245
T
EACHING
S
UGGESTIONS
Teaching Suggestion 16.1:
Use of Matrix Algebra.
Markov analysis requires the use of matrix algebra, primarily ma
trix multiplication. You may want to have students review basic
concepts in matrix algebra before the material in the chapter is
covered. If you plan to cover absorbing state analysis in detail,
more advanced matrix algebra will be needed, including the iden
tity matrix, matrix subtraction, and the inverse of a matrix. See
Module 5.
Teaching Suggestion 16.2:
Matrix of Transition.
Markov analysis requires a known and stable matrix of transition.
Students should be told that Markov analysis is not valid if the
matrix of transition does not remain the same. A small change in
the matrix of transition can make a big difference in equilibrium
calculations.
Teaching Suggestion 16.3:
Application of Markov Analysis.
There are a number of applications of Markov analysis. The appli
cations box in this chapter presents an example. Students can be
asked to Fnd additional applications in quantitative analysis/
management science journals such as
Interfaces.
In addition, stu
dents can be asked to develop their own problems. ±or example,
Markov analysis can be used to predict the percentage of students
who will be in certain majors next year or in the long run.
Teaching Suggestion 16.4:
Sensitivity Analysis and
Markov Analysis.
Although sensitivity analysis is not a formal part of the material
discussed in this chapter, it is an important and interesting topic.
Students can be asked to determine how sensitive the results of
Markov analysis are to changes in probability values.
Teaching Suggestion 16.5:
Equilibrium Conditions and the
Beginning State or Condition.
As mentioned in this chapter, equilibrium conditions do not de
pend on the initial state or condition. The only factor that needs to
be considered is the matrix of transition. While this is true, the
time or number of periods needed to approach equilibrium is a
function of the beginning state. Students can be asked to deter
mine what impact the initial state has on the number of periods it
takes to reach equilibrium.
Teaching Suggestion 16.6:
Absorbing State Analysis and
Matrix Algebra.
Absorbing state analysis requires more complex matrix algebra,
including the inverse of the (
I
2
B
) matrix. If you plan to get into
the mathematics of absorbing state analysis, you may have to
spend additional time covering more advanced matrix algebra. An
alternative approach is to cover the assumptions and overall ap
proach of the model and leave the computations to the computer.
A
LTERNATIVE
E
XAMPLES
Alternative Example 16.1:
Scuba Discovery (Store 1) currently
splits the market for scuba classes with Bob’s Dive Shop. Given
the matrix of transition probabilities below, what will the market
shares be next month (period)?
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 Spring '11
 MichaelHanna
 Markov chain

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