PM3_03FEB10

# PM3_03FEB10 - Chapter Precedence Networks and The Critical...

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1 Chapter  Precedence Networks and The Critical Path Method (CPM)

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2 Precedence Relationships Finish-to-start (FS = α ): Task B cannot start until α days after task A is finished Start-to-start (SS = α ): Task B cannot start until α days after task A has started Finish-to-finish (FF = α ): Task B cannot finish until α days after task A is finished Start-to-finish (SF = α ): Task B cannot finish until α days after task A has started The most common precedence network has FS = 0. Several types of precedence requirements occur in practice.
3 Precedence Networks Networks represent immediate precedence relationships  among tasks  and milestones  identified by the work  breakdown structure Milestones are tasks that take no time and have no cost,  but indicate significant events in the life of the project (e.g.,  completion of a project phase) Two types of networks:  Activity-on-Node (AON)        Activity-on-Arc (AOA) All networks must have only  one  starting and  one   ending  point. This can always be achieved artificially, where  necessary.

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4 Precedence Networks:   Activity-on-Node (AON) A B C D Start End

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6 AON  vs  AOA  Arguments for AON AON is easier to explain and understand AON is used in most PM software (e.g., Microsoft Project) AON does not require the use of dummy tasks to represent precedence  relationships  Arguments for AOA The PERT model (Chapter 6) is based on AOA AOA can be drawn using arc lengths corresponding to task durations,  which adds intuition to the network representation
7 Critical Path Method: AON with Two Paths Task A 7 months Task B 3 months End Task C 11 months Start The minimum time needed to complete a project is  equal to the  length of the longest path  through the  network; this path is known as a  Critical Path Activities along the critical path are called  Critical  Activities .

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8 Start Task A 7 months Task B 3 months Task C 11 months End ES Start = 0 LF Start = 0 ES A = 0 LF A = 8 ES B = 7 LF B = 11 ES C = 0 LF C = 11 ES End = 11 LF End = 11 ES j = Earliest starting time for task (milestone) j LF j = Latest finish time for task (milestone) j
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## This note was uploaded on 12/20/2010 for the course IEOR E4510 taught by Professor Mosherosenwein during the Spring '10 term at Columbia.

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PM3_03FEB10 - Chapter Precedence Networks and The Critical...

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