A two-phase procedure for allotting geostationary orbital locations to communications satellites

We consider the problem of allotting locations in the geostationary orbit to communication satellites, subject to angle of elevation and electromagnetic interference constraints. An optimization framework is used as a means of finding feasible allotment plans. Specifically, we present a two-phase solution procedure for the satellite location problem (SLP). The objective in SLP is to allot geostationary orbital locations to satellites so as to minimize the sum of the absolute differences between the locations prescribed for the satellites and corresponding specified desired locations. We describe two heuristics, an ordering procedure and a k-permutation algorithm, that are used in tandem to find solutions to SLP. Solutions to a worldwide example problem with 183 satellites serving 208 service areas are summarized.     

Landmarks in defense literature

Achtung-Panzer! By Major General Heinz Guderian, Translated by Christopher Duffy with Introduction and Notes by Paul Harris. (Arms & Armour Press £16.99. ISBN 1-85409-138-7, 220 pages)     

Book Reviews

Strategic Geography. By Hugh Faringdon. Routledge, London (1989), ISBN 0-415-00980-4, £40.00

Field Artillery and Firepower. By J. B. A. Bailey. The Military Press, Oxford (1989), ISBN 0-85066-810-7, £25.00 (hardback), ISBN 0-85066-811-5, £14.50 (paperback)

U.S.-Soviet Security Cooperation. Edited by Alexander L. George, Philip J. Farley and Alexander Dallin. Oxford University Press, New York (1988), ISBN 0-19-505397-4, £30.00 (hardback), $19.95 (paperback)

Non-production by Industry of Chemical-warfare Agents: Technical Verification under a Chemical Weapons Convention. Edited by S. J. Lundin. SIPRI/Oxford University Press, Oxford (1988), ISBN 0-19-829129-9, £19.50

Ireland's Terrorist Trauma: Interdisciplinary Perspectives. Edited by Alan O'Day and Yonah Alexander. Harvester Wheatsheaf, Hemel Hempstead (1989), ISBN 7450-049003, £27.50 ($48.65)

Pilots and Rebels: the Use of Aircraft in Unconventional Warfare 1918-1988. By P. A. Towle. Brassey's (UK), London (1989), ISBN 0-08-036712-7, £29.95 ($53.95)     

Optimal stopping problems for differential equations perturbed by a poisson process

We investigate a class of optimal stopping problems for dynamical systems described by one-dimensional differential equations with an additive Poisson disturbance. The rate of the disturbance may depend upon the current state of the system. A dynamic programming equation for the optimal stopping cost is derived along with conditions which must be met at the boundary of the optimal stopping set. These boundary conditions depend upon whether or not the stopping set may be entered by smooth motion.     

A linear programming approach to geometric programs

A cutting plane method, based on a geometric inequality, is described as a means of solving geometric programs. While the method is applied to the primal geometric program, it is shown to retain the geometric programming duality relationships. Several methods of generating the cutting planes are discussed and illustrated on some example problems.     

On convexity proofs in location theory

It is often assumed in the facility location literature that functions of the type ø_i(x_i, y) = β_i[(x_i-x)²+(y_i-y)²]^K/2 are twice differentiable. Here we point out that this is true only for certain values of K. Convexity proofs that are independent of the value of K are given.     

Optimality conditions for the bilevel programming problem

The bilevel programming problem (BLPP) is a sequence of two optimization problems where the constraint region of the first is determined implicitly by the solution to the second. In this article it is first shown that the linear BLPP is equivalent to maximizing a linear function over a feasible region comprised of connected faces and edges of the original polyhedral constraint set. The solution is shown to occur at a vertex of that set. Next, under assumptions of differentiability, first-order necessary optimality conditions are developed for the more general BLPP, and a potentially equivalent mathematical program is formulated. Finally, the relationship between the solution to this problem and Pareto optimality is discussed and a number of examples given.