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Ivars Peterson's MathTrek September 11, 2000 Defending the Roman Empire Years ago, when I was in high school and college, the board games Risk and Diplomacy served as wonderful playing fields where I could develop and exercise my tactical and negotiating skills. One issue that often came up in my forays into international intrigue was how to deploy my limited forces to defend far-flung territories while I plotted to conquer the world. Such questions of military strategy can be handled mathematically. Charles S. ReVelle of Johns Hopkins University in Baltimore and Kenneth E. Rosing, recently retired from Erasmus University Rotterdam, describe their approach in the August-September American Mathematical Monthly. ReVelle is a pioneer in the relatively new and rapidly growing field of location science, which involves the use of mathematical techniques to determine the best places to put fire stations, hospitals, fast-food restaurants, or even military units. One classic case goes back to the years of the Roman empire's decline. In the 3rd century, Rome dominated Europe and could station 50 legions throughout its territories, securing even the most distant lands. A century later, it had only about half as many legions to defend the empire. Emperor Constantine (274-337) had to decide how to disperse the legions at his disposal to protect the empire's fringes without leaving Rome itself open to attack. He devised a "defense-in-depth" strategy to cope with the diminished power of his forces. He expected local, part-time militias to slow down and fragment invading barbarian hordes, and he dispatched well-equipped and highly trained mobile field armies, when needed, to halt or throw back the enemy or suppress an insurrection. | |
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