Constructing Systems and Information: A Process View
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#1998 Operational Research Society Ltd. All rights reserved. 0160-5682/98 $12.00 http://www.stockton-press.co.uk/jor
Book Selection Edited by JM Wilson JE Beasley (Ed): Advances in Linear and Integer Programming J Kallrath and JM Wilson: Business Optimisation: Using mathematical programming M Crowe, R Beeby and J Gammack: Constructing Systems and Information: A Process View MH Karwan, J Spronk and J Wallenius: Essays in Decision Making: A volume in Honour of Stanley Zionts
Advances in Linear and Integer Programming JE Beasley (Ed) Oxford University Press, Oxford, 1996. xii 288 pp. £40.00. ISBN 0 19 853856 1 To a reviewer there are three types of book: those which are so good that one enjoys reading them in depth; those which are so bad that one knows one does not need to; and those in between. This book falls in that last category. To some extent this is inevitable with what is in effect a series of review articles on algorithms for solving linear and integer programming problems. But one looks in vain for the new insights that come from the best review articles, the connections made between what had appeared to be disjoint results. The stated purpose is `to bring together in a single text an accessible exposition of . . . the state of the art in linear and integer programming'. The bulk of the book (four articles) is concerned with interior point methods, but there are also articles on simplex methods and branch-and-cut for integer programming. Notable by its absence is a discussion of branch-and-bound algorithms for integer programming: perhaps these are considered too empirical for academic authors. The ®nal article sits somewhat oddly, being neither a review article nor about algorithms; it is about the relationship between computational logic and integer programming. The ®rst article, by Istvan Maros and Gautam Mitra, is on simplex methods. It traces the issues involved in implementing the Sparse Simplex Method: data structures; basis factorisation; pricing; updates, crash procedures; handling degeneracy. These provide a useful introduction to the issues involved but would not put someone in a position to write an effective implementation of the algorithm. Computational results are presented using the authors' own Fort MP code and comparisons are made with MINOS, CPLEX and OSL. As the authors recognise, these must all be taken with a large pinch of salt because
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of the dif®culty of establishing a fair basis for comparison. The authors note, for instance, CPLEXs inability to solve the problem with the largest number of non-zeros on their test con®guration. Yet they do not explore the trade-off between memory and CPU cycles which almost certainly lies behind this, and behind CPLEXs apparently superior performance. It is the sort of practical issue which altogether receives insuf®cient attention in this book. The next two articles are probably the best in the book. Cornelis Roos and Jean-Philippe Vial provide a theoretical introduction to interior point methods while Jacek Gondzio and Tamas Te
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