A NETWORK MODEL TO MAXIMIZE NAVY PERSONNEL READINESS AND ITS SOLUTION

The problem of optimally (re)allocating Navy personnel to combat units is compounded by several considerations: availability of trained pers onnel, staffing of positions by occupation groups or ranks, and mainta ining an acceptable level of readiness. In this paper we model this pr oblem as a nonlinear nondifferentiable optimization problem. A reformu lation of the nonlinear optimization problem as a network flow problem is then developed. The formulation results in a network flow problem with side constraints. An additional, nonnetwork, variable measures th e readiness level. This new formulation permits the use of network opt imization tools in order to solve effectively very large problems. We then develop two numerical methods for solving this problem. One metho d is based on a heuristic that solves (approximately) the nondifferent iable problem. The second method is based on a Linear-Quadratic Penalt y (LQP) algorithm, and it exploits the embedded network structure by p lacing the side constraints into the objective function. The resulting nonlinear network program is solved using a simplicial decomposition of the network constraint set. Numerical results indicate the viabilit y of this approach on problems with up to 36,000 arcs and 17,000 nodes with 3,700 side constraints.