Considering a Cadre Augmented Army - RAND Corporation

-95- A Budgetary Analysis of Cadre
APPENDIX A—COST, TRADEOFF, AND STRESS CALCULATIONS
This appendix describes the calculations required to derive the results in the body of
this paper. The first section shows how we calculate the relative cost of a unit from each force
averaged over periods of peace and war. The second section shows how we calculate the
annual cost of a unit from each force. The third section shows how we calculate the number
of units needed to sustain one unit deployed from each force. The fourth section shows how
we calculate stress on the AC. The final section shows how we calculate the cost savings
from a cadre augmented force relative to a non-cadre force. For ease of presentation, we
define all of the variables used in this appendix below.
• i: force index. 1= AC, 2=RC, 3=Cadre
• c i : average per unit cost of force i
• m i : mobilization length for force i
• p i : post-mobilization training required for force i
• d i = m i – p i : deployment length for force i
• h i : “dwell time”, time at home between deployments for force i
l
=
i
•
i
mi
+
m
: percentage of time units in force i are mobilized in each cycle
h
i
• r i : non-mobilized per unit cost of force i (mobilized cost assumed equal for all
forces)
• α: fraction of time at “war” (equivalent to fraction of cycles “reserves” mobilized)
A.1—RELATIVE FORCE COSTS
The average long-run costs calculated in the body of this paper rely on relative unit
cost calculations to compare different force structures. This appendix begins by deriving
generic relative cost equations for each force and then plugs in “best estimates” to replicate