Optimal assembly of systems using schur functions and majorization

A general assembly of n systems from k types of components is considered. The techniques of majorization and Schur function are utilized to pinpoint the optimal assembly under several criteria. Earlier results of Derman. Leiberman, and Ross [2] and El-Neweihi, Proschan, and Sethuraman [3] are generalized.     

Short-term retrenchment planning in hierarchical manpower systems

We address 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 we study 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, we develop a heuristic in which the promotion proportions of all the grades are successively fixed, starting from the lowest grade. We prove 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. © 1995 John Wiley & Sons, Inc.     

A probability model for initial crack size and fatigue life of gun barrels

With constant firing, metal fatigue produces cracks in a gun barrel. The useful life of the barrel comes to an end when a crack develops to a critical size. The theory of Fracture Mechanics suggests a formula for crack size growth rate. This formula can be used to determine the life of a barrel, depending on the initial and critical crack sizes and other factors. The initial crack size turns out to be a dominant factor. Unfortunately, accurate measurements are not generally available on the initial crack size. In this paper, we propose a simple probability model for the initial crack size and this, in turn, leads to a probability distribution of the life of the barrel. This last distribution is the well-known exponential distribution with a location shift. The simplicity of this final result is one of the factors that make the model appealing.