Flow Shop Scheduling: Theoretical Results, Algorithms, and Applications

345 Pages·2013·2.864 MB·English

by  Hamilton Emmons, George Vairaktarakis (auth.)

International Series in Operations
Research & Management Science
Volume 182
SeriesEditor:
FrederickS.Hillier
StanfordUniversity, CA, USA
Special Editorial Consultant:
Camille C. Price
Stephen F. Austin State University, TX, USA
(cid:70)(cid:111)(cid:114)(cid:102)(cid:117)(cid:114)(cid:116)(cid:104)(cid:101)(cid:114)(cid:118)(cid:111)(cid:108)(cid:117)(cid:109)(cid:101)(cid:115)(cid:58)
http://www.springer.com/series/6161

Hamilton Emmons • George Vairaktarakis
Flow Shop Scheduling
Theoretical Results, Algorithms,
and Applications
Hamilton Emmons George Vairaktarakis
Weatherhead School of Management Weatherhead School of Management
Case Western Reserve University Case Western Reserve University
Cleveland, OH 44106 Cleveland, OH 44106
USA USA
[email protected] [email protected]

ISSN 0884-8289
ISBN 978-1-4614-5151-8 ISBN 978-1-4614-5152-5 (eBook)
DOI 10.1007/978-1-4614-5152-5
Springer New York Heidelberg Dordrecht London

Library of Congress Control Number: 2012947403

© Springer Science+Business Media New York 2013
This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of
the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or
information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar
methodology now known or hereafter developed. Exempted from this legal reservation are brief
excerpts in connection with reviews or scholarly analysis or material supplied specifically for the
purpose of being entered and executed on a computer system, for exclusive use by the purchaser of
the work. Duplication of this publication or parts thereof is permitted only under the provisions of the
Copyright Law of the Publisher’s location, in its current version, and permission for use must always
be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright
Clearance Center. Violations are liable to prosecution under the respective Copyright Law.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publication does not imply, even in the absence of a specific statement, that such names are exempt
from the relevant protective laws and regulations and therefore free for general use.
While the advice and information in this book are believed to be true and accurate at the date of
publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for
any errors or omissions that may be made. The publisher makes no warranty, express or implied, with
respect to the material contained herein.

Printed on acid-free paper

Springer is part of Springer Science+Business Media (www.springer.com)
Στη μν´ημη των φ´ιλων μoυ
Γιω´ργoυ Aγγ(cid:14)λλo´πoυλoυ και Δημ´ητρη Kωνσταντα´κη
G.V.
For Lin, with love
H.E.

Preface
The idea for this monograph was born during lunch conversations between
the authors. By that time, both of us had a lot of exposure in scheduling
research, and observed that a constant stream of invitations to review was
fillingourdesks withpapers onflowshopresearch. Wecouldn’thelpnoticing
that,even though several monographsand edited volumes haveappeared on
scheduling in general, most of these works survey the field by contributing a
singlechapter toevery production system such as the flow shop.In contrast,
flow shop systems appear to be the most studied in all of scheduling liter-
ature, offering unique contributions, occupying the research efforts of many
researchers around the globe.
Thismonographisallaboutflowshops.Wehaveorganizedselectedresults
intotendistinctflowshopsystemsandwheneverpossible,wehaveattempted
to exploit the connections. We used our subjective personal discretion in se-
lectingtheresults presented, andweapologizeinadvancetothose(hopefully
few) in the audience whom we leave disappointed. We also include a limited
number of results that have not been published before. We have sought to
make the material accessible to a broad readership, and have tried hard to
simplify notation and reveal unifying concepts. In all, we know of no other
text dedicated to flow shop research at the breadth attempted here.
It is our hope that, by organizing in one place a huge body of flow shop
knowledge along distinct design features, we help scholars and practitioners
to identify easily what is known in the literature on problems of interest.
Moreover, we hope that results unique to flow shop research willprovide the
seed for research inother areas of scheduling and in optimizationin general.
Finally,ourmonographmayprovidetheimpetusformethodsandtechniques
thathave been tried successfully in other areas ofoptimizationto be applied
to flow shop problems that are intractable as of now.
We are very grateful for the helpful suggestions of many friends and col-
leagues, notable among whom are Kenneth Baker, Xiuli Chao,Sel¸cuk Kara-
bati,Michael Pinedo, Ruben Ruiz, and Gideon Weiss. Also, many thanks to
our Editor and friend, Frederick Hillier,forhis patience and encouragement.
Hamilton Emmons and George Vairaktarakis
Cleveland, OH, U.S.A.
vii

Contents
1 INTRODUCTION........................................ 1
1.1 Assumptions and Conventions............................ 2
1.2 Terminology ........................................... 3
1.2.1 Problem Classification and Notation ................ 5
1.3 Precedence ............................................ 7
1.3.1 Precedence versus Dominance...................... 9
1.4 The Permutation Flow Shop ............................. 10
1.5 Graphic Representation of Flow Shop Schedules ............ 11
1.6 Dominance Properties................................... 12
1.6.1 Sequencing using Dominance....................... 14
1.7 Heuristics and Worst Case Analysis....................... 16
1.7.1 Cyclic Flow Shops................................ 17
References ................................................. 18
2 THE TWO-MACHINE FLOW SHOP .................... 21
2.1 Examples.............................................. 21
2.2 F2|(perm),(pmtn)|Cmax: Johnson’s Rule.................. 22
2.2.1 F2|(perm),rj|Cmax and F2|(perm)|Lmax ............ 26
2.2.2 F2|(perm),prec|Cmax ............................. 28
2.2.3 F2|perm,sij,tij|Cmax ............................. 29
2.2.4 Manufacturing Cells .............................. 29
2.2.5 F2|sij|Cmax with a Single Server ................... 29
2.2.6 Lot Streaming ................................... 31
2.3 The Choice of Objective................................. 34
2.4 F2|(perm)|ΣC ........................................ 35
j
2.4.1 PolynomiallySolvable Cases ....................... 35
2.4.2 Lower Bounds ................................... 35
2.4.3 OptimalAlgorithms and Heuristics ................. 40
2.4.4 F2|(perm)|ΣC with Setups ....................... 42
j
| |
2.5 F2 (perm) (ΣCj|minCmax).............................. 44
| |
2.6 F2 (perm) (αΣCj+βCmax).............................. 45
ix
x Contents
| |
2.7 F2 (perm) fmax........................................ 45
| |
2.7.1 F2 (perm),sj Lmax or Tmax ....................... 46
| |
2.8 F2 (perm) ΣT ........................................ 48
j
2.8.1 Dominance properties............................. 49
2.8.2 Lower Bounds ................................... 49
2.8.3 Branch-and-Bound Algorithms ..................... 51
2.8.4 Heuristics ....................................... 51
| |
2.8.5 F2 (perm),prep ΣT ............................. 52
j
| |
2.9 F2 (perm),d =d Σw U ............................... 52
j j j
| |
2.9.1 The Complexityof F2 (perm),d =d ΣU .......... 52
j j
| |
2.9.2 F2 (perm),(pmtn),d =d Σw U .................. 54
j j j
| |
2.10 F2 (perm),pij=uij−vijrij (Σijrij|Cmax ≤D) ............. 54
2.11 Bicriteria Objectives .................................... 55
2.11.1 Branch-and-Bound for a Bicriteria Objective......... 56
| |
2.11.2 F2 (perm) (ΣCj,Cmax) ........................... 57
2.11.3 Bicriteria InvolvingCmax and a Measure of Tardiness . 57
2.12 Related Problems ...................................... 61
2.12.1 G2|(pmtn)|Cmax ................................. 61
2.12.2 O2|(pmtn)|Cmax ................................. 62
2.12.3 S2||Cmax and S2|pmtn|Cmax ..................... 63
2.13 Closing Remarks ....................................... 63
References ................................................. 63
3 TRANSFER LAGS IN THE FLOW SHOP............... 67
3.1 Preliminaries........................................... 67
3.1.1 Applications ..................................... 68
3.1.2 Types of Lags.................................... 69
3.1.3 Notation ........................................ 72
3.2 The Two-Machine Flow Shop with Lags................... 72
3.2.1 F2|perm,(cid:4)j|Cmax................................. 73
3.2.2 When are Permutation Schedules Optimal?.......... 75
3.2.3 F2|rvrs,(cid:4)j|Cmax ................................. 76
3.2.4 F2|(cid:4)j|Cmax ...................................... 77
3.2.5 F2|(perm),prec|Cmax ............................. 80
3.2.6 Two-Stage Manufacturing Cells as Flow Shops with
Lags............................................ 83
3.3 The Two-Stage Hybrid Flow Shop with Lags .............. 86
3.3.1 Preliminaries .................................... 87
3.3.2 F(k1,k2)|perm,(cid:4)j|Cmax ........................... 88
3.3.3 F(k1,k2)|rvrs,(cid:4)j|Cmax ............................ 90
3.3.4 F(k1,k2)|(cid:4)j|Cmax................................. 91
3.3.5 SummaryofPerformance RatioandComplexityResults 92
3.3.6 ComputationalExperiments ....................... 92
3.4 The m-Machine Flow Shop with Lags ..................... 93