Production and Operation Managements Project Scheduling Dr.Na GeNG Prof.Zhibin JIANG Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Dr. Na GENG Prof. Zhibin JIANG Department of Industrial Engineering & Management Shanghai Jiao Tong University Project Scheduling
Content The nature of project management 国 Techniques for project scheduling Resource constraints Activity crashing Incorporating uncertainty in activity times 国 Problems with implementing critical path analysis Monitoring projects 2 上浒充通大粤
Content The nature of project management Techniques for project scheduling Resource constraints Activity crashing Incorporating uncertainty in activity times Problems with implementing critical path analysis Monitoring projects 2
Critical Path Analysis Critical path method: The critical path method(CPM)is an approach to determine the start and finish dates for individual activities in a project. A result of this method is the identification of a critical path. ·Procedures: 。Draw the network Provides activity information Earliest(ES)&latest(LS)start,Earliest(EF)&latest(LF)finish Slack(S):Allowable delay Identifies critical path Longest path in network Shortest time project can be completed Activities have 0 slack Any delay on activities delays project 上浒充通大粤
Critical Path Analysis Critical path method: The critical path method (CPM) is an approach to determine the start and finish dates for individual activities in a project. A result of this method is the identification of a critical path. • Procedures: • Draw the network • Provides activity information Earliest (ES) & latest (LS) start, Earliest (EF) & latest (LF) finish Slack (S): Allowable delay • Identifies critical path Longest path in network Shortest time project can be completed Activities have 0 slack Any delay on activities delays project
Techniques for project management Table 10.2 Notation for critical path method Item Symbol Definition Expected activity duration t The expected duration ofan activity Early start ES The earliest time an activity can begin ifall previous acivities began at their earliest times The earliest time an activity can be completed if it is Early finish EF started at its early start time The latest time an activity can begin without delaying Late start LS the completion of the project The latest time an activity can be completed if it is Late finish LF started at its latest start time The amount of time an activity can be delayed without Total slack TS delaying the completion of the project ES=EFpredecessor (max) LF=LSsuccessor (min) TS=LF-EF or EF=ES+t LS=LF-t TS=LS-ES 4 上浒充通大姿
4 Techniques for project management Item Symbol Definition Expected activity duration t The expected duration of an activity Early start ES The earliest time an activity can begin if all previous acivities began at their earliest times Early finish EF The earliest time an activity can be completed if it is started at its early start time Late start LS The latest time an activity can begin without delaying the completion of the project Late finish LF The latest time an activity can be completed if it is started at its latest start time Total slack TS The amount of time an activity can be delayed without delaying the completion of the project Table 10.2 Notation for critical path method ES = EFpredecessor (max) EF = ES + t LF = LSsuccessor (min) LS = LF - t TS = LF - EF or TS = LS - ES
Techniques for project management Critical path method Ex.10.3 Tennis tournament-critical path analysis A2) C(3) D2) G(4) Start E(10) I3) J2) B(8) F(4) Fig.10.4 PERT chart (AON network)for tennis tournament TS-LS-ES ES=EFpredecessor EF-ES+t LS-LF-t LF-LSsuccesor 5 上泽充鱼大粤
Critical path method • Ex. 10.3 Tennis tournament - critical path analysis 5 Techniques for project management