Problem Solving Operations Course

1. 1Slide
Slides by
JOHN
LOUCKS
St. Edward’s
University
INTRODUCTION TO
MANAGEMENT
SCIENCE, 13e
Anderson
Sweeney
Williams
Martin

2. 2Slide
Chapter 1
Introduction
 Body of Knowledge
 Problem Solving and Decision Making
 Quantitative Analysis and Decision Making
 Quantitative Analysis
 Models of Cost, Revenue, and Profit
 Management Science Techniques

3. 3Slide
Body of Knowledge
 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

4. 4Slide
 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).
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6. Implement the selected alternative.
7. Evaluate the results.
Problem Solving and Decision Making

5. 5Slide
Quantitative Analysis and Decision Making
Define
the
Problem
Identify
the
Alternatives
Determine
the
Criteria
Identify
the
Alternatives
Choose
an
Alternative
Structuring the Problem Analyzing the Problem
 Decision-Making Process

6. 6Slide
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
Quantitative Analysis and Decision Making

7. 7Slide
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
Quantitative Analysis and Decision Making

8. 8Slide
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.

9. 9Slide
Quantitative Analysis
 Quantitative Analysis Process
•Model Development
•Data Preparation
•Model Solution
•Report Generation

10. 10Slide
Model Development
 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

11. 11Slide
Advantages of Models
 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.

12. 12Slide
Mathematical Models
 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
 Decision Variables – controllable inputs; decision
alternatives specified by the decision maker, such as the
number of units of Product X to produce

13. 13Slide
Mathematical Models
 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.

14. 14Slide
Mathematical Models
 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.

15. 15Slide
Transforming Model Inputs into Output
Uncontrollable Inputs
(Environmental Factors)
Controllable
Inputs
(Decision
Variables)
Output
(Projected
Results)
Mathematical
Model

16. 16Slide
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, land-
scaping, 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.).

17. 17Slide
Example: Project Scheduling
 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.

18. 18Slide
Example: Project Scheduling
 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

19. 19Slide
Example: Project Scheduling
 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.

20. 20Slide
Example: Project Scheduling
 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.

21. 21Slide
Example: Project Scheduling
 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.