7/28/2019 21331201
1/3
Lev: Book Reviews274 Interfaces 36(3), pp. 272278, 2006
INFORMS
interesting and unusual and are likely to appeal to
applied students. They are designed to test the con-
cepts. The authors provide answers to many of the
problems.To sum up, the authors give a good account of
optimization techniques. The irritating typographical
errors are a definite drawback. I think the authors
should correct the errors and bring out a revised edi-
tion. At $79.95, the book would be quite expensive
for Indian students, and a less-expensive paperback
edition would be welcome.
References
Sharma, J. K. 2003. Operations Research: Theory and
Applications.
Macmillan India Ltd., New Delhi, India.
Taha, Hamdy A. 2002. Operations Research: An Introduction.
Prentice-Hall, Inc., Upper Saddle River, NJ.
M. Z. Anis
Indian Statistical Institute, 203 B. T. Road,
Calcutta 700108, India, [email protected]
Maros, Istvan. 2003. Computational Techniques ofthe Simplex
Method. Kluwer Academic Publishers,
Dordrecht, The Netherlands. 325 pp. $139.00.
In Computational Techniques of the Simplex Method,
Istvan Maros, a Hungarian mathematician at the
Imperial College of London, describes the simplex
method and its implementation in real problems.Andrs Prkopa, one
of his professors, provides an
introduction highlighting the books features and
virtues. Maros has an original outlook on the simplex
method, which helps him explain the difficulties of
applying it in real cases and the computational tech-
niques for specific linear programs.
The book is aimed at professors and students who
want to look deeply into the computational tech-
niques of the simplex method in linear programming
(LP). Researchers can also benefit, finding new proce-
dures for constructing new algorithms in other areas
of operations research. Hence, I highly recommend
Maross book as a reference for graduate students in
computing and linear programming.
In the first part of the book, Maros describes the pre-
liminaries and main aspects of linear programming;
in the second part, he focuses on the computational
aspects of the simplex method. Three chapters con-
stitute the first part: the main elements of linear pro-
gramming (Chapter 1), the essentials of the simplexmethod
(Chapter 2), and large linear-programming
problems (Chapter 3). The second part contains eight
chapters on computational issues in implementingthe simplex
method, including the characteristics oflinear-programming software
(Chapter 4), a techni-cal description of data structures and basic
opera-
tions (Chapter 5), the standard linear-programmingproblem and
its mathematical programming systems
(MPS) format (Chapter 6), and the preprocessing pro-cedure for
linear programs before the simplex method(Chapter 7). In Chapter 7,
the author explains ways
of reducing the size of the problem, improving itsnumerical
characteristics, and detecting infeasibility
or unboundedness without solving the problem. He
also explains sparsity reduction of a matrix of coef-ficients
and problem scaling, which are essential to
solving large linear programs. In Chapter 8, Maroscovers
algebraic techniques for LP matrices, such as
basis inverse and matrices factorization, triangularmatrices,
and lower and upper triangular factoriza-tion.
Chapters 9 and 10 are longer and more complexthan the preceding
chapters. In Chapter 9, Maros
devotes 100 pages to explaining the primal method,highlighting
computational procedures for solving
linear programs. He discusses different ratio tests,
handling degeneracy, numerical stability, memoryrequirements,
and computational effort. He quotes
from Dantzig (1963) extensively. He also describesWolfes
algorithm and the Devex pricing method and
real cases of problems related to tolerance, pertur-bation, and
shifting. In Chapter 10, he covers thedual algorithm, including
such topics as dual feasibil-
ity, improving dual solutions, extended general dualalgorithms,
degeneracy, and the dual Devex pricing
method.Finally, Chapter 11 is devoted to miscellaneous
aspects of implementing the simplex method. Maros
also summarizes some of the main points of the previ-ous
chapters and suggests further topics for research,
such as tuning parameters, performance evaluation,and
alternatives to the simplex method.
The book ends with a list of references and a short
glossary. A more extensive glossary might have beenuseful.
This interesting book about linear programmingand related
computational techniques should be use-
7/28/2019 21331201
2/3
Lev: Book ReviewsInterfaces 36(3), pp. 272278, 2006 INFORMS
275
ful to graduate students and researchers who wish to
learn the key concepts of the simplex method. Many
readers, students, and researchers can update their
knowledge about linear programming by studyingMaross book.
Reference
Dantzig, G. B. 1963. Linear Programming and Extensions.
Princeton
University Press, Princeton, NJ.
Javier Faulin
Department of Statistics and Operations Research, Public
University of Navarra, 31006 Pamplona, Spain
Tkindt, Vincent, Jean-Charles Billaut.2002. Multicriteria
Scheduling: Theory, Models and Algo-
rithms. Springer-Verlag, Berlin, Germany. 303 pp.$107.00.
Scheduling problems are hard. They are even
harder when multiple objectives must be considered.
Improving customer service, maximizing resource uti-
lization, and reducing inventory are among the many
important objectives that one faces when trying to
solve a scheduling problem. Choosing a way to
address the multiple objectives is the first difficult
step. You could form a new objective that is a linear
combination of the objectives or optimize one objec-
tive while satisfying bounds on the others. You could
minimize the distance from an ideal (but unreach-able) solution
or optimize the objectives in sequence.
You could resort to finding any solution that satis-
fies constraints on the objectives or find the complete
set of solutions that are not dominated by any other
solution.
The literature on scheduling problems with a single
objective is extensive, whereas published academic
research on scheduling problems with two or more
objectives is not. However, it is an ever-growing body
of knowledge. In Multicriteria Scheduling, Tkindt and
Billaut have carefully organized this material for those
who are studying this complex topic and for those
who need to locate an algorithm or review the com-
plexity of a particular problem.
The book, translated from French by Henry Scott,
begins with introductory material on scheduling and
multicriteria optimization. The scheduling material is
adequate and similar to that found in other texts,
including Brucker (2004) and Pinedo (2005). In the
chapter on multicriteria optimization, the authors,
who are faculty members at the University of Tours,
provide a systematic overview that covers a wide
range of relevant topics. They precisely define dif-ferent types
of Pareto optimal solutions and discuss
different techniques, including lexicographical orders,
interactive methods, and goal programming.
The chapter on multicriteria scheduling problems
includes a useful classification of solution approaches.
When faced with such problems, decision makers
may want a unique solution that balances the various
criteria. In this case, they must provide parameters
that can be used to establish the relative priority of the
objectives. Alternatively, decision makers can partici-
pate in the search process, in which case they look at
each solution generated and select new search direc-tions until
they obtain a satisfactory solution. Finally,
decision makers may want to obtain a set of nondom-
inated solutions from which to choose a solution.
The authors have organized the book into chapters
covering different types of multicriteria scheduling
problems: single-machine problems, parallel-machine
problems, flow-shop problems, job-shop problems,
open-shop problems, and hybrid flow-shop prob-
lems. They formulate particular scheduling problems,
present exact algorithms and heuristics, give exam-
ples to help explain the algorithms, and discuss com-
putational complexity results. The problems cover a
wide variety of combinations of objectives, includ-
ing some for which the authors have previously pub-
lished original results. The authors provide citations
for all of the results, enabling interested readers to
investigate selected topics further.
In the appendices, the authors review the notation
and present summary tables that classify multicrite-
ria scheduling problems according to their complex-
ity. The 18 pages of references span over 50 years of
academic research into scheduling problems.
Multicriteria Scheduling is a unique resource. It is
similar in spirit to Peter Bruckers 2004 text, Schedul-
ing Algorithms, in that both books are concerned
with organizing scheduling problems using the tra-
ditional three-field classification scheme, describing
their complexity, and presenting solution algorithms.
This book is a useful complement to Scheduling Algo-
rithms because Brucker does not cover problems with
multiple criteria extensively. Likewise, Leungs (2004)
