Richard E. Rosenthal

Optimizing Military Airlift

We describe a large-scale linear programming model for optimizing strategic (intercontinental) airlift capability. The model routes cargo and passengers through a specified transportation network with a given fleet of aircraft subject to many physical and policy constraints. The time-dynamic model captures a significant number of the important aspects of an airlift system in a large-scale military deployment, including aerial refueling, tactical (intracontinental) aircraft shuttles, and constraints based on crew availability. The model is designed to provide insight into issues associated with designing and operating an airlift system. We describe analyses for the U.S. Air Force system concerning fleet modernization and concerning the allocation of resources that affect the processing capacity of airfields.

Steaming on Convex Hulls

This is a sea story about using a simple classroom example to save a great deal of money, as well as to convince beginning Postgraduate Naval School operations research students---experienced, skeptical military officers---that mathematical analysis can yield immediate results. The application is planning a ships transit from one point to another in a fixed amount of time, given that the ship can operate with one or more of its propulsion plants idled to save fuel. Simple analysis yields nonintuitive results that US Navy shipboard energy-conservation guides overlook. One of the authors (Kline) solved this homework problem as a student and subsequently applied this example when he took command of USS AQUILA, a patrol hydrofoil missile ship. AQUILA achieved results so striking in comparison to her sister ships that the squadron material officer inspected her engineering plant to ensure that no safety settings were being overridden to achieve this record. Klines spreadsheet decision-support tool was provided to other hydrofoil commanders. A more general version has been conveyed to the US Navy. Considering that our navy spends about a billion dollars per year on fuel for surface-combatant ships alone, this development promises substantial, long-term returns. “But thou, contracted to thine own bright eyes, Feedst thy lightst flame with self-substantial fuel.” Shakespeare, Sonnet I

Optimization Tradecraft: Hard-Won Insights from Real-World Decision Support

Practitioners of optimization-based decision support advise commerce and government on how to coordinate the activities of millions of people who employ assets worth trillions of dollars. The contributions of these practitioners substantially improve planning methods that benefit our security and welfare. The success of real-world optimization applications depends on a few trade secrets that are essential, but that rarely, if at all, appear in textbooks. This paper summarizes a set of these secrets and uses examples to discuss each. “Thou shalt never get such a secret from me but by a parable.” Shakespeare, The Two Gentlemen of Verona

Optimizing Flight Operations for an Aircraft Carrier in Transit

Suppose that an aircraft carrier is in transit to an assigned position within strike range of a designated target, and is required to be there at a specified time. The carrier may use aircraft assets for defense against threats that may be encountered en route, but doing so will encumber the carriers progress toward the required objective. We present a highly detailed integer programming model for scheduling aircraft launches and recoveries, to achieve an optimal balance between the conflicting needs of self-protection and on-time arrival.

Representing inverses in pure network flow optimization

Abstract A basis for a pure network flow problem always exhibits special structure, whose exploitation has led to the development of extremely efficient network optimization software. The backbone of these programs is a data structure which represents the basis as a tree and is used to perform the linear algebraic steps required for optimization. We demonstrate that the basis inverse also possesses a special structure which we call the inverse-tree. We develop a data structure to represent the inverse tree, and we show that it obeys a symmetric relationship with the basis-tree data structure. (The predecessor function of the inverse-tree is the preorder link function of the basis-tree and vice versa). We develop efficient computational procedures for exploiting these results and show that using the inverse-tree requires computation of the same order as the basis-tree.

Scheduling Peacetime Rotation of Pakistan Army Units

Abstract : Since Pakistan has greatly varying climates and terrains, the Pakistan Army rotates its units between locations so that no unit endures inequitable hardship or enjoys unfair advantage. Army peacetime policy specifies strict constraints on unit rotations, including restriction on: the length of a units stay in any location, the number of units moving at any time, and the allowable replacements for any moving unit. Scheduling rotations manually in accordance with these rules, as is currently practiced, is extremely difficult and time-consuming. This thesis presents an integer programming model that finds feasible, minimum-cost schedules for planning horizons of up to eight years. The model also ensures that the units are positioned at the end of the planning horizon so that feasible schedules exist for future planners. The model is implemented with commercially available software: the GAMS algebraic modelling language and the XA and OSL optimizers. Schedules are obtained for realistic test problems in less than an hour on a 486/33 personal computer.