European Journal of Operational Research 168 (2006) 275–277

www.elsevier.com/locate/ejor

Book review

V. T�Kindt and J.C.Billaut, Multicriteria Schedul-

ing. Theory, Models and Algorithms, Springer

Verlag, 2002, ISBN 3-540-43617-0, 303 pp., EUR

74.95.

1. Introduction

Scheduling has received much attention in the lit-erature since the pioneering work of S.M. Johnsonin 1954. In the first 30 years, it was usual to consideronly one objective function as performance crite-rion. However, in many practical situations a deci-sion-maker has to take into account simultaneouslyseveral objectives. For instance, at the medium-term planning phase several costs have to be takeninto account (supply costs, stock costs and costs ofmodifying production systems) while e.g. at theshort-term planning phase, such objectives as thecustomer satisfaction and minimization of work-in-process as well as manufacturing costs have tobe considered. Therefore, the investigation of multi-criteria scheduling problems has begun about 20years ago with a growing interest nowadays. Onthe other side, recent results in this area are not con-tained in the monographs about scheduling (may bewith the exception of single machine earliness-tardi-ness problems) which appeared in the last decade(see e.g. [2,3,5] or others). Therefore, there was cer-tainly a need for writing a book dealing intensivelywith multicriteria scheduling problems.

2. Content of the work

The book consists of nine chapters and twoappendices. It can roughly be divided into fourparts. The first part (Chapters 1 and 2) gives ashort introduction to scheduling and the complex-

doi:10.1016/j.ejor.2004.09.023

ity of problems and algorithms. Here the standardajbjc classification presented by Graham et al. [4]together with many extensions have been intro-duced. Some fundamental notions such as domi-nant set of schedules, active and nondelayschedules are presented. At the end of Chapter 1,some basic scheduling rules and algorithms are re-viewed which are later used as tools for treatingmulticriteria problems. In Chapter 2 the basicconcepts of complexity of algorithms andproblems are shortly discussed in a standardway.

The second part (Chapters 3 and 4) deals withmulticriteria decision making and multicriteriascheduling problems. Chapter 3 is the longestchapter of the book (about 60 pages) and presentsan introduction to multicriteria scheduling. First,a few comments on multicriteria decision makingas a descriptive approach and multicriteria deci-sion aid as a constructive approach are given.One section deals with the definition of optimalityin the multicriteria case with the focus on Paretooptima. Further, a geometric interpretation ofPareto optima by means of dominance cones isgiven. Another section is dedicated to the determi-nation of Pareto optima. In this context, convexcombinations of criteria, a parametric analysis,the application of an �-constraint approach, theuse of the Tchebycheff and the weighted Tcheby-cheff metrics as well as the goal-attainment ap-proach are reviewed. Some basic results andalgorithms for multicriteria linear programmingand multicriteria mixed integer programming aregiven. Then some general complexity results formulticriteria optimization problems are presented.A very short discussion of interactive methods andan overview of goal programming approaches fin-ish Chapter 3.

276 Book review / European Journal of Operational Research 168 (2006) 275–277

Chapter 4 specializes to multicriteria schedulingproblems and discusses a three-phase approach forthe multicriteria scheduling problem of finding aPareto optimal schedule which partitions the prob-lem into three subproblems: modelling of the prob-lem, taking into account of criteria, andscheduling. Then several types of resolution meth-ods (a priori, interactive and a posteriori methods)are discussed. Finally some general complexity re-sults in connection with multicriteria schedulingproblems are given.

The third part (Chapters 5 up to 7) discussesseveral types of multicriteria scheduling problems.Chapters 5 and 6 deal with single machine prob-lems. In particular, Chapter 5 considers just-in-time scheduling problems. Such problems canbe interpreted as a multicriteria problem since typ-ically earliness and tardiness measures are used asoptimization criteria. Chapter 6 presents polyno-mially solvable, NP-hard and open problems forother multicriteria single machine problems. Thelatter two chapters cover that part of multicriteriascheduling problems which has most intensivelybeen investigated up to now. Chapter 7 deals withmulticriteria shop scheduling problems, where thefocus is on flow shop problems, particularly two-machine flow shop problems. For all presentedflow shop problems, only permutation schedulesare considered. A few comments on job and openshop problems finish this chapter.

The last part of the book (Chapters 8 and 9)deals with multicriteria scheduling problems whichinclude assignment problems. These are such prob-lems, where a job resp. an operation has to be per-formed on one machine of a center, i.e. one has toassign each operation to a machine of the corre-sponding center, and if all assignments have beendone, the schedules for the operations assignedto the same machine have to be determined. Typ-ical problems of this class are parallel machineproblems and hybrid (or flexible) shop schedulingproblems. Chapter 8 discusses results for parallelmachine problems with identical, uniform andunrelated machines, where most results are pre-sented for the case of identical parallel machines.The last chapter deals very shortly (seven pages)with k-stage hybrid flow shop problems, wherethe jobs have to follow the same route through

the k stages and at each stage, a set of identicalparallel machines is available for performing thecorresponding operation.

The list of references contains more than 250papers in journals and conference proceedings,many of them have appeared only in the last dec-ade. The first appendix presents the usual nota-tions from single-criterion scheduling problemsbased on the 3-parameter classification schemeby Graham et al. [4] and later extensions. The sec-ond appendix summarizes the most important re-sults presented in the book in seven tables. Here,the reader can quickly inform about the border-lines between polynomial algorithms and NP-hardproblems.

3. Discussion

This book might be considered as a first (butrather successful) attempt to review the recent lit-erature in the field of multicriteria scheduling. Asthe authors write, ‘‘the purpose of this book is toprovide a survey, based on a proposed methodo-logy, of the existing methods for solving multicri-teria scheduling problems, considering bothmethods of multicriteria optimization and schedu-ling fields’’. Therefore, the book is of interest bothfor scientists and graduate students working in dif-ferent scientific disciplines such as operations re-search, computer science, engineering or appliedmathematics.

The main concepts are presented in an exactand clear form. The book is strongly algorithmi-cally oriented. Most algorithms discussed in thebook are given in a detailed Pseudo-code formula-tion (there are about 60 detailed descriptions ofalgorithms), which is sometimes a bit technical,but in any case helpful for the reader or peoplethat intend to implement specific algorithms. Con-cerning just-in-time problems, the inclusion of par-allel and shop scheduling problems in an updatedversion would be desirable since in this area, thereis a particular large potential for further research.It is worth noting that most of the lemmata andtheorems have been carefully proven in detail,and many of the presented algorithms are illus-trated by an example. Here the authors did really

Book review / European Journal of Operational Research 168 (2006) 275–277 277

a very good job. To my opinion, the large numberof illustrations will help the reader to understandthe concepts presented in the book. Summarizing,the book is quite pleasant to read. Most relevantliterature in this area has been included and dis-cussed, and so the book gives indeed an up-to-datepresentation of multicriteria scheduling.

In most parts the book is well written, and onecan be grateful to the authors that they have cer-tainly filled some gap in the existing scheduling lit-erature with presenting this book. For thosereaders not so familiar with the basics of multicri-teria optimization, the second part of this bookcould be a bit more detailed, but many referencesto the original literature are given so that the read-er has a lot of additional sources for information.

4. Conclusion

I think that the book has the potential to serveas a reference book for scientists, graduate stu-dents and partially also for practitioners dealingwith scheduling problems including several optimi-zation criteria. Since the topics covered in thisbook have been investigated only recently, youngresearchers can find interesting open problemsand fields for future research. In this way, the bookwill certainly stimulate new developments in this

area. Without any doubts, I can recommend thisbook for those people who wants to get an over-view on the state-of-the-art in the area of multicri-teria scheduling problems.

References

[1] P. Brucker, Scheduling Algorithms, Springer-Verlag, Berlin,1998.

[2] J. Blazewicz, K. Ecker, E. Pesch, G. Schmidt, J. Weglarz,Scheduling Computer and Manufacturing Processes,Springer-Verlag, Berlin, 1996.

[3] R.L. Graham, E.L. Lawler, J.K. Lenstra, A.H.G. RinnooyKan, Optimization and approximation in deterministicsequencing: A survey, Annals of Discrete Mathematics 5(1979) 287–326.

[4] M. Pinedo, Scheduling—Theory, Algorithms, and Systems,Prentice Hall, Englewood Cliffs, NJ, 1995.

Frank WernerFakultat fur Mathematik

Otto-von-Guericke-Universitat Magdeburg

PSF 4120, 39016 Magdeburg

Germany

Tel.: +49 391 6712025; fax: +49 391 6711171

E-mail address: frank:werner@mathematik:uni-magdeburg:de

Available online 21 December 2004