Gantt Chart Graph or bar chart with a bar for each project activity that shows passage of time Provides visual display of project schedule Slack amount of time an activity can be delayed without delaying the project

Example of Gantt Chart Month 0 2 4 6 8 10 | | | | | 1 3 5 7 9 Activity | | | | | Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work 0 2 4 6 8 10 Month 1 3 5 7 9

The Project Network Use of nodes and arrows Arrows  An arrow leads from tail to head directionally Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work. Nodes  A node is represented by a circle - Indicate EVENT, a point in time where one or more activities start and/or finish.

CPM/PERT Critical Path Method (CPM) DuPont & Remington-Rand (1956) Deterministic task times Activity-on-node network construction Project Evaluation and Review Technique (PERT) US Navy, Booz, Allen & Hamilton Multiple task time estimates Activity-on-arrow network construction

Project Network Activity-on-node (AON) Node Activity-on-arrow (AOA) nodes represent activities, and arrows show precedence relationships Activity-on-arrow (AOA) arrows represent activities and nodes are events for points in time Event completion or beginning of an activity in a project 1 3 2 Branch/Activity Node

AON Network for House Building Project 1 3 2 4 5 6 7 Start Design house and obtain financing Order and receive materials Select paint Select carpet Lay foundations Build house Finish work

Critical Path Critical path 4 2 7 1 Start 3 6 5 A: 1-2-4-7 3 + 2 + 3 + 1 = 9 months B: 1-2-5-6-7 3 + 2 + 1 + 1 + 1 = 8 months C: 1-3-4-7 3 + 1 + 3 + 1 = 8 months D: 1-3-5-6-7 3 + 1 + 1 + 1 + 1 = 7 months Critical path Longest path through a network Minimum project completion time

Activity Start Times 4 2 7 1 3 6 5 Start at 5 months Finish at 9 months Finish

Calculation of Required Time (Te) t0 + 4 tm + tp Te= 6 te=weighted arithmetic average time to= Optimistic Time tm= most likely time tp= pessimistic time

Networking 2 15 13 5 2 1 2 12 8 3 4

Calculation of Required Time (Te) Activity optimistic Most likely Pessimistic Average Time (Te) A 1-2 9 12 21 13 B 1-3 6 18 C 2-4 1 1.5 5 2 D 3-4 4 8.5 10 8 E 2-5 14 24 15 F 4-5 3

Slack=LF-EF, LS-ES Activity Slack Each event has two important times associated with it : Earliest time , Te , which is a calendar time when a event can occur when all the predecessor events completed at the earliest possible times Latest time , TL , which is the latest time the event can occur with out delaying the subsequent events and completion of project. Difference between the latest time and the earliest time of an event is the slack time for that event Slack=LF-EF, LS-ES Positive slack : Slack is the amount of time an event can be delayed without delaying the project completion

Mode Configuration 1 3 Activity number Earliest start Earliest finish 3 Latest finish Activity duration Latest start

Forward Pass Start at the beginning of CPM/PERT network to determine the earliest activity times Earliest Start Time (ES) earliest time an activity can start ES = maximum EF of immediate predecessors Earliest finish time (EF) earliest time an activity can finish earliest start time plus activity time EF= ES + t

Earliest Activity Start and Finish Times 1 3 2 5 4 6 8 7 9 Start Design house and obtain financing Select paint Lay foundations Select carpet Build house Finish work Order and receive materials

Earliest Activity Start and Finish Times 1 3 2 5 4 6 8 7 9 Start Design house and obtain financing Select paint Lay foundations Select carpet Build house Finish work Order and receive materials * 0+3 3+1 * For forward pass maximum EF time would be taken in calculating ES time

Backward Pass Determines latest activity times by starting at the end of CPM/PERT network and working forward Latest Start Time (LS) Latest time an activity can start without delaying critical path time LS= LF - t Latest finish time (LF) latest time an activity can be completed without delaying critical path time LS = minimum LS of immediate predecessors

Latest Activity Start and Finish Times 1 3 2 5 4 6 7 8 9 Start Design house and obtain financing Select pain Lay foundations Select carpet Build house Finish work Order and receive materials

Activity Slack Slack S EF LF ES LS Activity * Critical Path 9 8 *7 1 7 9 8 *7 1 7 6 5 *4 4 3 *2 *1 Slack S EF LF ES LS Activity