5 Practice Questions on Network Analysis (Part 1)

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1.Â Â Â Â Â Â Â Â  The time and the cost estimates and precedence relationship of different activities constituting a project are given below :

 Activity Intermediate Predecessor Time (in weeks) Direct Cost (in `) Normal Crash Normal Crash A — 4 3 60 90 B — 6 4 150 250 C — 2 1 38 60 D A 5 3 150 250 E C 2 2 100 100 F A 7 5 115 175 G D, E, B 4 2 100 240

Indirect cost varies as follows :

 Days 15 14 13 12 11 10 9 8 7 6 Cost (`) 600 500 400 250 175 100 75 50 5 25

(a)Â Â Â Â  Draw an arrow diagram for the project.

(b)Â Â Â Â  Determine the project duration which will return in minimum total project cost.

2.Â Â Â Â Â Â Â Â  The time and cost estimates and precedence relationship of the different activities constituting a project are given below :

 Activity Predecessor Time (in weeks) Direct Cost (in `) Normal Crash Normal Crash A — 3 2 80 190 B — 8 6 6 10 C B 6 4 100 120 D B 5 2 40 100 E A 13 10 30 90 F A 4 4 150 150 G F 2 1 12 14 H C, E, G 6 4 35 45 I F 2 1 70 80

(a)Â Â Â Â  Draw a project network diagram and find the critical path.

(b)Â Â Â Â  If a deal line of 17 weeks is imposed for completion of the project which activities will be crashed, what should be the additional cost and what would be the critical activities of the crashed network after crashing?

3.Â Â Â Â Â Â Â Â  The following tab le gives the activities in a construction project and other relevant information.

 Activity Preceding Activity Normal Time (Days) Crash Time (Days) Normal Cost (`) Crash Cost (`) 1 â€“ 2 — 20 17 600 720 1 â€“ 3 — 25 25 200 200 2 â€“ 3 1 â€“ 2 10 8 300 440 2 â€“ 4 1 â€“ 2 12 6 400 700 3 â€“ 4 1 â€“ 3, 2 â€“ 3 5 2 300 420 4 â€“ 5 2 â€“ 4, 3 â€“ 4 10 5 300 600

(i)Â Â Â Â Â  Draw the activity network of the project.

(ii)Â Â Â Â  Find the critical Path

(iii)Â Â Â  Using the above information, Crash or Shorten the activity step by step until the shortest duration is reached.

4.Â Â Â Â Â Â Â Â  For an activity in a network the normal duration is 12 days and the normal cost isÂ Â Â  ` 2000/-, For the same activity the crash duration is 8 days with crashing cost as Â Â Â Â ` 3,200/-. Find the cost slope of this activity.

5.Â Â Â Â Â Â Â Â  The table below provides cost and time estimates of seven activities of a project.

 Activity Time estimates Â (in weeks) Direct Cost estimates Â (` In 000) Normal Crash Normal Crash 1 â€“ 2 2 1 10 15 1 â€“ 3 8 5 15 21 2 â€“ 4 4 3 20 24 3 â€“ 4 1 1 7 7 3 â€“ 5 2 1 8 15 4 â€“ 6 5 3 10 16 5 â€“ 6 6 2 12 36

(i)Â Â Â Â Â  Draw the project network corresponding to normal time.

(ii)Â Â Â Â  Determine the critical path and the normal duration and normal cost of the project.

(iii)Â Â Â  Crash the activities so that the project completion time reduces to 9 weeks with minimum additional cost.

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