INTRODUCTION TO
MANAGEMENT
SCIENCE, 13e
Anderson
Sweeney
Williams
Martin
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slides by
JOHN
LOUCKS
St. Edward’s
University
Slide 1
Chapter 1
Introduction
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Body of Knowledge
Problem Solving and Decision Making
Quantitative Analysis and Decision Making
Quantitative Analysis
Models of Cost, Revenue, and Profit
Management Science Techniques
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 2
Body of Knowledge
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The body of knowledge involving quantitative
approaches to decision making is referred to as
• Management Science
• Operations Research
• Decision Science
It had its early roots in World War II and is flourishing
in business and industry due, in part, to:
• numerous methodological developments (e.g.
simplex method for solving linear programming
problems)
• a virtual explosion in computing power
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 3
Problem Solving and Decision Making
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Single criterion decision problem
Multicriteria decision problem
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2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 4
Problem Solving and Decision Making
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7 Steps of Problem Solving
(First 5 steps are the process of decision making)
1. Identify and define the problem.
2. Determine the set of alternative solutions.
3. Determine the criteria for evaluating alternatives.
4. Evaluate the alternatives.
5. Choose an alternative (make a decision).
--------------------------------------------------------------------6. Implement the selected alternative.
7. Evaluate the results.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 5
Quantitative Analysis and Decision Making
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Decision-Making Process
Structuring the Problem
Define
the
Problem
Identify
the
Alternatives
Determine
the
Criteria
Analyzing the Problem
Identify
the
Alternatives
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2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Choose
an
Alternative
Slide 6
Quantitative Analysis and Decision Making
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 7
Quantitative Analysis and Decision Making
Analysis Phase of Decision-Making Process
 Qualitative Analysis
• based largely on the manager’s judgment and
experience
• includes the manager’s intuitive “feel” for the
problem
• is more of an art than a science
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 8
Quantitative Analysis and Decision Making
Analysis Phase of Decision-Making Process
 Quantitative Analysis
• analyst will concentrate on the quantitative facts
or data associated with the problem
• analyst will develop mathematical expressions
that describe the objectives, constraints, and
other relationships that exist in the problem
• analyst will use one or more quantitative
methods to make a recommendation
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 9
Quantitative Analysis and Decision Making

Potential Reasons for a Quantitative Analysis
Approach to Decision Making
• The problem is complex.
• The problem is very important.
• The problem is new.
• The problem is repetitive.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 10
Quantitative Analysis

Quantitative Analysis Process
• Model Development
• Data Preparation
• Model Solution
• Report Generation
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 11
Model Development
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Models are representations of real objects or situations
Three forms of models are:
• Iconic models - physical replicas (scalar
representations) of real objects
• Analog models - physical in form, but do not
physically resemble the object being modeled
• Mathematical models - represent real world
problems through a system of mathematical
formulas and expressions based on key
assumptions, estimates, or statistical analyses
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 12
Advantages of Models
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Generally, experimenting with models (compared to
experimenting with the real situation):
• requires less time
• is less expensive
• involves less risk
The more closely the model represents the real
situation, the accurate the conclusions and predictions
will be.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 13
Mathematical Models
Max. P  10 x
s.t. 5 x  40 

x0 

Objective Function – a mathematical expression that
describes the problem’s objective, such as maximizing
profit or minimizing cost
Constraints – a set of restrictions or limitations, such as
production capacities
Uncontrollable Inputs – environmental factors that are
not under the control of the decision maker (parameters)
Decision Variables – controllable inputs; decision
alternatives specified by the decision maker, such as the
number of units of Product X to produce
5x  40
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
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 14
Mathematical Models
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Deterministic Model – if all uncontrollable inputs to the
model are known and cannot vary
Stochastic (or Probabilistic) Model – if any uncontrollable
are uncertain and subject to variation
Stochastic models are often more difficult to analyze.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 15
Mathematical Models
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Cost/benefit considerations must be made in selecting
an appropriate mathematical model.
Frequently a less complicated (and perhaps less
precise) model is more appropriate than a more
complex and accurate one due to cost and ease of
solution considerations.
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©
2008 Thomson South-Western. All Rights Reserved
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Slide 16
Transforming Model Inputs into Output
Uncontrollable Inputs
(Environmental Factors)
Controllable
Inputs
(Decision
Variables)
Mathematical
Model
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2008 Thomson South-Western. All Rights Reserved
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Output
(Projected
Results)
Slide 17
Transforming Model Inputs into Output
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2008 Thomson South-Western. All Rights Reserved
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Slide 18
Example: Project Scheduling
Consider the construction of a 250-unit apartment
complex. The project consists of hundreds of activities
involving excavating, framing,
wiring, plastering, painting, landscaping, and more. Some of the
activities must be done sequentially
and others can be done at the same
time. Also, some of the activities
can be completed faster than normal
by purchasing additional resources (workers, equipment,
etc.).
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 19
Example: Project Scheduling
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
Question:
What is the best schedule for the activities and
for which activities should additional resources be
purchased? How could management science be used
to solve this problem?
Answer:
Management science can provide a structured,
quantitative approach for determining the minimum
project completion time based on the activities'
normal times and then based on the activities'
expedited (reduced) times.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 20
Example: Project Scheduling
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Question:
What would be the uncontrollable inputs?
Answer:
• Normal and expedited activity completion times
• Activity expediting costs
• Funds available for expediting
• Precedence relationships of the activities
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 21
Example: Project Scheduling
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Question:
What would be the decision variables of the
mathematical model? The objective function? The
constraints?
Answer:
• Decision variables: which activities to expedite and
by how much, and when to start each activity
• Objective function: minimize project completion
time
• Constraints: do not violate any activity precedence
relationships and do not expedite in excess of the
funds available.
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 22
Example: Project Scheduling
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
Question:
Is the model deterministic or stochastic?
Answer:
Stochastic. Activity completion times, both normal
and expedited, are uncertain and subject to variation.
Activity expediting costs are uncertain. The number of
activities and their precedence relationships might
change before the project is completed due to a project
design change.
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 23
Example: Project Scheduling
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
Question:
Suggest assumptions that could be made to
simplify the model.
Answer:
Make the model deterministic by assuming
normal and expedited activity times are known with
certainty and are constant. The same assumption
might be made about the other stochastic,
uncontrollable inputs.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 24
Data Preparation
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Data preparation is not a trivial step, due to the time
required and the possibility of data collection errors.
A model with 50 decision variables and 25 constraints
could have over 1300 data elements!
Often, a fairly large data base is needed.
Information systems specialists might be needed.
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 25
Model Solution
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The analyst attempts to identify the alternative (the
set of decision variable values) that provides the
“best” output for the model.
The “best” output is the optimal solution.
If the alternative does not satisfy all of the model
constraints, it is rejected as being infeasible, regardless
of the objective function value.
If the alternative satisfies all of the model constraints,
it is feasible and a candidate for the “best” solution.
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 26
Model Solution
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One solution approach is trial-and-error.
• Might not provide the best solution
• Inefficient (numerous calculations required)
Special solution procedures have been developed for
specific mathematical models.
• Some small models/problems can be solved by
hand calculations
• Most practical applications require using a
computer
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 27
Model Solution

A variety of software packages are available for
solving mathematical models.
• Microsoft Excel
• The Management Scientist
• LINGO
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 28
Model Testing and Validation
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Often, goodness/accuracy of a model cannot be
assessed until solutions are generated.
Small test problems having known, or at least
expected, solutions can be used for model testing and
validation.
If the model generates expected solutions, use the
model on the full-scale problem.
If inaccuracies or potential shortcomings inherent in
the model are identified, take corrective action such
as:
• Collection of more-accurate input data
• Modification of the model
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 29
Report Generation
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A managerial report, based on the results of the
model, should be prepared.
The report should be easily understood by the
decision maker.
The report should include:
• the recommended decision
• other pertinent information about the results (for
example, how sensitive the model solution is to the
assumptions and data used in the model)
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 30
Implementation and Follow-Up
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Successful implementation of model results is of
critical importance.
Secure as much user involvement as possible
throughout the modeling process.
Continue to monitor the contribution of the model.
It might be necessary to refine or expand the model.
© 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 31
Models of Cost, Revenue, and Profit
P( x)  R( x)  C ( x)
 5 x  (3000  2 x)  3000  3 x


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Fixed cost vs. Variable cost
Marginal cost : cost increase per unit,
may change depend upon the volume.
Margenal revenue : increase of total revenue per unit,
may also change depend upon the volume.
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2008 Thomson South-Western. All Rights Reserved
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Slide 32
Breakeven Analysis
P( x)  R( x)  C ( x)
 5 x  (3000  2 x)  3000  3 x
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2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 33
Management Science Techniques
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Linear Programming
Integer Linear
Programming
PERT/CPM
Inventory Models
Waiting Line Models
Simulation
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Decision Analysis
Goal Programming
Analytic Hierarchy
Process
Forecasting
Markov-Process Models
Dynamic Programming
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2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 34
The Management Scientist Software

12 Modules
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2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 35
End of Chapter 1
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©
2008 Thomson South-Western. All Rights Reserved
publicly accessible website, in whole or in part.
Slide 36