Short-term retrenchment planning in hierarchical manpower systems

The paper addresses the issue of short-term retrenchment planning required of organizations that are phasing down their manpower levels at rates faster than are allowed by natural attrition. Specifically, the problem it studies is as follows: given the initial and target grade populations in a hierarchical manpower system at the end of a finite time horizon and the per-period rate of natural attrition for each grade, find a stationary manpower policy that minimizes the maximum per-period rate of retrenchment across all the grades over all stationary policies that yield the target grade populations at the end of the horizon. Because the problem is a nonconvex, nonseparable, nonlinear program, the paper develops a heuristic in which the promotion proportions of all the grades are successively fixed, starting from the lowest grade. It proves optimality of the heuristic policy in three nontrivial situations. In a computational experiment, in 135 out of 150 randomly generated instances (i.e., in 90% of the cases), the heuristic yielded a solution that was as good or better than that yielded by a benchmark computer program that solves the present problem as a nonlinear program. Further, the average computational time under the heuristic was an order of magnitude less than that under the program.