Considering a Cadre Augmented Army - RAND Corporation

-121- A Budgetary Analysis of Cadre
The stock of AC units deployed for more than one period is equal to the number of
AC units deployed one less period in the last time period minus the number of AC units that
are redeployed. This is formalized as:
∀ i > 1: S(AC,D,i,t) = S(AC,D,i-1,t-1)-X(AC,D,i,t)
The stock of RC units deployed for more than one period is just equal to the number
of RC units deployed one less period in the last time-period because the model assumes that
RC units can only be deployed from home. This is formalized as:
∀ i > 1: S(RC,D,i,t) = S(RC,D,i-1,t-1)
Units Home for One Period
The stock of AC units at home for one period is equal to the number of units in the
last period of deployment in the last time period minus the sum of the number of units
deployed with one period at home and the number of units redeployed from the last period
of deployment:
S(AC,H,1,t) = S(AC,D, ACMaxD,t-1)-X(AC,H,1,t)-X(AC,D, ACMaxD ,t)
The stock of RC units at home for one period is equal to the number of units in the last
period of deployment in the last time-period minus the number of RC units deployed with
one period at home:
S(RC,H,1,t) = S(RC,D, RCMaxD ,t-1)-X(RC,H,1,t)
Units Home More than One Period But less than Maximum
The number of AC and RC units at home for more than one period, but less than
the maximum number of periods is equal to the number of units at home for one less period