Time and resource constrained scheduling : a constraint
Citation for published version (APA):
Nuijten, W. P. M. (1994). Time and resource constrained scheduling : a constraint satisfaction approach.
Eindhoven: Technische Universiteit Eindhoven. https://doi.org/10.6100/IR431902
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SATISFACTION APPROACH Sched u
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Time and Resource Constrained
A Constraint Satisfaction Approach
CIP-GEGEVENS KONINKLIJKE BIBLIOTHEEK, DEN HAAG
Nuijten, Wilhelmus Petronella Maria
Time and Resource Constrained Scheduling: A Constraint
Satisfaction Approach I
Wilhelmus Petronella Maria Nuijten. -Eindhoven: Eindhoven
University of Technology
Thesis Eindhoven. - With index, ref. - With summary in
Subject headings: scheduling, constraint satisfaction.
druk: Ponsen & Looijen, Wageningen
omslag: Eric Roovers
© 1994 by W.P.M. Nuijten, Tilburg, The Netherlands
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system, or transmitted, in any form or by any means, electronic, mechanical,
photocopying, recording or otherwise, without prior permission of the author.
Time and Resource Constrained
A Constraint Satisfaction Approach
ter verkrijging van de graad van doctor aan de
Technische Universiteit Eindhoven,
op gezag van de Rector Magnificus, prof. dr. J.H. van Lint,
voor een commissie aangewezen door het College van Dekanen
in het openbaar te verdedigen op
vrijdag 9 december 1994 om 14.00 uur
Wilhelmus Petronella Maria Nuijten
geboren te Gilze
Dit proefschrift is goedgekeurd
door de promotoren
prof. dr. E.H.L. Aarts
prof. dr. K.M. van Hee
This thesis would never have become what is right now, if it were not for the
interest and support of several people. I would like to start with expressing my
gratitude to some of them.
First of a11, I want to thank Emile Aarts for his enthusiastic support and
encouragements in the process of writing this thesis. He has taught me a lot
on how to do and especially on how to report on research in a proper way. His
petfectionism and ability to think in cooperation with me, have improved my
I want to thank Kees van Hee for his enthusiastic disapproval of my work
when I first turned to using constraint satisfaction for scheduling, and his
similar support when it proved to work out fine. His early criticisms kept me
on my toes, his later approval strengthened my belief I did weB.
I am also indebted to Hannie van Iersel, Lucas Janssen, Trudy Kunnen,
and Robert-Jan Nobel, who did their M.Sc. work or other research on subjects
related to my own research. Special thanks go to Paul van Erp who also helped
implementing a great deal of the ideas. I, furthermore, thank Frank Dignum
and Marco Verhoeven for carefully reading drafts of my thesis. The Research
Institute on Knowledge Systems in Maastricht is acknowledged for giving me
the opportunity to test my approach on real-life problems.
I want to thank my parents for giving me everything I ever needed and for
never telling, but always advising, me what to do.
Finally, I thank Annemiek for her endless love and support. Having
someone to share your life with, is ever more important than earning the right
to put two extra letters and a dot in front of your name.
Tilburg, December 1994 Wim Nuijten
1.1 Informal Problem Formulation .
1.2 Towards Solving the Problem
1.3 Thesis Outline . . . . . . . . .
2 Constraint Satisfaction in Combinatorial Search 7
2.1 Search Problems and Computational Complexity 7
2.2 The Constraint Satisfaction Problem 1 0
2.3 Solving the CSP . . . . . . . . . . . 12
2.3.1 Consistency Checking . . . . 15
2.3.2 Variable and Value Selection . 17
2.3.3 Dead End Handling . . . . . 18
3 Time and Resource Constrained Scheduling 19
3.1 The Time and Resource Constrained Scheduling Problem 19
3.2 Related Work . . . . . . . . . 24
3.2.1 Optimization Problems . . . . . . 24
3.2.2 Search Problems . . . . . . . . . . 31
3.3 Towards a Constraint Satisfaction Approach 33
3.3.1 Introduction . . . . . . . . . . . . 33
Operation and Assignment Selection .
Dead End Handling . . . . . .
The Algorithms SOLVE and INF . . .
4 Consistency Checking for the Mandatory Constraints 41
4.1 Forward Checking . . . . . . . . . . . . . . . . . . . . . . 41
4.2 2-Consistency . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Sequencing Checking for Resource Sets with Unit Capacity . 46
4.3.1 LBe.,,andUBtct....... 46
4.3.2 Calculating LBesr and UB1c1 • 48
4.3.3 LB2e,1 and UB2tct . . . . . . 53
4.3.4 Calculating LB2est and UB2tct 55
4.4 Sequencing Checking for Multiple Capacitated Resource Sets . 56
4.4.1 IJJest and UB,c, . . . . . . . 56
4.4.2 Calculating LBest and UBtcz 59
4.4.3 LB2esr and UB2tcr ...... 62
4.4.4 Calculating LB2e.vt and UB2tct 63
4.4.5 LB3est and UB3tcr ...... 64
4.4.6 Calculating LB3est and UB3/c, 65
4.4.7 The algorithm SEQUENCINGCHECK 66
4.5 Sequencing Checking with Alternative Resource Set Assign-
ments ......................... 66
4.6 Sequencing Checking with Conflicting Resource Sets 69
4.7 Checking with Remaining Capacity .... t ........ 74
5 Consistency Checking for the Additional Constraints 77
5.1 Introduction •• 0 0 • 77
5.2 Time Constraints . . . 80
5.3 Resource Constraints . 86
6 Computational Studies for Theoretical Problems 91
6.1 Job Shop Scheduling . . . . . . . . . . . . 91
6.1.1 The Job Shop Scheduling Problem . 91
6.1.2 Computational Results . . . . . . . 93
6.2 Multiple Capacitated Job Shop Scheduling. 99
6.2.1 The Multiple Capacitated Job Shop Scheduling Problem 99
6.2.2 Computational Results ................. 100
6.3 Job Shop Scheduling with Resource Set Alternatives ..... 104
6.3.1 The Job Shop Scheduling Problem with Resource Set
Alternatives . . . . . . . 104
6.3.2 Computational Results ................. 106
7 Computational Studies for Practical Problems 109
7 .I Examination Time Tabling . . . . . . . . . . . . . . . . . . . 109
7.1.1 The Examination Time Tabling Problem ........ 109
7 .1.2 Modeling the ETTP as a special case of the TRCSP . . 112
7.1.3 Computational Results . . . . . . . . . . . 115
7.2 Frit Production Scheduling. . . . . . . . . . . . . . . . . . 117
7.2.1 The Frit Production Scheduling Problem . . . . . . 117
7 .2.2 Modeling the FPSP as a special case of the TRCSP . 120
7.2.3 Computational Results . . 122
7.3 School Time Tabling . . . . . . . . . . . . . . . . . . . . . 124
The School Time Tabling Problem . . . . . . . . .
Modeling the STTP as a special case of the TRCSP
Computational results . . . . . . . . . . . . . . .