Concise RLT forms of binary programs: A computational study of the quadratic knapsack problem

The reformulation‐linearization technique (RLT) is a methodology for constructing tight linear programming relaxations of mixed discrete problems. A key construct is the multiplication of “product factors” of the discrete variables with problem constraints to form polynomial restrictions, which are subsequently linearized. For special problem forms, the structure of these linearized constraints tends to suggest that certain classes may be more beneficial than others. We examine the usefulness of subsets of constraints for a family of 0–1 quadratic multidimensional knapsack programs and perform extensive computational tests on a classical special case known as the 0–1 quadratic knapsack problem. We consider RLT forms both with and without these inequalities, and their comparisons with linearizations derived from published methods. Interestingly, the computational results depend in part upon the commercial software used. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

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)     

The demand for defense in East Asia: Modeling security alternatives∗

An interactive economic model of military spending is proposed. It is quantified on the basis of cross section data for East Asia. Projections of military spending to the end of the decade suggest that the growth of military spending in the region will decline slightly in the current decade. East Asian military spending can, however, be greatly influenced by the path of Chinese and US military efforts. An expansion of military spending by China could cause neighboring countries to greatly increase their military expenditures.