98 BOOK REVIEWS

SCHEDULING UNDER FUZZINESS. Roman S lowiVnskiand Maciej Hapke (eds), Physica-Verlag (ASpringer-Verlag Company). ISBN 3-7908-1249-8

This is an excellent book within the series ‘Stud-ies in Fuzziness and Soft Computing’. The book isdevoted to an important and complex class of de-cision problems related to making schedules in thepresence of uncertainty. A large number of mod-els and algorithms have been developed within thedeterministic scheduling theory that assume idealsituations where all parameters are known andprecisely de=ned. However, underlying almost allreal-world scheduling problems are uncertain andimprecise data. This often prevents the results ofthe deterministic scheduling theory from being ap-plied in practice. Fuzzy scheduling models have re-cently attracted a great interest among the schedul-ing research community and the number of paperspublished in journals and conference proceedingsis continuously increasing. However, to the bestof my knowledge this is the =rst book devoted en-tirely to this subject.

Reading through this volume the reader can seethat scheduling under fuzziness yields many fas-cinating =elds of study. After reading 13 papersin this volume it seems clear that no single for-mulation and no single method will be powerfulor comprehensive enough to treat a wide range ofdiGerent types of real-world scheduling problems.This book serves to underline that such a com-plex problem as scheduling under fuzziness givesrise to mathematical and computational questionsof great diIculty.

Fuzzy sets could be used in scheduling prob-lems in diGerent ways. The majority of the papersemploy fuzzy sets with more than one semantics.The papers of this volume are organized into threeparts according to the semantics that are dominantin them.

Part I focuses upon approximate reasoning anddiscusses related issues on fuzzy rules, and simi-larity and closeness of linguistic terms. It containstwo papers.

(1) Caster Scheduling System Analysis withFuzzy Technology, by I. B. Turksen, M.H. F. Zarandi and M. Dudzic, presents afuzzy system for steel continuous casting. Itmodels non-linear and complex interactionsamong the input variables and their eGectson the output variables.

(2) Dynamic Scheduling on Distributed Real-Time Systems by Self-Learning Fuzzy Al-gorithms, by M. Litoiu, and R. Tadei, ex-plains a distributed dynamic scheduling al-gorithm which uses fuzzy decision rules indispatching of the tasks.

Fuzzy sets are also applied to express prefer-ences of human schedulers, and to contribute toHexibility in calculating constraint satisfaction.These topics are treated in the four papers ofPart II.

(1) The Use of Possibilistic Decision The-ory in Manufacturing, Planning and Con-trol: Recent Results in Fuzzy Master Pro-duction Scheduling, by H. Fargier and C.Thierry, investigates the use of possibil-ity theory in manufacturing planning andcontrol. The authors propose a system forbuilding an estimated schedule when ordersand demand are not well known. The sys-tem calculates the robustness of alternativeschedules with respect to satisfaction of thedemand.

(2) Introducing Flexibility in Scheduling: thePreference Approach, by P. Fortemps, pro-poses a preference model which derivesfrom possibility theory and allows the ex-pression of preferences concerning satisfac-tion of Hexible constraints on precedence,resources and duration of jobs.

(3) Scheduling Problems with Fuzzy Con-straints, by H. Ishii, describes fuzzy ver-sions of a number of classical schedulingproblems with fuzzy constraints on prece-dence, due dates, resources, and processingtime.

(4) Flowshop Scheduling with Fuzzy Due-date and Fuzzy Processing Time, by H.Ishibuchi and T. Murata, proposes a ge-netic algorithm for fuzzy Howshop schedul-ing problems. The authors discuss multi-objective scheduling problems where eachjob has diGerent scheduling criteria and de-velop a multi-objective genetic algorithmfor optimization of aggregated schedulingcriteria.

There are seven papers in Part III which discussdiGerent sources and types of uncertainty. In thosepapers parameters that are most often imprecise orincomplete are processing times and due dates.

Copyright ? 2002 John Wiley & Sons, Ltd. J. Sched. 2002; 5:93–102

BOOK REVIEWS 99

(1) A Methodology for Solving a Range ofScheduling Problems under Uncertainty,by G. Adamopoulos, C. P. Pappis andN. I. Karacapilidis, addresses a conceptualframework for formulation and solution ofa class of scheduling problems with impre-cise data. The proposed methodology is ex-empli=ed through a class of scheduling jobson parallel unrelated processors where theinput data is given as linguistic terms, pro-cessing times of jobs are both uncertain andcontrollable, and due dates may or may notbe decision variables.

(2) Two Approaches to Fuzzy Flow ShopProblem, by S. Chanas, A. Kasperski andD. Kuchta, considers a fuzzy How shop se-quencing problem with fuzzy processingtimes. Two new approaches are proposed:the =rst that minimizes the expected valueof the makespan given as a fuzzy number,and the second in which the possibility de-gree of the fuzzy makespan exceeding afuzzy goal is maximized.

(3) Fuzzy Set Approach to Multi-Objectiveand Multi-Mode Project Scheduling un-der Uncertainty, by M. Hapke and R.S lowiVnski, describes a multiobjective sim-ulated annealing approach to resource con-strained project scheduling problems withfuzzy time parameters. The methodologypresented is general enough to be ap-plied to solving other classes of fuzzymultiobjective combinatorial optimizationproblems.

(4) Single Machine Scheduling under Fuzzi-ness, by M. Vlach, clari=es some issueson scheduling involving a single machinein a fuzzy environment where due dates,processing times and precedence relationsare fuzzy.

(5) Scheduling of Heterogeneous Data UsingFuzzy Logic in a Customer–SubcontractorContext, by L. Geneste, B. Grabot and

P. Moutarlier, describes a method forscheduling in a customer-subcontractorcontext which takes into account both un-certainties of manufacturing orders due tothe possibility for their cancellation and im-precision of the processing time.

(6) Virus-Evolutionary Genetic Algorithm forSequencing Jobs in Fuzzy Environment, byN. Kubota and T. Fukuda, applies fuzzyset theory and a special type of genetic al-gorithm called a virus-evolutionary geneticalgorithm. A self-organising manufacturingsystem for sequencing jobs and path plan-ning of conveyor units is built.

(7) Fuzzy Set Approaches to Lot Sizing, byN. I. Karacapilidis, C. P. Pappis and G.Adamopoulos, introduces a methodology todeal with uncertainties present in lot siz-ing in a batch type production system. Inthese problems the estimated future demandis usually imprecise and given by linguisticterms.

The book ends with the list of full addresses of25 contributing authors, who are among the lead-ing experts in the =eld, which will enable inter-ested readers to follow up many of the sources ofmaterials introduced in the papers. The foreword,written by D. Dubois and H. Prade, and preface,written by R. S lowiVnski and M. Hapke, providean excellent introduction to the book. This is abook this reviewer would strongly recommendto scheduling researchers. The book representsa signi=cant step forward in bridging the gapbetween the theory and practice of scheduling andmay help practitioners in real-world schedulingproblems. However, those new to the concepts ofuncertainty will probably need to consult someother introductory texts in fuzzy sets and fuzzylogic before reading this book.

SANJA PETROVIC

University of Nottingham, U.K.

(DOI: 10.1002=jos.108)

SCHEDULING AND AUTOMATIC PARALLELIZATION.Alain Darte, Yves Robert and FrVedVeric Vivien,BirkhMauser, New York, ISBN 0-8176-4149-1

This book deals with task graph schedulingand loop nest scheduling. The main objective

is to present a unifying theory of loop trans-formations that can be used to auto-matically parallelize program code de=ningnested loops. It presents the current state of theart in automatic parallelism detection in nestedloops.

Copyright ? 2002 John Wiley & Sons, Ltd. J. Sched. 2002; 5:93–102