,Project management & scheduling
1. Introduction ________________________________________________________________ 3
1. Scope and relevance of project scheduling _____________________________________________ 3
2. Classification of project scheduling problems ___________________________________________ 3
2. The project scheduling process – Temporal analysis of activity-on-node and activity-on-arc
networks _______________________________________________________________________ 4
1. Activity on the node representation _____________________________________________________ 4
Time analysis _______________________________________________________________________ 4
Generalization to precedence diagramming ______________________________________________ 5
2. Activity on the arc representation ______________________________________________________ 6
Characteristics _____________________________________________________________________ 6
Time analysis _______________________________________________________________________ 7
LP flow formulation to find CP _________________________________________________________ 8
3. PERT ______________________________________________________________________________ 9
3. The resource-constrained project scheduling problem: ____________________________ 10
1. Linear programming based approaches ______________________________________________ 10
Time-indexed _____________________________________________________________________ 10
Forbidden set-based ________________________________________________________________ 11
Feasible subset-based_______________________________________________________________ 12
Resource flow-based _______________________________________________________________ 13
2. Branch-and-bound procedures _____________________________________________________ 14
Precedence tree ___________________________________________________________________ 14
Extension alternatives ______________________________________________________________ 15
Minimal delaying alternatives ________________________________________________________ 16
Minimal forbidden sets______________________________________________________________ 17
Implicit enumeration/DH-procedure ___________________________________________________ 18
3. Heuristic procedures ________________________________________________________________ 22
3.1. Definitions ________________________________________________________________ 22
3.2. Constructive heuristics _______________________________________________________ 22
3.3. Improvement heuristics ______________________________________________________ 29
4. Resource leveling: the resource leveling problem and the resource availability cost problem
32
1. The resource leveling problem ________________________________________________________ 32
Problem formulation _______________________________________________________________ 32
The Burgess and Killebrew levelling procedure ___________________________________________ 33
Voorbeeld ________________________________________________________________________ 34
2. The resource availability cost problem __________________________________________________ 36
Problem formulation _______________________________________________________________ 36
Solution methodology ______________________________________________________________ 36
Search strategy ____________________________________________________________________ 36
5. Introducing money: max-npv and time/cost trade-off problems _____________________ 41
1. Temporal analysis under the unconstrained max npv objective ______________________________ 41
The deterministic max-npv problem ___________________________________________________ 41
An exact recursive procedure for the max-npv problem ____________________________________ 42
2. Resource-constrained project scheduling problem with discounted cash flows __________________ 43
Problem formulation _______________________________________________________________ 43
A branch-and-bound algorithm for the RCPSPDC _________________________________________ 43
3. Continuous time/cost trade-off problems _______________________________________________ 44
Linear cost-duration functions ________________________________________________________ 44
Other continuous cost-duration functions _______________________________________________ 48
Set of discrete points for the time-cost trade off function __________________________________ 49
1
,6. Project control: earned value managements and critical chain buffer management _____ 50
1. Earned value management ___________________________________________________________ 50
Managing Costs____________________________________________________________________ 50
Key Metrics _______________________________________________________________________ 51
Performance measurements _________________________________________________________ 51
New Key Metric ___________________________________________________________________ 52
Forecasting _______________________________________________________________________ 52
2. Critical Chain/Buffer Management by Goldratt ___________________________________________ 53
7. Robust project scheduling ____________________________________________________ 55
1. Proactive/reactive scheduling ______________________________________________________ 55
1. Robustness types and measures__________________________________________________ 55
2. Solution robust project scheduling under activity duration uncertainty ___________________ 56
3. Robust scheduling in a one-phase approach ___________________________________________ 60
4. Proactive/reactive policy: Markov decision process _____________________________________ 61
2. Dominating policies: colors and consistent policies _____________________________________ 64
8. Managing risks in projects ___________________________________________________ 65
1. Why risk management? ___________________________________________________________ 65
2. Good risk management ___________________________________________________________ 65
3. A risk management framework _____________________________________________________ 65
2
, 1. Introduction
1. Scope and relevance of project scheduling
The QCD objective (goals of a project: quality, cost and timing):
“You can either have your job done cheap, quick or right: pick two.”
PERT CPM
R&D projects Routine projects
- Stochastic - Deterministic
- Critical path - Critical path
- Activity network - Activity network
- Time - Time/cost trade-off
2. Classification of project scheduling problems
!|#|$ classification scheme for machine scheduling problems
o !: machine environment
o #: task and resource characteristics
o $: optimality criterion
3
1. Introduction ________________________________________________________________ 3
1. Scope and relevance of project scheduling _____________________________________________ 3
2. Classification of project scheduling problems ___________________________________________ 3
2. The project scheduling process – Temporal analysis of activity-on-node and activity-on-arc
networks _______________________________________________________________________ 4
1. Activity on the node representation _____________________________________________________ 4
Time analysis _______________________________________________________________________ 4
Generalization to precedence diagramming ______________________________________________ 5
2. Activity on the arc representation ______________________________________________________ 6
Characteristics _____________________________________________________________________ 6
Time analysis _______________________________________________________________________ 7
LP flow formulation to find CP _________________________________________________________ 8
3. PERT ______________________________________________________________________________ 9
3. The resource-constrained project scheduling problem: ____________________________ 10
1. Linear programming based approaches ______________________________________________ 10
Time-indexed _____________________________________________________________________ 10
Forbidden set-based ________________________________________________________________ 11
Feasible subset-based_______________________________________________________________ 12
Resource flow-based _______________________________________________________________ 13
2. Branch-and-bound procedures _____________________________________________________ 14
Precedence tree ___________________________________________________________________ 14
Extension alternatives ______________________________________________________________ 15
Minimal delaying alternatives ________________________________________________________ 16
Minimal forbidden sets______________________________________________________________ 17
Implicit enumeration/DH-procedure ___________________________________________________ 18
3. Heuristic procedures ________________________________________________________________ 22
3.1. Definitions ________________________________________________________________ 22
3.2. Constructive heuristics _______________________________________________________ 22
3.3. Improvement heuristics ______________________________________________________ 29
4. Resource leveling: the resource leveling problem and the resource availability cost problem
32
1. The resource leveling problem ________________________________________________________ 32
Problem formulation _______________________________________________________________ 32
The Burgess and Killebrew levelling procedure ___________________________________________ 33
Voorbeeld ________________________________________________________________________ 34
2. The resource availability cost problem __________________________________________________ 36
Problem formulation _______________________________________________________________ 36
Solution methodology ______________________________________________________________ 36
Search strategy ____________________________________________________________________ 36
5. Introducing money: max-npv and time/cost trade-off problems _____________________ 41
1. Temporal analysis under the unconstrained max npv objective ______________________________ 41
The deterministic max-npv problem ___________________________________________________ 41
An exact recursive procedure for the max-npv problem ____________________________________ 42
2. Resource-constrained project scheduling problem with discounted cash flows __________________ 43
Problem formulation _______________________________________________________________ 43
A branch-and-bound algorithm for the RCPSPDC _________________________________________ 43
3. Continuous time/cost trade-off problems _______________________________________________ 44
Linear cost-duration functions ________________________________________________________ 44
Other continuous cost-duration functions _______________________________________________ 48
Set of discrete points for the time-cost trade off function __________________________________ 49
1
,6. Project control: earned value managements and critical chain buffer management _____ 50
1. Earned value management ___________________________________________________________ 50
Managing Costs____________________________________________________________________ 50
Key Metrics _______________________________________________________________________ 51
Performance measurements _________________________________________________________ 51
New Key Metric ___________________________________________________________________ 52
Forecasting _______________________________________________________________________ 52
2. Critical Chain/Buffer Management by Goldratt ___________________________________________ 53
7. Robust project scheduling ____________________________________________________ 55
1. Proactive/reactive scheduling ______________________________________________________ 55
1. Robustness types and measures__________________________________________________ 55
2. Solution robust project scheduling under activity duration uncertainty ___________________ 56
3. Robust scheduling in a one-phase approach ___________________________________________ 60
4. Proactive/reactive policy: Markov decision process _____________________________________ 61
2. Dominating policies: colors and consistent policies _____________________________________ 64
8. Managing risks in projects ___________________________________________________ 65
1. Why risk management? ___________________________________________________________ 65
2. Good risk management ___________________________________________________________ 65
3. A risk management framework _____________________________________________________ 65
2
, 1. Introduction
1. Scope and relevance of project scheduling
The QCD objective (goals of a project: quality, cost and timing):
“You can either have your job done cheap, quick or right: pick two.”
PERT CPM
R&D projects Routine projects
- Stochastic - Deterministic
- Critical path - Critical path
- Activity network - Activity network
- Time - Time/cost trade-off
2. Classification of project scheduling problems
!|#|$ classification scheme for machine scheduling problems
o !: machine environment
o #: task and resource characteristics
o $: optimality criterion
3
