Considering a Cadre Augmented Army - RAND Corporation

-253- An Operational Analysis of Cadre
C.1.3—Model Limitations
Promotion of officers/NCOs lends itself well to a Markov process because
individuals transition from one period to the next at regular time intervals. The promotion
process can be modeled with uniform, fixed time periods and well-defined states that are
mutually exclusive and closed. However, there are a few assumptions required to model
promotions that may limit the realism of the model. First, the model assumes that soldiers
face promotion after set intervals (the minimum time in service requirement) and are either
promoted or separated at this point. In reality, soldiers not promoted initially have another
chance to be promoted before they are separated. The simple Markov model used here does
not capture this reality. 179 Secondly, the model assumes that separations due to lack of
promotion are the only way that individuals leave the force. A more realistic model would
include retention rates at each transition. However, this would lead to a much more complex
transition matrix and would add little value if we assume that retention rates remain the same
under different promotion policies as discussed earlier. Lastly, we assume that the
probabilities in each row of the transition matrix are fixed over time. In reality, these rates
change from year-to-year and would depend on promotion rates from previous years.
However, to a first order, the Markov process is an appropriate model to determine the
effect of changes in promotion policies on the number of officers/NCOs required in
peacetime cadre units.
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179 A more complex Markov model with more states would be capable of capturing this reality. However, this
would require estimating both initial and secondary promotion rates. Because we did not have access to this
data, we were unable to model this aspect of the promotion system.