Question

Given the following information about a small project,

Task     Duration         Immediate

Estimates        Predecessors

A          2 days              None

B          5 days              A

C          4 days              B

D          9 days              A

E          4 days              B & D

F          12 days            E & C

1. Draw a network diagram.
2. Identify the critical path, earliest start and finish and slack for each task.
3. Using MS Excel, produce a Gantt chart for this project.
4. What would happen if a new estimate for task D increases its expected duration from 9 days to 11 days? Would the project take longer? Would anything else change?

Answer 1

Below is the AON network for the project.

Early Start and Early Finish for a activity is calculated as follows. Early start is the earliest the activity can start. Early finish is determined by adding the duration of the activity to the early start time. Early Start of successor activities is the early finish of the predecessor activity. If there are more than one predecessor activity early start of the successor activity is the early finish of the predecessor activity which finishes the latest.

Once we calculate the early start and early finish of all the activities we can determine the time a project will take which will equal to the early finish of the last activity.

Late Start and Late Finish for a activity is calculated as follows. Late finish is the latest the activity can finish without delaying the project. Late start is determined by subtracting the duration of the activity to the late finish time. Late finish of predecessor activities is the late start of the successor activity. If there are more than one successor activity late finish of the predecessor activity is the late start of the successor activity which start the earliest.

Once the late start and late finish is calculated, we can calculate the slack for each activity and the critical path of the project. Slack is calculated as the difference between early start and late start or early finish and late finish of the particular activity. Slack is the amount of time an activity can be delayed without delaying the overall project. The critical path is the path traced by all those activities where slack is zero. In other words there can be no delay in any activities which make up the critical path without delaying the project.

Using the above logic, the early start (ES), early finish (EF), late start (LS), late finish (LF) are as shown in the below diagram.

The above details are tabulated in the below table along with slack and the critical path

The critical path is thus A-D-E-F

Below is the Gantt Chart for the project

If the expected duration for D increase from 9 to 11, the project would take longer as activity D falls on the critical path. In addition activity E will also be delayed as this activity is also part of critical path.