Considering a Cadre Augmented Army - RAND Corporation

-250- An Operational Analysis of Cadre
chance of remaining in the same grade. This assumption is appropriate for calculating the
difference in grade structure under different promotion policies because the extra
Colonels/E-9s that would have transitioned out or up are subtracted out in the base case.
After creating the transition matrix, the Markov Promotion Model creates a vector
with the initial stock of personnel in each state (I). The model takes the initial force structure
by grade entered by the user and spreads it uniformly across the states corresponding to that
grade. For instance, in the previous example with two periods in each grade, the model
would divide the total number of soldiers initially in each grade by two. Since the highest
grade only has one state (Colonel/E-9), the initial stock is equal to the stock specified by the
user. The initial stock of separated personnel is set to zero. For the initial distribution of
officers shown in Figure C.1, the initial state vector is shown in Figure C.3.
Figure C.3—Initial State Vector Example (Officers)
State Stock
LT1 9358
LT2 9358
CAP3 12096
CAP3 12096
MAJ5 7564
MAJ6 7564
LTCOL7 4744
LTCOL8 4744
COL9 3957
SEP 0
The model uses the initial state vector (I) and the Markov transition matrix (M) to
calculate the distribution of personnel in the force after n time periods in a results vector (R).
First, the model multiplies the Markov transition matrix (M) by itself n times to determine
the relative distribution of personnel after n periods (D n ).
D n = M n