PROJECT SCHEDULINGA Research Handbook

INTERNATIONAL SERIES INOPERATIONS RESEARCH & MANAGEMENT SCIENCEFrederick S. Hillier, Series Editor Stanford University

Gal, T. & Greenberg, H. / ADVANCES IN SENSITIVITY ANALYSIS ANDPARAMETRIC PROGRAMMING

Prabhu, N.U. / FOUNDATIONS OF QUEUEING THEORY

Fang, S.-C., Rajasekera, J.R. & Tsao, H.-S.J. / ENTROPY OPTIMIZATIONAND MATHEMATICAL PROGRAMMING

Yu, G. / OPERATIONS RESEARCH IN THE AIRLINE INDUSTRYHo, T.-H. & Tang, C. S. / PRODUCT VARIETY MANAGEMENTEl-Taha, M. & Stidham , S. / SAMPLE-PATH ANALYSIS OF QUEUEING SYSTEMSMiettinen, K. M. / NONLINEAR MULTIOBJECTIVE OPTIMIZATIONChao, H. & Huntington, H. G. / DESIGNING COMPETITIVE ELECTRICITY MARKETSWeglarz, J. / PROJECT SCHEDULING: Recent Models, Algorithms & ApplicationsSahin, I. & Polatoglu, H. / QUALITY, WARRANTY AND PREVENTIVE MAINTENANCETavares, L. V. / ADVANCED MODELS FOR PROJECT MANAGEMENTTayur, S., Ganeshan, R. & Magazine, M. / QUANTITATIVE MODELING FOR SUPPLY

CHAIN MANAGEMENTWeyant, J./ ENERGY AND ENVIRONMENTAL POLICY MODELINGShanthikumar, J.G. & Sumita, U. /APPLIED PROBABILITY AND STOCHASTIC PROCESSESLiu, B. & Esogbue, A.O. / DECISION CRITERIA AND OPTIMAL INVENTORY PROCESSESGal, T., Stewart, T.J., Hanne, T./ MULTICRITERIA DECISION MAKING: Advances in MCDM

Models, Algorithms, Theory, and ApplicationsFox, B. L./ STRATEGIES FOR QUASI-MONTE CARLOHall, R.W. / HANDBOOK OF TRANSPORTATION SCIENCEGrassman, W.K./ COMPUTATIONAL PROBABILITYPomerol, J-C. & Barba-Romero, S. / MULTICRITERION DECISION IN MANAGEMENTAxsäter, S. / INVENTORY CONTROLWolkowicz, H., Saigal, R., Vandenberghe, L./ HANDBOOK OF SEMI-DEFINITE

PROGRAMMING: Theory, Algorithms, and ApplicationsHobbs, B. F. & Meier, P. / ENERGY DECISIONS AND THE ENVIRONMENT: A Guide

to the Use of Multicriteria MethodsDar-El, E./ HUMAN LEARNING: From Learning Curves to Learning OrganizationsArmstrong, J. S./ PRINCIPLES OF FORECASTING: A Handbook for Researchers and

PractitionersBalsamo, S., Personé, V., Onvural, R./ ANALYSIS OF QUEUEING NETWORKS WITH BLOCK1NGBouyssou, D. et al/ EVALUATION AND DECISION MODELS: A Critical PerspectiveHanne, T./ INTELLIGENT STRATEGIES FOR META MULTIPLE CRITERIA DECISION MAKINGSaaty,T. & Vargas, L./ MODELS, METHODS, CONCEPTS & APPLICATIONS OF THE ANALYTIC

HIERARCHY PROCESSChatterjee, K. & Samuelson, W./ GAME THEORY AND BUSINESS APPLICATIONSHobbs, B. et al/ THE NEXT GENERATION OF ELECTRIC POWER UNIT COMMITMENT MODELSVanderbei, R.J./ LINEAR PROGRAMMING: Foundations and Extensions, 2nd Ed.Kimms, A./ MATHEMATICAL PROGRAMMING AND FINANCIAL OBJECTIVES FOR

SCHEDULING PROJECTSBaptiste, P., Le Pape, C. & Nuijten, W./ CONSTRAINT-BASED SCHEDULINGFeinberg, E. & Shwartz, A./ HANDBOOK OF MARKOV DECISION PROCESSES: Methods

and ApplicationsRamík, J. & Vlach, M. / GENERALIZED CONCAVITY IN FUZZY OPTIMIZATION

AND DECISION ANALYSISSong, J. & Yao, D. / SUPPLY CHAIN STRUCTURES: Coordination, Information and

OptimizationKozan, E. & Ohuchi, A./ OPERATIONS RESEARCH/ MANAGEMENT SCIENCE AT WORKBouyssou et al/ AIDING DECISIONS WITH MULTIPLE CRITERIA: Essays in

Honor of Bernard RoyCox, Louis Anthony, Jr./ RISK ANALYSIS: Foundations, Models and MethodsDror, M., L’Ecuyer, P. & Szidarovszky, F. / MODELING UNCERTAINTY: An Examination

of Stochastic Theory, Methods, and ApplicationsDokuchaev, N./ DYNAMIC PORTFOLIO STRATEGIES: Quantitative Methods and Empirical Rules

for Incomplete InformationSarker, R., Mohammadian, M. & Yao, X./ EVOLUTIONARY OPTIMIZATION

PROJECT SCHEDULINGA Research Handbook

by

Erik L. DemeulemeesterWilly S. Herroelen

Department of Applied EconomicsKatholieke Universiteit, Leuven

Belgium

KLUWER ACADEMIC PUBLISHERSNEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: 0-306-48142-1

Print ISBN: 1-4020-7051-9

©2002 Kluwer Academic PublishersNew York, Boston, Dordrecht, London, Moscow

Print ©2002 Kluwer Academic Publishers

All rights reserved

No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,mechanical, recording, or otherwise, without written consent from the Publisher

Created in the United States of America

Visit Kluwer Online at: http://kluweronline.comand Kluwer's eBookstore at: http://ebooks.kluweronline.com

Dordrecht

Contents

ContentsPreface

Chapter 1. Scope and relevance of project scheduling1. Attributes of a project2. The essence of project management3. The project management process

3.1 The concept phase3.2 The definition phase

3.2.1 Project objectives3.2.2 Project scope3.2.3 Project strategy

3.3 The planning phase3.4 The scheduling phase3.5 The control phase3.6 The termination phase

4. Exercises

Chapter 2. The project scheduling process1. Activity networks

1.1 Work breakdown structure (WBS) andorganisational breakdown structure (OBS)

1.2 Activities and events1.2.1 Activity-on-arc representation (AoA)

1.2.1.1 Minimising the number of dummy activities1.2.1.1.1 Computational complexity1.2.1.1.2 of the minimum

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dummy activity problem1.2.1.2 Characterising a network by its

reduction complexity1.2.1.2.1 The reduction complexity1.2.1.2.2 Constructing the complexity graph

1.2.1.2.2.1 Constructing the dominator trees1.2.1.2.2.2 Constructing the complexity graph1.2.1.2.2.3 The minimum node cover of C(G)

1.2.1.3 Cuts in l,n-dags1.2.2 Activity-on-node representation (AoN)1.2.3 Generalised precedence relations

1.2.3.1 Minimal time-lags1.2.3.1.1 Finish-start relation1.2.3.1.2 Start-start relation1.2.3.1.3 Finish-finish relation1.2.3.1.4 Start-finish relation1.2.3.1.5 Combined relations

1.2.3.2 Maximal time-lags1.2.3.3 Cycles

1.2.4 Transforming an AoN network into an AoAnetwork with minimal reduction complexity

2. Resources2.1 Basic resource categories2.2 Other resource categories

2.2.1 Partially renewable resources2.2.2 Resource divisibility and preemption2.2.3 Dedicated resources2.2.4 Cumulative resources2.2.5 Spatial resources

3. Estimating task times3.1 Deterministic task durations

3.1.1 Single-time estimates3.1.2 Execution scenarios and trade-offs

3.2 Dealing with uncertainty3.2.1 Stochastic activity durations: the PERT model3.2.2 Stochastic activity durations: other forms of DF3.2.3 Fuzzy activity durations

3.2.3.1 Fuzzy sets and fuzzy numbers3.2.3.2 Creating a membership function for

the activity duration4. Specifying the time-lags

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5. Creating a feasible base schedule5.1 Project scheduling objectives

5.1.1 Time-based objectives5.1.2 Resource-based objectives5.1.3 Financial objectives5.1.4 Quality oriented objectives5.1.5 Regular and nonregular objectives5.1.6 Multiple objectives

5.2 Multiple project scheduling6. Exercises

Chapter 3. Classification of project scheduling problems1. Classification of project scheduling problems

1.1 Field resource characteristics1.2 Field activity characteristics1.3 Field performance measures

2. Use of the classification scheme3. Exercises

Chapter 4. Temporal analysis: the basic deterministic case1. Temporal analysis in networks with strict finish-start

precedence relations1.1 Critical path analysis in AoN networks:

problem1.1.1 Forward and backward pass calculations1.1.2 Activity float

1.1.2.1 Total float1.1.2.2 Free float1.1.2.3 Safety float

1.2 Critical path analysis in AoA networks:problem1.2.1 Standard forward and backward pass calculations1.2.2 Activity floats

1.2.2.1 Total float1.2.2.2 Free float1.2.2.3 Safety float

1.2.3 The dependence of activity floats onproject representation

1.2.4 Multiple critical paths and k longest paths1.3 A flow network interpretation of the determination of the

critical path

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2. Temporal analysis in networks with generalisedprecedence relations2.1 GPRs, in standardised form2.2 Computing the earliest start schedule2.3 Activity criticality in activity networks with GPRs

2.3.1 Cycles and tree structures2.3.2 Types of criticality

2.4 Activity flexibility in activity networks with GPRs2.5 Activity floats in activity networks with GPRs

3. Exercises

Chapter 5. Temporal analysis: advanced topics1. Project scheduling with start-time dependent costs

1.1 Integer programming formulations1.2 Reduction to a minimum cut problem

2. Temporal analysis under the max-npv objective2.1 Strict finish-start precedence relations with zero

time-lags: problem cpm,2.1.1 The deterministic max-npv problem

2.1.1.1 Problem formulation2.1.1.2 Transformation into a linear programming

problem2.1.1.3 Characteristics of the optimal solution

2.1.2 An exact recursive procedure for themax-npv problem

2.1.2.1 A numerical example2.1.2.2 Computational experience

2.1.2.2.1 Problem sets I and II: Computationalexperience for the PSPLIB and RanGeninstances

2.1.2.2.2 Problem set III: Computational experiencefor the 1,210 RanGen instances

2.1.2.3 A forward-backward recursive searchprocedure

2.1.3 A steepest ascent procedure2.1.3.1 Finding the steepest ascent direction2.1.3.2 Ascending to the next vertex2.1.3.3 The steepest ascent algorithm2.1.3.4 Numerical example2.1.3.5 Computational results

2.1.4 The recursive search algorithm revised

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2.2 Time dependent cash flows2.2.1 The problem

2.2.1.1 Problem formulation2.2.1.2 An exact recursive procedure

2.2.1.2.1 Description of the algorithm2.2.1.2.2 Computational experience

2.3 Generalised precedence relations:problem2.3.1 Problem formulation2.3.2 Transformation into a linear programming problem2.3.3 The adapted steepest ascent procedure

2.3.3.1 Numerical example2.3.3.2 Computational experience

2.3.4 The modified recursive procedure2.3.5 The adapted combined procedure2.3.6 Computational experience

3. Minimising weighted earliness-tardiness penalty costs3.1 Strict finish-start precedence relations:

problem cpm|early/tardy3.1.1 The weighted earliness-tardiness project scheduling

problem3.1.2 An exact recursive search procedure

3.1.2.1 Pseudocode3.1.2.2 Numerical example3.1.2.3 Computational experience

3.2 Maximising npv with progress payments4. Exercises

Chapter 6. The resource-constrained project scheduling problem1. proof2. Exact procedures

2.1 Linear programming based approaches2.1.1 Conceptual formulation2.1.2 The formulation by Pritsker et al. (1969)2.1.3 The formulation by Kaplan (1988)2.1.4 The formulation by Klein (2000)2.1.5 The formulation by Alvarez-Valdés and

Tamarit(1993)2.1.6 The formulation by Mingozzi et al. (1998)

2.2 Branch-and-bound procedures2.2.1 Precedence tree2.2.2 Extension alternatives

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2.2.3 Minimal delaying alternatives2.2.4 Minimal forbidden sets2.2.5 Schedule schemes

2.2.5.1 The basic version2.2.5.2 The binary version

2.2.6 Float splitting2.2.6.1 Heads and tails2.2.6.2 The n-machine problem2.2.6.3 Jackson preemptive schedule2.2.6.4 The branching scheme

2.2.7 Binding precedence relations2.3 The use of dominance rules

3. Heuristic procedures3.1 Types of schedules3.2 Constructive heuristics

3.2.1 Scheduling schemes3.2.1.1 The serial scheduling scheme3.2.1.2 The parallel scheduling scheme3.2.1.3 Backward planning3.2.1.4 Bidirectional planning

3.2.2 Priority rules3.2.2.1 Activity based priority rules3.2.2.2 Network based priority rules3.2.2.3 Critical path based priority rules3.2.2.4 Resource based priority rules3.2.2.5 Composite priority rules

3.2.3 Multi-pass methods3.2.3.1 Multi-scheduling scheme methods3.2.3.2 Multi-priority rule methods3.2.3.3 Sampling methods

3.3 Improvement heuristics3.3.1 Neighbourhood

3.3.1.1 Representation schemes3.3.1.1.1 Priority list representation3.3.1.1.2 Priority rule representation3.3.1.1.3 Random key representation3.3.1.1.4 Shift vector representation3.3.1.1.5 Schedule scheme representation

3.3.1.2 Neighbourhood operators3.3.1.2.1 Unary neighbourhood operators

3.3.1.2.1.1 Pairwise interchange3.3.1.2.1.2 The shift operator

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3.3.1.2.1.3 The change operator3.3.1.2.2 Binary neighbourhood operators

3.3.1.2.2.1 One point crossover3.3.1.2.2.2 Two-point crossover3.3.1.2.2.3 Uniform crossover

3.3.2 Descent approaches3.3.2.1 Steepest descent3.3.2.2 Fastest descent3.3.2.3 Iterated descent

3.3.3 Metaheuristic approaches3.3.3.1 Tabu search3.3.3.2 Simulated annealing3.3.3.3 Genetic algorithms

3.3.4 Other approaches3.3.4.1 Truncated branch-and-bound methods3.3.4.2 Disjunctive arc based methods3.3.4.3 Integer programming based methods3.3.4.4 Block structure based methods

4. Lower bound calculations4.1 Simple lower bound calculations

4.1.1 Critical path based lower bounds4.1.1.1 Critical path lower bound4.1.1.2 Critical sequence lower bound4.1.1.3 Extended critical sequence lower bound

4.1.2 Resource based lower bounds4.1.2.1 Basic resource based lower bound4.1.2.2 Extended resource based lower bound

4.1.3 Combined lower bounds4.1.3.1 Zaloom’s lower bound4.1.3.2 The n-machine lower bound4.1.3.3 The weighted node packing lower bound

4.1.3.3.1 Basic logic4.1.3.3.2 Improvements of the basic version4.1.3.3.3 The n-machine based version

4.1.3.4 The generalised weighted node packinglower bound

4.1.4 The subproject based lower bound4.2 Destructive improvement

4.2.1 Reduction by core times4.2.2 Reduction by precedence

5. Exercises

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Chapter 7. Resource-constrained project scheduling:advanced topics

1. The generalised resource-constrained projectscheduling problem1.1 The precedence diagramming case

1.1.1 The search tree1.1.2 Node fathoming rules

1.2 Generalised precedence relations1.2.1 The search tree1.2.2 Node fathoming rules

1.3 Computational experience2. The preemptive resource-constrained project scheduling

problem2.1 Problem formulation2.2 A branch-and-bound algorithm for the PRCPSP

2.2.1 Description of the branch-and-bound logic2.2.2 Node fathoming rules2.2.3 The algorithm2.2.4 A numerical example for the PRCPSP2.2.5 Computational experience for the PRCPSP

2.2.5.1 Constant resource availabilities2.2.5.2 Variable resource availabilities

3. The resource levelling problem3.1 Problem formulation3.2 The Burgess and Killebrew levelling procedure3.3 Branch-and-bound

4. The resource availability cost problem4.1 Problem formulation4.2 Solution methodology4.3 Search strategy

4.3.1 General strategy4.3.2 Graphical example4.3.3 Solution procedure4.3.4 A numerical example for the RACP4.3.5 Computational experience

4.3.5.1 The adapted Patterson problem set4.3.5.2 The influence of the number of resource types

5. The resource-constrained project scheduling problemwith discounted cash flows5.1 The deterministic RCPSPDC

5.1.1 Problem formulation5.1.2 A branch-and-bound algorithm for the RCPSPDC

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5.1.2.1 Description of the branch-and-bound logic5.1.2.2 Node fathoming rule5.1.2.3 The algorithm5.1.2.4 A numerical example for the RCPSPDC

5.1.3 Computational experience for the RCPSPDC5.2 The deterministic RCPSPDC-GPR

5.2.1 Lagrangean relaxation of the resource constraints5.2.2 Branch-and-bound

6. The resource-constrained project scheduling problem under theearliness/tardiness objective6.1 Problem formulation6.2 A branch-and-bound algorithm for the RCPSPWET

6.2.1 Description of the branch-and-bound logic6.2.2 A numerical example for the RCPSPWET

6.3 Computational experience for the RCPSPWET7. Exercises

Chapter 8. Project scheduling with multiple activity executionmodes

1. Time/cost trade-off problems1.1 Continuous time/cost trade-off problems

1.1.1 Linear cost-duration functions: problem

1.1.1.1 Problem formulation1.1.1.2 Solution procedures

1.1.1.2.1 The Fulkerson/Kelley flow algorithm1.1.1.2.2 Numerical example

1.1.1.3 Algorithm refinements and extensions1.1.2 Other continuous cost-duration functions

1.1.2.1 Convex cost-duration functions:problem

1.1.2.2 Concave cost-duration functions:problem

1.1.2.2.1 Piecewise-linear approximation1.1.2.2.2 Branch-and-bound

1.2 Discrete cost-duration functions1.2.1 Problem

1.2.1.1 Integer programming1.2.1.2 The dynamic programming formulation

of Hindelang and Muth1.2.2 Problem1.2.3 Problem

1.2.3.1 Exact network reduction procedures

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1.2.3.1.1 Series/parallel networks1.2.3.1.2 Network reduction

1.2.3.1.2.1 Minimising the number of activitiesto be fixed

1.2.3.1.2.2 Minimising the expected number ofleaves of the resulting fixing tree

1.2.3.1.2.3 Computational results1.2.3.2 Exact horizon-varying procedure

1.2.3.2.1 The branch-and-bound algorithm1.2.3.2.2 Computing the lower bound1.2.3.2.3 The horizon-varying algorithm1.2.3.2.4 An illustrative example1.2.3.2.5 Computational results

1.2.4 Approximation algorithms2. The time/cost trade-off problem with generalised

precedence constraints2.1 Problem2.2 Problem2.3 Problem

3. The time/resource trade-off problem3.1 Definition of problem3.2 Solution procedures

3.2.1 A dedicated branch-and-bound procedure3.2.1.1 The search process3.2.1.2 Dominance rules

3.2.1.2.1 Dominance rule 1: redundantactivity-mode combinations

3.2.1.2.2 Dominance rule 2: single-modeleft-shift dominance rule

3.2.1.2.3 Dominance rule 3: cutset dominance rule3.2.1.2.4 Dominance rule 4: multi-mode left-shift

rule3.2.1.3 Bounding rules3.2.1.4 Computational experience

3.2.2 Local search methods3.2.2.1 Truncated complete enumeration3.2.2.2 Improvement procedures

3.2.2.2.1 Descent methods3.2.2.2.2 A random procedure3.2.2.2.3 Tabu search

3.2.2.2.3.1 Neighbourhood3.2.2.2.3.2 Short-term recency-based memory

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admissibility3.2.2.2.3.4 Termination criteria3.2.2.2.3.5 Medium and long-term

frequency-based memory3.2.2.2.3.5.1 Frequency information3.2.2.2.3.5.2 Diversification3.2.2.2.3.5.3 Intensification3.2.2.2.3.5.4 Combined diversification and

intensification3.2.2.2.3.5.5 Phases

3.2.2.3 Computational experience4. The standard multi-mode problem

4.1 Definition of problem4.2 Exact algorithms

4.2.1 The precedence tree4.2.2 Mode and delay alternatives4.2.3 Mode and extension alternatives4.2.4 Dominance rules

4.2.4.1 The use of time windows4.2.4.2 The use of preprocessing4.2.4.3 The local left-shift rule4.2.4.4 The multi-mode left-shift rule4.2.4.5 The order swap rule4.2.4.6 Cutset rule4.2.4.7 Immediate selection4.2.4.8 Precedence tree rule

4.2.5 Computational results4.3 Heuristic procedures

4.3.1 A multi-mode genetic algorithm4.3.1.1 The crossover operator4.3.1.2 The mutation operator4.3.1.3 The selection operator4.3.1.4 Computational results

5. The multi-mode problem with generalisedprecedence relations5.1 A branch-and-bound procedure

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5.2 Local search5.2.1 Preprocessing5.2.2 Determining a feasible initial solution5.2.3 Infeasible moves5.2.4 Lower bounds

5.3 Computational experience6. The mode-identity resource-constrained project

scheduling problem7. Multiple crashable modes

7.1 Problem definition7.2 Exact solution procedures7.3 A heuristic procedure

8. Exercises

Chapter 9. Stochastic project scheduling1. Stochastic scheduling in the absence of resource constraints

1.1 Characterising the distribution function ofthe project duration

1.2 Exact procedures for computing the projectduration distribution: problem

1.2.1 The case of series-parallel networks1.2.2 Network decomposition using node reductions

1.3 Bounding the project duration distribution1.3.1 The bounds of Kleindorfer1.3.2 The upper bound of Dodin1.3.3 The bounds of Spelde1.3.4 The Ludwig et al. experiment

1.4 Monte Carlo sampling1.4.1 Crude Monte Carlo sampling1.4.2 Improved techniques

1.5 Path criticality and activity criticality1.5.1 The path criticality index1.5.2 The activity criticality index1.5.3 The significance index1.5.4 The cruciality index1.5.5 Sensitivity problems in probabilistic networks

1.5.5.1 Sensitivity of mean-mean1.5.5.2 Sensitivity of variance-mean1.5.5.3 Sensitivity of variance-variance1.5.5.4 Sensitivity of mean-variance

2. Optimal activity delays in the absence of resource constraints

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3. Stochastic scheduling with resource constraints3.1 The stochastic RCPSP

3.1.1 The stochastic RCPSP as a multi-stagedecision process

3.1.2 Preselective policies3.1.2.1 Priority policies3.1.2.2 Early start (ES) policies3.1.2.3 Preselective (PRS) policies3.1.2.4 Linear preselective (LIN) policies3.1.2.5 Activity based (ABP) priority policies

3.1.3 Optimal schedules3.1.4 Branch-and-bound algorithms

3.1.4.1 Branching schemes3.1.4.1.1 The forbidden set branching scheme3.1.4.1.2 The precedence tree branching scheme

3.1.4.2 Initial upper bound3.1.4.3 Lower bound calculation3.1.4.4 Dominance rules

3.1.4.4.1 ES policies3.1.4.4.2 Preselective policies3.1.4.4.3 Linear preselective policies3.1.4.4.4 Activity based priority policies

3.1.4.5 Computational results3.1.5 Heuristic models for the stochastic RCPSP

3.1.5.1 The Golenko-Ginsburg/Gonik procedure3.1.5.2 Tabu search

4. The stochastic discrete time/cost trade-off problem4.1 The stochastic programming approach of Wollmer4.2 Stochastic branch-and-bound

5. Multi-mode trade-off problems in stochastic networks6. Project scheduling under fuzziness

6.1 The fuzzy resource-constrained projectscheduling problem

6.1.1 The weak comparison rule6.1.2 The strong comparison rule6.1.3 Simulated annealing6.1.4 The fuzzy multi-mode problem with

generalised precedence relations7. Exercises

Chapter 10. Robust and reactive scheduling1. The critical chain/buffer management approach

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1.1 The fundamentals of critical chain scheduling1.1.1 Basic methodology1.1.2 Multi-projects

1.2 The merits and pitfalls of CC/BM1.2.1 Project duration as a performance measure

1.2.1.1 Makespan as the number one objective1.2.1.2 Minimising work-in-progress (WIP)1.2.1.3 Financial objective functions1.2.1.4 Other objectives and models

1.2.2 Uncertainty and time estimation1.2.3 Resources and the elimination of multi-tasking1.2.4 The critical chain

1.2.4.1 Creating the baseline schedule1.2.4.2 Baseline scheduling and WIP reduction

1.2.5 Buffers1.2.5.1 Project buffers and feeding buffers

1.2.5.1.1 Buffer size1.2.5.1.2 Inserting the feeding buffers1.2.5.1.3 Roadrunner mentality and the

projected schedule1.2.5.1.4 The use of buffers as a

proactive protection mechanism1.2.6 Rescheduling and stability1.2.7 Multiple projects: strategic resource buffers

1.3 Computational experiments: validating theCC/BM mechanics1.3.1 Factorial experiment1.3.2 Estimating the project duration1.3.3 Estimating the project duration1.3.4 Activity crashing and buffer management1.3.5 Resource conflicts on schedule updates

1.4 Conclusions2. Robust scheduling and schedule repair

2.1 Resource flow networks2.2 Inserting new activities2.3 Constructing robust baseline schedules

3. Exercises

ReferencesName indexSubject index

PREFACE

Managing projects dates back at least 4,500 years. The builders of thepyramids in Egypt and the Maya temples in Central America are often citedas the world’s first project managers. They had no computers nor planningsoftware to assist them, no PERT (Program Evaluation and ReviewTechnique) nor CPM (Critical Path Method), which date back to the end ofthe fifties (see Kelley and Walker (1959) and Malcolm et al. (1959)). Yet,they managed exceptionally complex projects, using the simplest of tools.Nowadays projects, sets of activities which have a defined start point and adefined end state and which pursue a defined goal and use a defined set ofresources, come in many and various forms. The Manhattan project whichcreated the first atom bomb, the Apollo moon program, the construction ofthe Channel tunnel, the design of the Airbus, the development of newproducts, the construction of large office buildings, the relocation of afactory, the installation of a new information system, as well as thedevelopment of a marketing plan are all well-known examples of projects.

The use of project management, which can be broadly defined as theprocess of managing, allocating and timing resources to achieve givenobjectives in an efficient and expedient manner (Badiru (1991)), continues togrow rapidly. Interest in the field is booming. Recent estimates indicateproject management to be an $850 million industry that is expected to growby as much as 20 percent per year (Bounds (1998)). The ProjectManagement Institute (PMI), the professional association of projectmanagers, increased its world-wide membership population to over 70,000.World-wide market sales for the popular project management software

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packages easily run in the hundreds of millions of dollars. The need forefficient and effective project management is widely recognized. In its 1993report, the World Bank (World Bank Report (1993)), which has loaned morethan $300 billion to developing countries over the last fifty years, providesevidence for the need of integrated project management by recognizing thatthere has been a dramatic rise in the number of failed projects around theworld and by identifying the lack of an integrated project managementapproach as one of the major causes of failure. More than $250 billion isspent in the United States each year on approximately 175,000 informationtechnology projects. Only 26 percent of these projects are completed on timeand within budget (Bounds (1998)). Project management has indeed becomea hot topic.

The field of project management theory and practice has takentremendous strides forward in the past few decades. The capabilities ofproject management software packages have been considerably expandedover the past few years (Kolisch (1999), Maroto et al. (1998)). Books onproject management find their way to the popular management literature,bringing the recent message that crucial insights gained in the field ofproduction management can be successfully transferred to the managementof projects (Goldratt (1997), Leach (2000), Newbold (1998)). The scope ofinterest as well as the power of analysis have surpassed the originallyenvisaged temporal considerations involved in computing the so-calledcritical path(s). The conceptual problems posed and the solution proceduresdeveloped over the years for their resolution transcend the projectmanagement area. The management of the often counterintuitive interplaybetween activity durations, precedence relations, resource requirements andavailabilities is now widely recognized to lie at the very heart of modern leadtime management. Researchers continue to report considerable progress intackling the numerous complex problems created by this interplay (see e.g.Weglarz (1998)). The literature on project scheduling, the process of layingout the activities of the project in the time order in which they have to beperformed, is actually booming. The link between the fields of projectscheduling and machine scheduling has been and continues to be exploredand tightened.

In writing this book, we had a number of objectives in mind. First, toprovide a unified scheme for classifying the numerous project schedulingproblems occurring in practice and studied in the literature; second, toprovide a unified and up-to-date treatment of the state-of-the-art proceduresdeveloped for their solution; and third, to alert the reader to variousimportant problems that are still in need of considerable research effort. Assuch, this book should differ from other project scheduling books in its use

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of an innovative unified resource scheduling classification scheme, and aunified treatment of both exact and heuristic solution procedures.

The audience for which this book has been written includes those whoare professionally concerned with a fundamental understanding of projectscheduling which goes deeper than what can be distilled from the majority ofwidely available practice-oriented project management books. They includestudents at the advanced undergraduate and graduate levels in the curriculaof operations management, operations research, management science,quantitative methods in business administration, industrial engineering andengineering management, construction engineering, systems engineering andmanagement informatics. The book should also be appealing to Ph.D.students and researchers in the field. Last but not least, we hope the book tofind its way to the shelf of the sophisticated practitioner, project managerand management consultant.

The subject matter of this book has been divided into four parts. The firstpart consists of three chapters. Chapter 1 intends to clarify the scope andrelevance of project scheduling. It provides an overview of projectmanagement concepts. The reader is made familiar with the definition of aproject and its attributes, the project life cycle and the nature of the projectmanagement process, encompassing the basic managerial functions ofplanning, scheduling and control. Chapter 2 further elaborates on the natureof project scheduling. The notation and terminology of the network modelsused in the project management process are introduced. The functions ofplanning, scheduling and control as well as the tools, techniques andperformance measures involved in them are studied in sufficient detail.Chapter 3 then introduces the unified scheme that will be used in subsequentchapters for the identification and classification of the project schedulingproblems studied in this book.

Part II focuses on the time analysis of project networks. Morespecifically, Chapter 4 deals with the issues involved in the computation ofthe critical path(s) and the analysis of the resulting activity slack values. Adistinction is made between the base case of the zero-lag finish-startprecedence relations used in the basic PERT and CPM models and othermore general types of precedence relations involving minimal as well asmaximal time-lags. Chapter 5 concentrates on more advanced time analysisproblems associated with the use of more advanced performance measuressuch as the problem of maximizing the net present value of projects, theoptimisation problems resulting from the use of earliness/tardinessperformance measures and the use of multiobjective functions.

Part III carries the discussion further into the crucial topic of schedulingunder scarce resources. The basic resource-constrained project schedulingproblem forms the subject matter of Chapter 6. Both exact and heuristic

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methods for scheduling project activities subject to zero-lag finish-startprecedence relations as well as the limited availability of the renewableresources in order to minimize the project duration are discussed. Theconsiderable progress made in solving this fundamental project schedulingproblem over the past few years paved the way for the development ofefficient and effective exact and heuristic procedures for solving moreadvanced and more realistic project scheduling problems. Chapter 7 dealswith resource-constrained project scheduling with precedence diagrammingand generalized precedence relations, with activity preemption, and withresource leveling and resource availability cost problems. Also the netpresent value and earliness/tardiness objectives are considered whenresources are introduced into the project scheduling problem. Multimodeproblems, in which various possible execution modes are specified for anactivity, are the subject of Chapter 8. Here the reader will encounter anumber of intriguing and complex issues involved in solving time/cost andtime/resource trade-off problems, problems with so-called partiallyrenewable resources and multi-mode problems involving time/cost,time/resource as well as resource/resource trade-offs.

Part IV deals with robust scheduling and stochastic scheduling issues.Chapter 9 deals with stochastic project scheduling. The reader will first finda treatment of important topics in stochastic scheduling without resourceconstraints. Topics covered include exact methods for computing the projectduration distribution, methods for computing stochastic bounds on themakespan distribution, Monte Carlo sampling, and the issue of path andactivity criticality. Attention is given to the problem of determining theoptimal amount of activities’ delay beyond their earliest start times in orderto maximize the expected present value of the project. The discussioncontinues with a treatment of the stochastic resource-constrained projectscheduling problem, methods for solving the stochastic discrete time/costtrade-off problem, and the multi-mode trade-off problems in stochasticproject networks. A discussion of project scheduling under fuzzinessconcludes the chapter. Chapter 10 then focuses on robust and reactivescheduling. We review the fundamentals of the Critical Chain/BufferManagement approach (Goldratt (1997), Leach (2000), Newbold (1998))and highlight the merits and pitfalls of the approach. New reactivemechanisms for repairing disturbed baseline schedules conclude the chapter.

Numerous tables and figures are used throughout the book to enhance theclarity and effectiveness of the discussions. For the interested and motivatedreader, the problems at the end of each chapter should be considered as anintegral part of the presentation. Concepts which could not be properlydeveloped in the text because of the size constraints of the manuscript areoften relegated to a problem. In some cases, the problems refer to research

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questions which, although important, did not find their way to the main bodyof the text. An extensive bibliography is presented at the end of the book.

Any book of this size and complexity will undoubtedly contain errors.They solely remain the responsibility of the authors. We would be pleased tolearn about any comments that you might have about this book, includingerrors that you might find.

We are indebted to many people who have helped us greatly in writingthis book. We benefited from the fruitful discussions we could have over theyears with numerous members of the international project schedulingcommunity. We are much indebted to Bajis Dodin (University of Californiaat Riverside), Salah Elmaghraby (North Carolina State University) and JimPatterson (Indiana University) who were so kind to act as our co-authorsover the past years. Much of the presented material heavily relies on theexcellent research work of our former research assistants and friends Bert DeReyck, currently Associate Professor of Decision Sciences at the LondonBusiness School (UK), and Mario Vanhoucke, currently Assistant Professorof Operations and Technology Management at the Vlerick-Leuven-GhentManagement School (Belgium); not only did they act as co-author, theydefinitely influenced our thinking. Chapter 10 exploits much of the recentwork done by our research assistant Roel Leus. We are especially grateful toour research assistant Jeroen Beliën who suffered through preliminary draftsof the manuscript and made numerous suggestions for improvement. TheFund for Scientific Research - Flanders (Belgium) (F.W.O) supported muchof our research. We are indebted to the Department of Applied Economics ofthe Faculty of Economics and Applied Economics, Katholieke UniversiteitLeuven (Belgium) for providing us with an excellent environment forwriting this book. Last but not least, our sincere gratitude goes to ourfamilies for their patience and support.

LeuvenFebruary 2002 Erik Demeulemeester

Willy Herroelen