Resource Allocation in Project Management

198 Pages·2005·11.32 MB·English

by  Professor Dr. Christoph Schwindt (auth.)

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IX,164 pages.2005.ISBN 3-540-25318-1
Christoph Schwindt
Resource Allocation
in Project Management
With 13 Figures
and 12 Tables
123
Professor Dr.Christoph Schwindt
Institut für Wirtschaftswissenschaft
TU Clausthal
Julius-Albert-Straße 2
38678 Clausthal-Zellerfeld
E-mail:[email protected]
Library ofCongress Control Number:2005926096
ISBN 3-540-25410-2 Springer Berlin Heidelberg New York
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Preface
This monograph grew out of my research in the ficld of resourcc-constraincd
project scheduling conducted from 1995 to 2004 during my work as teaching
assistant and assistant professor at the Institute for Economic Theory and
Operations Research of thc Univcrsity of Karlsruhe. The aim of the book is
to givc an introduction to quantitative concepts and methods for resource
allocation in project managcmcnt with an cmphasis on an ordcr-theoretic
framework allowing for a unifying treatment of various problem types. In order
to make the work accessible for general readers, the basic concepts nccded arc
rcviewed in introductory scctions of the book.
Many pcople have contributed to the outcome of this research. First and
foremost, I would like to express my deep appreciation to my supervisor Pro-
fessor Klaus Ncumann, who introduced me to the field and the community
of project schcduling. I have greatly benefited from his comprehensive scien-
tific knowlcdgc and expertise, his continuous encouragement, and his support.
During all these years, his departmcnt has bcen a stimulating and attractive
place for doing research and teaching in Operations Rcsearch.
Moreover, I would like to thank my formcr collcagucs for many fruitful
discussions on various research topics and their continuing interest in my
work. A major part of my rcsearch has been done in collaboration with the
colleagues of the Karlsruhe project scheduling group, Birger Franck, Cord-
Ulrich Fundeling, Karsten Gentner, Steffen Hagmaycr, Dr. Thomas Hartung,
Dr. Roland Heilmann, Christoph Mellentien, Dr. Hartwig Nubel, Dr. Thomas
Selle, PD Dr. Norbert Trautmann, and Professor Jiirgcn Zimmcrmann. Our
work has been greatly influenccd by the activities of a research unit on proj-
ect scheduling funded by the Deutsclle Forschungsgemcinschaft and involving
colleagucs from the universities of Bcrlin (Profcssor Rolf Mijhring), Bonn (Pro-
fessor Erwin Pcsch), Karlsruhe (Professor Klaus Ncumann), Kicl (Professor
Andreas Drexl), and Osnabriick (Professor Peter Brucker). Numerous joint
workshops on project scheduling and the "cooperative-competitive" spirit in
this group havc been a great incentive to work even harder.
viii Preface
Finally, I grateful acknowledge the help of several peoplc in preparing the
manuscript of this monograph: Klaus Neumann for many valuable comments
on different versions of the manuscript, Gerhard Grill for carefully proof-
reading and improving the English wording of the manuscript, Frederik Stork
for pointing me to state-of-the-art contributions in convex programming, and
Jiirgcn Zimmermann for making experimental results on rcsourcc levelling
problems availablc to me. Of course thc faults and dcficicncics rcmaining are
entircly my own.
Clausthal-Zellerfeld, February 2005 Christoph Schwindt
Contents
Introduction ................................................... 1
1 Models and Basic Concepts ................................ 7
1.1 Tcrnporal Constraints .................................... 7
1.1.1 Time-Feasible Schedules ............................ 7
1.1.2 Project Networks .................................. 9
1.1.3 Temporal Scheduling Computations ................. 11
1.2 Renewablc-Resource Constraints .......................... 16
1.2.1 Rcsourcc-Fcasiblc Schedules ........................ 16
1.2.2 Forbidden Sets and Delaying Alternatives ............ 19
1.2.3 Breaking up Forbidden Sets ........................ 21
1.2.4 Consistency Tests ................................. 23
1.3 Cumulative-Resource Constraints .......................... 28
1.3.1 Resource-Feasible Schedules ........................ 30
1.3.2 Forbidden Sets and Delaying Alternativcs ............ 32
1.3.3 Brcaking up Forbidden Sets ........................ 35
1.3.4 Consistency Tests ................................. 36
2 Relations. Schedules. and Objective Functions ............. 39
2.1 Resource Constraints and Feasible Relations ................ 39
2.1.1 Renewablc-Resource Constraints .................... 40
2.1.2 Cumulative-Resource Constraints .................... 46
2.2 A Classification of Schcdulcs .............................. 52
2.2.1 Global and Local Extreme Points of the Feasible Region 52
2.2.2 Vcrtices of Relation Polytopes ...................... 53
2.3 Objectivc Functions .....................................5 5
2.3.1 Regular and Convexifiable Objective Functions ........ 56
2.3.2 Locally Regular and Locally Concave Objective
Functions ........................................ 60
2.3.3 Preorder-Decreasing Objective Functions ............. 64
x Contents
3 Relaxation-Based Algorithms ..............................6 5
3.1 Regular Objcctivc Functions ..............................6 6
3.1.1 Enumeration Scheme .............................. 66
3.1.2 Solving the Relaxations ............................ 69
3.1.3 Branch-and-Bound ................................ 72
3.1.4 Additional Notes and References .................... 76
3.2 Corwexifiablc Objective Functions ......................... 82
3.2.1 Enumeration Scheme .............................. 83
3.2.2 Solving thc Rclaxations: Thc Primal Approach ........ 85
3.2.3 Solving the Relaxations: The Dual Approach .......... 94
3.2.4 Branch-and-Bound ................................ 97
3.2.5 Additional Notes and References .................... 99
4 Constructive Algorithms ................................... 107
4.1 Schedule-Generation Schcme ..............................1 09
4.2 Local Scarch ............................................ 115
4.3 Additional Notcs and Rcfererlccs .......................... 118
5 Supplements.. ............................................. 123
5.1 Break Calendars .........................................1 24
5.2 Scquencc-Dcpcndent Changeover Times ....................1 28
5.3 Alternative Execution Modes for Activities .................1 31
5.4 Continuous Cumulative Resources ......................... 135
6 Applications ..............................................1.4 1
6.1 Make-to-Order Production Scheduling ......................1 42
6.2 Small-Batch Production Planning in Manufacturing Industries 147
6.3 Production Scheduling in thc Proccss Industrics .............1 49
6.4 Evaluation of Investment Projects .........................1 55
6.5 Coping with Uncertainty ................................. 160
Conclusions ....................................................1 65
References ....................................................1.6 7
List of Symbols ...............................................1.8 1
Index .......................................................... 185
Introduction
Project management and resource allocation. A project is a major
one-time undertaking dedicated to some well-defined objective and involving
considerable money, personnel, and equipment. It is usually initiated cithcr by
some need of the parent organization or by a customer request. The life cycle
of a project can bc structurcd into five consecutivc phases involving specific
managerial tasks (cf. Klcin 2000, Section 1.2). Starting with some proposal,
sevcral preliminary studies such as a feasibility study, an economic analysis, or
a risk analysis are conducted in the project conception phase in order to decide
whcthcr or not a corresponding project will be performed. In the project defi-
nition phase, the objectives of the project are formulated, the type of project
organization is selected, resourccs are assigned to the project, and different
tasks with associated milestones are identified. Subsequently, the project plan-
ning phase at first decomposes each task into precedence-relatcd activities by
means of a structural analysis of the project. The time and resource estima-
tions then provide the duration and resource requirements for each activity as
well as temporal constraints between activities that are connected by prece-
dence relationships. The result of the structural analysis and the time and
resource estimations is the representation of the project as a network mod-
elling the activitics and thc prescribed prccedence relationships among them.
Next, the temporal scheduling of the project provides the earliest and latest
start times as well as thc slack times of the activitics, limitations with respect
to resourcc availability yet being disregarded. The last and most complcx is-
sue of project planning consists in allocating the scarcc resources over time
to the execution of the activities. During the project execution phase, the im-
plementation of the project is controlled by monitoring the project progress
against the schedule which has been established in thc projcct planning phase.
In case of significant deviations from schedulc, the resource allocation has to
be performed again. Thc final project termination phase evaluates and docu-
ments the project after its complction to facilitate thc managcment of futurc
projects.