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Operations Research Models and Methods
 
Computation Section
Subunit Discrete-Time Markov Chain
- Creating a Model
To create a new model, select the Markov Chain option on the OR_MM menu. This option creates the Matrix worksheet. The program presents a message requesting the name of the problem and the number of states. To enter the example, specify that the model has 5 states. We use Bulb for the name of the problem. Names should be only a few letters long with no spaces or punctuation marks. The name will be used for the names of the worksheets and many ranges on the worksheets. Once defined here, the name cannot be changed. Clicking the Make Random Problem button will cause random data to be entered into the transition matrix.

 

Pressing the OK button, causes the Matrix worksheet to be constructed. Two areas allow data entry. Representative names for the states are entered into the State Names area. The transition matrix is entered into the array on the right. Initially, generic names are assigned: State 0, State 1, etc. It is always best to change these to names meaningful to the problem. The initial transition matrix is the identity matrix. Entering the data for the example results in the worksheet below. The program expects each row of the matrix to sum to 1.
 

The buttons at the top of the worksheet perform various actions. The Change button brings up a dialog box that allows a new number of states. The several arrays on the worksheet are expanded or contracted to accommodate the new state number. Data currently entered in the matrix remain so that an expanded or contracted problem can easily be entered.

The Calculate button computes row and column sums and reports if the matrix entries do not define an acceptable Markov Chain transition matrix. The Analyze button divides the states into recurrent, transient, or absorbing classes. The example has only one class of recurrent states. When the model is changed by adding or deleting states or changing transition probabilities, it is necessary to click on the Analyze button. The analyze activity automatically updates arrays on related worksheets.

The buttons along the left side of the worksheet construct new worksheets to perform the analyses indicated.

 

 
  
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by Paul A. Jensen
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