Symposium on the Theory of Scheduling and Its Applications

446 Pages·1973·8.955 MB·English

by  Salah E. Elmaghraby (editor)

Lectu re Notes
in Economics and
Mathematical Systems
Operations Research, Computer Science, Social Science
Edited by M. Beckmann, Providence, G. Goos, Karlsruhe, and
H. P. KUnzi, ZUrich
86
Symposium on the Theory
of Scheduling
and Its Applications
Edited by S. E. Elmaghraby
Springer-Verlag
Berlin· Heidelberg· New York 1973
Advisory Board
H. Albach· A. V. Balakrishnan· F. Ferschl . R. E. Kalman· W. Krelle . G. Seegmiiller
N. Wirth
Professor Salah E. Elmaghraby
North Carolina State University
Grad. Program in Operations Research
Box 5511
Raleigh, NC 27607/USA
AMS Subject Classifications (1970): 60A30, 90B35
ISBN-13: 978-3-540-06437-4 e-ISBN-13: 978-3-642-80784-8
001: 10.1007/978-3-642-80784-8
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
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Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher,
the amount of the fee to be determined by agreement with the publisher.
© by Springer-Verlag Berlin' Heidelberg 1973. Library of Congress Catalog Card Number 73-14483.
PREFACE
The theory of scheduling is receiving increased emphasis in research and
practice for at least three good reasons. F~~t, the management of large scale
projects resolves itself, in the final analysis, into problems of scheduling
interacting activities subject to limited resources. Second, a great deal of
"fat" that used to exist in the past in production, distribution, and service
systems is eliminated, thanks to tighter managerial controls in information systems,
in financial management, in logistics, and in many other facets of industrial
enterprises and military installations. Tighter scheduling methods are therefore
called for. Thi~d, the study of scheduling problems involves the study of combina
torial problems and optimization over discrete spaces which represent a radical,
and interesting, departure from classical mathematics. This area of study has
attracted a good number of distinguished researchers, engineers as well as
mathematicians. There is a serious attempt to apply known number theory, and
perhaps develop new theory, that would cope with the new problems. The computer
enters the picture in novel and ingenious ways, which has not been possible before;
etc.
To those workinQ in the area, whether in theory or in practice, progress
proceeds at an exhilarating pace, with new mathematical structures and computational
approaches being continuously introduced to model and solve the problems in novel,
and oftentimes ingenious ways. This requires rather frequent 'stock taking' of
the progress achieved; which has been done at the rate of approximately once every
five years over the past thirteen years. To this end a Symposium on The Theory
of Scheduling and its Applications was held on the campus of North Carolina State
University at Raleigh, between May 15-17, 1972. It was sponsored by the Office of
Naval Research, and was attended by 46 people from several geographical regions
of the United States and Canada, who represented a wide spectrum of background,
occupation and contributions to the area of Scheduling.
The Sympos'ium was organized in few general sessions and several discussion
groups. The objective was to maximize interaction and cross-fertilization among
participants.
Almost all papers presented at the Symposium had been previously distributed
to the participants, and each paper presented in the general sessions was reviewed
and discussed by two discussants. Their comments were conveyed in writing to the
authors, who subsequently modified their paper in light of the criticisms presented
to them. On the other hand, contributed papers in discussion groups received
serious considerations from the audience, which was typically small in size and
had opted to attend a particular group because of interest in the subject matter
presented.
The upshot of all this is that while each paper bears the name of its author
(or authors), it is, in fact, the distillation of several contributions since, in
the majority of cases, the criticisms and contributions from discussants, or
"from the floor", were incorporated in the revised versions of the author's
manuscript. This "took care" of the discussants' remarks, and hence there was no
justification to print them in the Proceedings. In a few instances (to be more
specific, three cases), the discussant had a separate contribution to make; these
are appended separately in the Proceedings following the paper. In any event, the
discussants of a paper are identified, and to them go our thanks for the significant
cont ributions they have made.
IV
The Proceedings are organized in four sections according to the tenor of
the contribution: Survey Papers, Applications, Theory, and Models of Processes.
As the reader can imagine, it was sometimes difficult to draw the lines among
these categories, especially between the last two. I take the blame for any
error in designation, or apparent arbitrariness. The Index is organized by
Section, and the papers in each section are arranged alphabetically. There is
also a List of Participants, with the participant's contribution and the location
of his paper (if any).
In an effort to bring out the volume without undue delay, authors were
requested to submit their papers in typewritten form suitable for direct photo
graphic reproduction. This procedure accounts for the variations in type style
and arrangement.
Authors are, of course, solely responsible for the contents of their papers,
as no editorial work was done, except regarding some minor format considerations.
The Symposium afforded the workers in this area a unique chance to get
together, present their latest thoughts, exchange views, and in general assess
the future of the area. The present thinking of the foremost contributors to the
field are contained in these Proceedings. The serious reader will find not only
the latest in "what's up" in scheduling, in both theory and practice, but also the
trends of thought and applications. The collective lists of references in all the
papers should be a valuable asset to any researcher.
Ideas and thoughts are significant by their presence as well as by their
absence, because they elicit other ideas and thoughts. As the reader pores over
these contributions, he should also reflect on the significance, if any, of the
absence of papers applying the theory of queues; or the theory of dynamic
programming, or heuristics, etc. On the other hand, there is an abundance of
Models, but a relative scarcity of Applications (the ratio is almost two to one):
Is this due to the dearth of applications, or to the scarcity of "applicators"
who also write papers for presentation at Symposia? If the latter is closer to
the truth, what can be done to fill that void?
A Symposium invo]ving so many participants and requiring the expenditure of
several thousand dollars cannot materialize without the significant contributions
of a number of people. It isn't that they have "helped": they made it possible,
and without their input the Symposium would not have been realized. They are, in
a real sense, the co-organizers of the Symposium and the co-editors of these
Proceedings. These are: Drs. G. E. Bennington and H. L. W. Nuttle, both of the
Department of Industrial Engineering, N. C. State University, my secretary,
Mrs. Lillian Hamilton, Mr. Eugene Starnes of the Division of Continuing Education
at NCSU, and Mr. Richard Coppins, graduate student in the Operations Research
Program at NCSU.
Most importantly, the profession owes a debt of gratitude to Dr. Thomas Varley,
Director of the Operations Research Program, Office of Naval Research, for
encouraging the idea of the Symposium and for the financial support that made it
possible. I also owe a debt of thanks to Mr. Seymour M. Selig, Managing Editor.
Office of Naval Research, for his continuous encouragement and support, especially
relative to the various avenues of publication of the Proceedings.
Salah E. Elmaghraby
Raleigh, N. C.
CONTENTS
I. SURVEY PAPERS
Bennington, G. E. and 1. F. McGinnis, "A Critique of
Project Planning with Constrained Resources" • 1
Panwalker, S., R. Dudek and M. Smith, "Sequencing
Research and the Industrial Scheduling Problem" 29
II. APPLICATIONS
Florian, M., G. Guerin, and G. Bushell, "The Engine
Scheduling Problem in a Railway Network" - Abstract. 39
Giffler, B., "Detail Scheduling Models and Systems" 44
Haas, C. and T. J. Hodgson, "A Naval Air Rework Facility
Scheduling Problem". . . . . . . . . . . . . 56
Prabhakar, T., "Some Scheduling Applications in Chemical
Industry" . . . . . . . . 69
Salvador, M. S., "A Solution to a Special Class of Flow
Shop Scheduling Problem" . . . . • • . 83
Steinhoff, H. W., "Two Recent Developments in Scheduling
Applications". " • • . . . . .. ..•... 92
Wiest, J., "Toward a Man-Machine Interactive System for
Project Scheduling" • . . . . . . . . . . . 109
III. THEORY
Mitten, L. G. and C. A. Tsou, "Efficient Solution Procedures
for Certain Scheduling and Sequencing Problems". • . . 127
Murty, K., "On the Set Representation and the Set Covering
Problem" . . • . . . . . . . 143
Lawler, E. L. - Discussion of Murty's paper. 164
Rau, J., "Selected Comments Concerning Optimization
Techniques for Functions of Permutations" ......•..• 167
Baker, K. R. - Discussion of Rau's paper. . . • . . 201
VI
IV. MODELS OF PROCESSES
Ashour, S. and R. G. Parker, "An Out-of-Kilter Approach
for Machine Sequencing Problems" • . . . . . . . . . 206
Bradley, G., "Trading Rules for a Decentralized Exchange
Economy" .....••...•........... 224
Bratley, P., M. Florian and P. Robillard, "Scheduling with
Early Start and Due Date Constraints" - Abstract. 242
Elmaghraby, S. E. and A. Mallik, '~The Scheduling of a
Multi-Product Facility". ..... 244
Emmons, H., "The Two-Machine Job Shop with Exponential
Processing Times". . .. .......... 278
Fisher, M., "Optimal Solutions of Scheduling Prob lerns Using
Lagrange Multipliers, Part II" • . • . . 294
Zaloom, V. - Discussion of Fisher's paper 319"
Kapur, K. C., "On Project Cost-Duration Analysis Problem
with Quadratic and Convex Cost Functions" 324
Nuttle, H. L. W. and A. Aly, "A Problem in Single Facility
Scheduling with Sequence Independent Change-Over Costs". 359
Rosenshine, M. and J. Evans, "Random Patrol Scheduling
Under Operational Constraints" . . . . . . . . . . 381
Shwimer, J., "Interaction Between Aggregate and Detailed
Scheduling in a Job Shop" - Abstract. . • . 391
Sidney, J. B., "An Extension of Moore's Due Date Algorithm". 393
Srinivasan, V. and G. 1. Thompson, "Solving Scheduling
Problems by Applying Cost Operators to Assignment
Models". . . . . . . . . 399
Turksen, 1. B. and R. Shankar, "Some Extensions of Akers-
Friedman Production Scheduling Problem". . . . 426
Zaloom, V., "On a Feasibility Approach to Optimal Schedules" 433
LIST OF PARTICIPANTS
Discussant of Also Author of Paper
Participant Paper by on Page No.
Ashour, Said Fisher 206
Baker, Kenneth R. Rau 201
Bennington, Gerald E. l.
Bradley, Gordon 224
Dessouky, Mohamed I. Srinivasan & Thompson
Dudek, Richard Bratley, Florian & Robillard 29
Elmaghraby, Salah E. Giffler, and Srinivasan & Thompson 244
Emmons, Hamilton Sidney • 278
Fisher, Marshall Elmaghraby & Ma1lik. 294
Florian, Michael Parker & Ashour 39,242
Fulcher, Doily
Ghare, P. M• • Bennington & McGinnis
Giffler, Bernard Turksen & Shankar. • • 44
Hodgson, Thorn J. Florian, Guerin & Bushell 56
Johnson, Gary.
Kapur, Kailash C. Rosenshine 324
Lawler, Eugene L. Murty 164
Mallik, Arup • Parker & Ashour. 244
Maxwell, William L. Giff1er, and Rau
Mitten, Loring G. 127
Murty, Katta • 143
Nevins, Arthur
Nuttle, Henry L.W. 359
Panwalker, Shrlkant 29
Parker, R. G. Florian, Guerin & Bushell. 206
Prabhakar, T. Wiest 69
Ratliff, Donald Bradley.
Rau, John Sidney. 167
Robillard, Pierre. Bradley. 242
Rosenshine, Matthew. Wiest 381
Rubin, David • • • Brat ley , Florian & Robillard
Salvador, Michael Rosenshine • • • 83
VIII
Discussant of Also Author of Paper
Participant Paper by on Page No.
Schrage, Linus Mitten & Tsou
Schultz, George M.
Selig, Seymour M.
Shwimer, Joel Emmons 391
Sidney, Jeffrey B. Mitten & Tsou 393
Smith, Milton Turksen & Shankar 29
Steinhoff, Harry W. 92
Swarc, W. Elmaghraby & Mallik
Taha, Hamdy Emmons, and Nuttle & Aly.
Thompson, Gerald L. Kapur, and Giffler. 399
Turksen, Ismail B. 426
Varley, Thomas
Wiest, Jerome Bennington & McGinnis 109
Zaloom, Victor Fisher. 319,433
A CRITIQUE OF PROJECT PLANNING WITH CONSTRAINED RESOURCES
G. E. Bennington and L. F. McGinnis
North Carolina State University, Raleigh, North Carolina, USA
ABSTRACT
This paper surveys the current research in resource
constrained project scheduling. Although CPM and PERT
have gained wide acceptance and use, the problem of limiting
resources used by each activity remains unsolved for
practical-sized problems.
The past research follows three basic approaches. The
problem may be formulated as an integer linear program and
solved by standard integer programming techniques. A
second approach is to directly employ some enumerative
scheme for constructing an optimal schedule. Finally, the
problem may be formulated in terms of minimaximal paths in
a disjunctive graph and solved by network flow methods and
implicit enumeration. The approaches will be compared and
the essential difficulties of the several methods will be
identified.
*
This paper was prepared for presentation at the Symposium on
Scheduling Theory and Its Applications on May 15-17, 1972 in
Raleigh, N. C. This research was partially sponsored by ONR
Contract N0014-70A0120002, ARO-D Contract DA-ARO-D-3l-l24-72-Gl06,
and the National Science Foundation Traineeship Program.
2
1. Introduction
Project planning models based on network structure first appeared in 1958
under the acronyms PERT [30] and CPM [25]. These models have been further devel
oped and refined, and have gained wide acceptance, primarily because of the
relative ease with which they can be applied to large problems. PERT and CPM
assume unlimited resources, which in many real problems is not a valid assumption.
Many researchers in the past decade have addressed the problem of dealing with
limited resources.
Project planning under resource constraints is one of a class of scheduling and
sequencing problems which have been described as "combinatorial." Following
Lawler [28], these are combinatorial problems because they deal with the opt·ima1
arrangement or ordering of activities. As the literature amply illustrates, these
particular combinatorial problems have proved to be frustrating to deal with, and
no general solution techniques of practical value have been developed.
There are several reasons why project planning under constrained resources has
been such a frustrating problem:
(1) the problem is an extension of the PERT/CPM problem,
which was readily solved through the theory of
network flows,
(2) the problem is not difficult to visualize or state, and
(3) without exception, every solution procedure proposed has
been computationally impractical, either because the model
grows too large, or because the solution procedure is too
lengthy, or both.
There are few versions of the constrained resources problem for which exact solu
tion methods are known and almost all published results rely on some form of
enumeration.
1.1 Problem Statement
=
The CPM problem can be represented on a graph G (N,P) where N, the set of
nodes, corresponds to the activities and P, the set of arcs, corresponds to the