Ch16_245-256 - 72106 CH16 GGS 3/30/05 3:17 PM Page 245 C H...

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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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Ch16_245-256 - 72106 CH16 GGS 3/30/05 3:17 PM Page 245 C H...

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