1. Activity- Jobs Time (hours) Preceding Activities-Jobs Decorating & furnishing a spare bedroom 1 Remove old furniture Remove carpet Take down curtains & rail Remove wallpaper 0.5 2 A BC A B C D Prepare walls Prepare woodwork Paint walls & ceiling 1 st coat (& dry) Paint woodwork (& dry) Lay new carpet Put up curtain rail & hang curtains Arrange new furniture Paint walls & ceiling 2 nd coat (& dry) E F G H I J K L M 0.5 1.5 5 8 5 2 1 1 0.5 Put up posters D D E F G HI HI J I

2. Latest finish time Earliest start time Activity Duration How long it takes 1 B Latest finish time Earliest start time Activity Duration 0.5 1.5 Activity B Remove carpet Using Labels to Identify the Activity

3. K 1 End 0 M 0.5 L 1 I 5 G 5 F 1.5 E 0.5 D 2 C B 1 AStart 0 0 0 1 0 3.5 1.5 49 J 2 14 16 17 Draw an activity network Show the time needed for each activity 14 8 H 5 A starts at 0 and takes 1 hr So B starts at 1 C starts at 0 and takes 0.5 hr So D could start at 0.5 hrs B starts at 1 and takes 0.5 hr So D must start at 1.5 hrs as both B and C must be finished. D starts at 1.5 and takes 2 hr So E and F must start at 3.5 hrs I starts at 9 and takes 5 hr So J, K and M must start at 14 hrs H starts at 5 and takes 8 hr = 13hrs But J and K must start after both H and I so use 14 hrs L starts at 16 and takes 1 hr = 17 hrs So End is at 17 hrs K starts at 14 and takes 1 hr = 15 hrs M starts at 14 and takes 0.5 hr = 14.5 hrs But End must occur after M,L and K are finished so use 17 hrs Put up posters 1 Remove old furniture Remove carpet Take down curtains & rail Remove wallpaper 0.5 2 A BC A B C D Prepare walls Prepare woodwork Paint walls & ceiling 1 st coat (& dry) Paint woodwork (& dry) Lay new carpet Put up curtain rail & hang curtains Arrange new furniture Paint walls & ceiling 2 nd coat (& dry) E F G H I J K L M 0.5 1.5 5 8 5 2 1 1 0.5 D D E F G HI HI J I Carry out a forward pass to show earliest possible start times Latest finish time Earliest start time Activity Duration 1.5 0.5 13 14 13 14 14.5 15 17

4. K 1 End 0 M 0.5 L 1 I 5 G 5 F 1.5 E 0.5 D 2 C B 1 AStart 0 00 01 1 1.5 0 3.54 6 1.5 3.5 49914 J 2 16 14 17 1417 1617 Draw an activity network Carry out a reverse pass to show latest possible finish times Show the time needed for each activity 14 8 H 5 M ends at 17 and takes 0.5 hr so I could end at 17 – 0.5 = 16.5 hrs But J ends at 16 and takes 2 hrs so I ends at 16 – 2 = 14 hrs K ends at 17 and takes 1 hr so I could end at 17 – 1 = 16 hrs But I must end before M,J and K start so use 14 hrs – lowest value J ends at 16 and takes 2 hr so H ends at 16 – 2 = 14 hrs K ends at 17 and takes 1 hr so H could end at 17 – 1 = 16 hrs But H must end before J and K start so use 14 hrs – lowest value L ends at 17 and takes 1 hr so J ends at 17 – 1 = 16 hrs E ends at 4 and takes 0.5 hr so D ends at 4 – 0.5 = 3.5 hrs F ends at 6 and takes 1.5 hr so D could end at 6 – 1.5 = 4.5 hrs But D must end before E and F start so use 3.5 hrs – lowest value 16.51416 14

5. Critical activities must start on time if the project is not to be delayed. K 1 End 0 M 0.5 L 1 I 5 G 5 F 1.5 E 0.5 D 2 C B 1 AStart 0 00 01 1 1.5 0 3.54 6 1.5 3.5 49914 J 2 16 14 17 1417 1617 Draw an activity network Show the time needed for each activity 14 Find a critical path Start A B D E G I J L End 8 H 514 Earliest start time + duration = Latest finish time

6. Critical path analysis Step 1List the activities with a time estimate for each. Step 2 Note which activities must precede others. Step 3 Draw an activity network, including the time for each activity. Step 4 Carry out a forward pass to find the earliest possible start times. Step 5 Carry out a reverse pass to find the latest possible finish times. Step 6 Identify critical activities and find a critical path.

7. Critical activities must start on time if the project is not to be delayed. AFurniture removal B Carpet removal D Wallpaper removal E Wall preparation G 1 st coat on walls I 2 nd coat on walls J Carpet laying L Arranging new furniture must start at 0 hours – lasts 1hr must start at 1 hour – lasts 0.5hrs must start at 1.5 hours – lasts 2hrs must start at 3.5 hours – lasts 0.5hrs must start at 4 hours – lasts 5hrs must start at 9 hours – lasts 5hrs must start at 14 hours – lasts 2hrs must start at 16 hours Earliest start time + duration = Latest finish time They are those for which: Start A B D E G I J L End

8. Activity Earliest start Latest finish DurationFloat The other activities have some flexibility in their start time. C Remove curtain & rail F Prepare woodwork H Paint woodwork K Put up curtain & rail M Put up posters 0 1.5 1 h 3.5 6 1 h 5 14 1 h 14 17 2 h 14 17 2.5 h Float = latest finish time – earliest start time – duration 0.5 1.5 8 1 0.5

9. 1234567891011121314151617 ABDEGIJL C F H K Put the critical activities along the bottom M K 1 End 0 M 0.5 L 1 I 5 G 5 F 1.5 E 0.5 D 2 C B 1 A Start 000 01 1 1.5 0 3.54 6 1.5 3.5 49914 J 216 14 17 1417 1617 14 8 H 5 Gantt Chart These activities must be started and completed on timeNow put in the non–critical activities at their earliest start timeFinally show the float time How many people are needed to complete the job?

10. 1234567891011121314151617 ABDEGIJL CFHKM K 1 End 0 M 0.5 L 1 I 5 G 5 F 1.5 E 0.5 D 2 C B 1 A Start 000 01 1 1.5 0 3.54 6 1.5 3.5 49914 J 216 14 17 1417 1617 14 8 H 5 Gantt Chart One person can do the critical activities If activity M is completed after K then the 2 nd person can do the other jobs.

11. Alternative Gannt Chart – this is the version needed in the exam Duration Red Float Blue The critical activities have no float