# Numericals on Project Crashing

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(Project Crashing)

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1.Â Â Â Â Â Â Â Â  For the data given in the table below, draw the network. Crash systematically the activities and determine the optimal project duration and cost. Indirect cost is ` 70 per day. Â (April 2003)

 Activity 1 – 2Â 1 – 3 2 – 4 2 – 5 3 – 4 4 – 5 Normal Time (Days) 8 4 2 10 5 3 Normal Cost (`) 100 150 50 100 100 80 Crash Time (Days) 6 2 1 5 1 1 Crash Cost (`) 200 350 90 400 200 100

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2.Â Â Â Â Â Â Â Â  The following is a table showing details of a project : Indirect cost is ` 200 per week.

 NODES Normal Crash Time (weeks) Cost (`) Time (weeks) Cost (`) 1 â€“ 2 8 1500 6 2000 1 â€“ 4 10 2000 7 3000 2 â€“ 4 5 800 4 1400 2 â€“ 3 6 1100 4 1500 2 â€“ 5 8 900 5 1500 3 â€“ 4 0 0 0 0 4 â€“ 6 12 300 8 400 5 â€“ 6 5 500 4 800

(a)Â Â Â Â  Construct the project network and identify the critical path. What is the normal duration and corresponding total cost of the project?

(b)Â Â Â Â  Crash the project systematically and find out minimum cost and optimal time and also find out the additional cost required to reach the optimal time.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (April, 10)

3.Â Â Â Â Â Â Â Â  The time and cost estimates and precedence relationship of different activities constituting a project are given.

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

4.Â Â Â Â Â Â Â Â  Following 7 activities are involved in completion of a small project.

 Activity Preceding Activity Time (Hrs.) Crash cost Â Â Normal Crash ` / Hour A – 3 1 40 B – 4 2 50 C B 0 0 ZERO (Nil) D A & C 5 3 20 E B 3 2 30 F D 3 2 10 G E 2 1 20

Determine which is the quickest possible time in which the project can be completed and how much is the additional cost for this purpose.

Normal project cost is ` 1500.

5.Â Â Â Â Â Â Â Â  The time and cost estimate of different activities of a project and their precedence relationship are given below :Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (Oct. 2007)

 Activity Preceding Activity Time in Weeks Cost in ` Â Â Normal Crash ` / Hour A 6 4 10,000 14,000 B 4 3 5,000 8,000 C A 3 2 4,000 5,000 D B 8 3 1,000 6,000 E B 14 6 9,000 13,000 F C, D 8 4 7,000 8,000

Overhead costs amount to ` 1,000 per week. Answer the following questions :

(i)Â Â Â Â Â  Crash the project to optimal extent. What will be the optimum project duration and total minimum cost?

(ii)Â Â Â Â  What will be the critical activities after such crashing?

(iii)Â Â Â  What will be the minimum project duration and corresponding total project costs?

6.Â Â Â Â Â Â Â Â  Following are the various activities involved in a project. The cost and time information for these activities is given below :

 Activity Immediately Proceeding Activity Normal Crash Time (days) Cost (`) Time (days) Cost (`) A 3 140 2 210 B 6 215 5 275 C – 2 160 1 240 D A 4 130 3 180 E A 2 170 1 250 F A 7 165 4 285 G B, D 4 210 3 290 H C, E 3 110 2 160

(a)Â Â Â Â  Draw the PERT network.

(b)Â Â Â Â  Find out the critical path and the expected project completion time.

(c)Â Â Â Â  What is the minimum possible project completion time after crashing the activities involved in the project and the associated cost of completing the project?Â Â Â Â  (Oct. 2009)

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