The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government. / Determining the best base stationing for military units can be modeled as a capacitated facility location problem with sole sourcing and multiple resource categories. Computational experience suggests that cross decomposition, a unification of Benders Decomposition and Lagrangean relaxation, is superior to other contemporary methods for solving capacitated facility location problems. Recent research extends cross decomposition to pure integer prograrnming problems with explicit application to capacitated facility location problems with sole sourcing; however, this research offers no computational experience. This thesis implements two cross decomposition algorithms for the capacitated facility location problem with sole sourcing and compares these decomposition algorithms with branch and bound methods. For some problems tested, cross decomposition obtains better solutions in less time; however, cross decomposition does not always perform better man branch and bound due to the time required to obtain the cross decomposition bound that is theoretically superior to other decomposition bounds.