Question

Consider a project having the following six activities:

                                                     Immediate                                                  Max            Crash cost

            Activity                           Predecessors          Time (weeks)             Crash*    per week

                  A                                none                                    7                          7         N/A

                  B                                none                                    3                          2        $500

                  C                                A                                       5                          3      $1000

                  D                                A, B                                    6                          4      $2000

                  E                                 C, D                                    4                          3      $1250

                  F                                D                                       3                          2      $1000

                                                                                                *Shortest possible time for the task

1. Draw the project network and list the earliest start (ES), earliest finish (EF), latest start (LS) and latest finish (LF) for each task (1.5 pts.)

2. List the tasks on the critical path (0.4 pts.)

3. What is the expected project duration in weeks? (0.4 pts.)

4. What is the slack for each activity? (1.2 pts.) A: B: C: D: E: F:  

5. The project needs to be crashed by 2 weeks. What are the activities crashed to achieve the 2 week crash at lowest cost? List the new duration of each task and any associated crash costs (0.5 pts.) Activity Duration Crash Cost A B C D E F

6. Draw the NEW project network and list the earliest start (ES), earliest finish (EF), latest start (LS) and latest finish (LF) for each task (0.6 pts.)

7. List the tasks on the critical path (0.4 pts.)

Answer 1

1. We draw project network listing the earliest start (ES), earliest finish (EF), latest start (LS) and latest finish (LF) for each task as follow:

The legend for the values mentioned in the box is shown in above figure at the top:

Earliest start = ES, earliest finish = EF, latest start = LS, latest finish = LF, Slack = SLK, Duration of activity = DUR

2) As seen from above network diagram, the path in red is critical path. Hence, task A-C-E are on critical path

3) As seen from above network diagram, the longest LF is 16 weeks. Hence, the project duration is 16 weeks.

4) As seen from above network diagram, slack on each activity:

A: 0 weeks

B: 4 weeks

C: 0 weeks

D: 4 weeks

E: 0 weeks

F: 4 weeks

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