involving nonlinear functions
of the decision variables.