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Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy's resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially "black box" functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.

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This document and trademark(s) contained herein are protected by law. This representation of RAND intellectual property is provided for noncommercial use only. Unauthorized posting of this publication online is prohibited. Permission is given to duplicate this document for personal use only, as long as it is unaltered and complete. Permission is required from RAND to reproduce, or reuse in another form, any of its research documents for commercial use. For information on reprint and linking permissions, please visit www.rand.org/pubs/permissions.The RAND Corporation is a research organization that develops solutions to public policy challenges to help make communities throughout the world safer and more secure, healthier and more prosperous. RAND is nonprofit, nonpartisan, and committed to the public interest. RAND's publications do not necessarily reflect the opinions of its research clients and sponsors.Support RAND Make a tax-deductible charitable contribution at www.rand.org/giving/contribute www.rand.org For more information on this publication, visit www.rand.org/t/RR2735