Relationships between Activities• A project is a sequence of activities. – Large projects have interrelated sequences.• These are called Precedent activities – They must be defined before the project begins.
Step 2 Develop a Network Model• A Network Diagram visually displays the interrelated activities using nodes (circles) and arcs (arrows) that depict the relationships between activities.• It is a graphical diagram.• Two types of Graphical Network Models – Activity On Arc (AOA) – Activity On Node (AON) (We will use AON)
Two Types of Network Models Activity-on-Arc (AOA)Time Time Time Activity D Activity E Activity-on-Node (AON) Activity Activity We will use D E this! Link
Precedent Relationships Precedent relationships determine a sequence for accomplishing activities. They specify that any given activity cannot start until its preceding activity or activities have been completed. Activity On Node approach In our AON approach, the nodes (circles) represent activities, and the arcs AON represent the sequential relationships between them. S T UNodes are simplified in the following examples. “S” precedes “T” which precedes “U”
Activity RelationshipsS & T must be completed T & U cannot begin until Sbefore U can be started. has been completed. S T U S T U
Activity Relationships U cannot begin until S & T have beenU & V can’t begin until S & T completed. V cannot begin until T hashave been completed. been completed. S U S U T V T V
Activity RelationshipsT & U cannot begin until S has beencompleted; V cannot begin until both T & Uhave been completed. S T V U
St. Adolf’s Hospital (A sample project) Immediate Activity Description Predecessor(s) *Responsibility A Select administrative and medical staff. — Johnson B Select site and do site survey. — Taylor C Select equipment. A Adams D Prepare final construction plans & layout. B Taylor E Bring utilities to the site. B Burton F Interview applicants and fill positions in A Johnson nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C Adams H Construct the hospital. D Taylor I Develop an information system. A Simmons J Install the equipment. E,G,H Adams K Train nurses and support staff. F,I,J Johnson*We won’t be using the “Responsibility” data, but it is important in project management.
St. Adolf’s Hospital Diagramming the Network Activity Times (wks) Immediate IPredecessorsA – 12 A F KB – 9C A 10D B 10 Start C G FinishE B 24F A 10G C 35 B D H JH D 40I A 15J E,G,H 4 EK F,I,J 6
St. Adolf’s Hospital I Paths are sequences of activities between a project’s start and finish. A F KPath Time (wks) Start C G FinishA-I-K33A-F-K28 B D H JA-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43 E
St. Adolf’s Hospital The longest path is the critical path! IPath Time (wks) A F KA-I-K33A-F-K28 Start C G FinishA-C-G-J-K 67B-D-H-J-K 69B-E-J-K 43 B D H JProject ExpectedTime is 69 wks. E
3. Develop the schedule• Now we insert the time estimates. – This is where we distinguish between PERT & CPM.• CPM is used when activity times are Certain. • It is Decision making under Certainty • You are certain of the time each activity will require to complete.• PERT is used when activity times are not certain. (Decision making under risk)
Using PERT • PERT is used when activity times are uncertain. – Decision making under risk (“P” for probabilistic) – Three time estimates are required for each activity. • OPTIMISTIC TIME: Best time if everything goes perfectly • REALISTIC TIME: Most likely time • PESSIMISTIC TIME: A worst-case situation B + 4M + P Expected Time = ------------------- 6In this example, the most likely time is given a weight of 4, and the other two times (pessimisticand optimistic) are each given weights of 1. Software allows you to change these as needed, butthe denominator must be the total of the weights given.
St. Adolf’s Hospital Developing the schedule• Earliest Start Time (ES) for an activity is the earliest finish time of the immediately preceding activity.• Earliest Finish Time (EF) for an activity is its earliest start time plus how long it takes to do it (estimated duration).• Latest Start Time (LS) is the latest you can finish the activity minus the activity’s estimated duration.• Latest Finish Time (LF) is the latest start time of the activity that immediately follows it. (Latest start and finish times for each activity are computed starting at the project’s last activity completion time and working forward.)