Question:

The following diagram shows a C.P.A.-network modeling the stages in the construction project. Each arc is labeled with the letter denoting the activity it represents and a weight that denotes the number of days needed to complete that activity. Activities A and B can start as soon as the project commences, and the project is finished when I and K have been completed. The arc labeled Z represents a dummy activity introduced to model the logical structure of the network.

(a) List the prerequisite activities for (i) G and (ii) I in this construction project. Explain why it is necessary to introduce the dummy activity Z to obtain the C.P.A.-network.

(b) Say what a vertex in a C.P.A.-network represents. Copy the network above and give its vertices an acyclic labeling v1, v2,..., v8, where v1 represents the start of the manufacturing process.

(c) Say what is meant by the early event time ET (v) and the late time event LT (v) for an event v. Calculate ET (v) and LT (v) for each event in this project, entering these times in the appropriate boxes on your diagram.

(d) What is the shortest time in which this project can be completed?

(e) Suppose an activity is represented by the arc vivj with weight w (vivj). Say how the total float time for this activity is calculated. Tabulate the total float time for each activity in this project.

(f) Identify all the critical activities in this project and find the critical path(s) in this C.P.A.-network.