Considering a Cadre Augmented Army - RAND Corporation

-251- An Operational Analysis of Cadre
For the analyses in this paper we raised the transition matrix to the fourth power (n=4). The
resulting matrix will be of the same size as the initial Markov transition matrix (a*a). We then
multiply the initial state vector (I) by the new transition matrix, the result of which is a
column vector (R) with the distribution of officers or NCOs after n time periods.
R 1*a = (I 1*a )*(M a*a ) n
Model Output
The model aggregates the information in the results vector (R) to output the number
of personnel in each grade. Since the Markov model does not allow inflows, the first n slots
in the result vector will have zeroes. The model fills there slots using the accessions per year
specified by the user. The model divides the accessions per year by the number of periods
per year and fills each of the first n slots with this value. The model then sums the number of
personnel by grade and outputs the results next to the input data as shown in Figure C.4.
Figure C.4—Output Example (Officers)
Time
Periods Per Year 2
Simulated Periods 4
Promotion Data
Interval Rate
Captain 2 0.98
Major 2 0.98
Lt. Colonel 2 0.89
Colonel 2 0.6
Force Structure Initial Results
New Accessions/Yr 5100
Lieutenants 18717 10200
Captains 24192 10200
Majors 15128 17975
Lt. Colonels 9489 21100
Colonels 3957 17728
Total 71483 77203