1. Activity Time (hours) Preceding Activities 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 start time Earliest start time Using Labels to Identify the Activity

3. Draw an activity network Show the time needed for each activity – Activity on Arc 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 A1 C0.5 B0.5 D2 H8 G5 I5 A and C have no predecessors.B follows A D follows B and C E and F follow D G follows E and I followsGF follows D and H follows F E0.5 F1.5

4. Draw an activity network Show the time needed for each activity 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 A1 C0.5 B0.5 D2 E0.5 F1.5 H8 G5 I5 M0.5 L1 0 J2 K1 K and J follow H and I – need a dummy M follows I L follows J End

5. 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 Show the early start time needed for each activity 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 Carry out a forward pass to show earliest possible start times 0 1 A1 C0.5 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17 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

6. Show the early start time needed for each activity Use the largest number when doing a forward pass i.e. For the 3 rd label 1 + 0.5 = 1.5 0 + 0.5 = 0.5 So Use 1.5 0 1 A1 C0.5 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17

7. Carry out a reverse pass to show latest possible start times Show the latest start time needed for each activity 0 1 A1 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17 14 16 14 9 4 17 – 1 = 16 Using activity L 16 – 2 = 14 using activity J 17 – 1 = 16 using activity KUse the smallest 17 – 0.5 = 16.5 using activity M 14 – 0 = 14 using dummy activity Use the smallest 14 – 5 = 9 using activity I 9 – 5 = 4 using activity G C0.5

8. Show the latest start time needed for each activity 0 1 A1 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17 3.5 14 16 14 6 9 4 1 1.5 0 4 – 0.5 = 3.5 Using activity E 6 – 1.5 = 4.5 using activity FUse the smallest 3.5 – 2 = 1.5 Using activity D 1.5 – 0.5 = 1 Using activity B 1 – 1 = 0 Using activity A 1.5 – 0.5 = 1 Using activity CUse the smallest C0.5

9. Critical activities must start on time if the project is not to be delayed. Finding the critical path Start A B D E G I J L End 0 1 A1 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17 3.5 14 16 14 6 9 4 1 1.5 0 Critical activities connect 2 nodes where: latest start time of next activity – early start time of previous activity – duration = 0 Right of right node – left of left node – duration = 0 C0.5

10. Critical path analysis – summary of steps 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 start times. Step 6 Identify critical activities and find a critical path.

11. 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 They are those for which: Start A B D E G I J L End

12. Activity Earliest start previous activity Latest start next activity 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 start time next activity – earliest start time previous activity – duration 0.5 1.5 8 1 0.5 Right of right node – left of left node – duration = Float RR – LL – D = Float = 0 if critical

13. 1234567891011121314151617 ABDEGIJL CFHK Put the critical activities along the bottom M 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 0 1 A1 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17 3.5 14 16 14 6 9 4 1 1.5 0 C0.5

14. 1234567891011121314151617 ABDEGIJL CFHK M Gantt Chart How many people are needed to complete the job? One person can do the critical activities If activity M is completed after K then the 2 nd person can do the other jobs. 0 1 A1 B0.5 D2 E0.5 F1.5 H8 J2 G5 M0.5 I5 L1 K1 0 1.5 3.5 4 5 9 14 16 17 3.5 14 16 14 6 9 4 1 1.5 0 C0.5

15. Gantt Chart The exam board like Gantt Charts like this!!! The Critical Activities clearly follow on from each other with no float i.e A, B, D, E, G, I, J, L

16. Resource Histogram 1234567891011121314151617 ABDEGIJL CFHK M This job appears to need 2 people if one person does the critical activities and the other person does the rest. However some activities may require more than one person. This means that the Gantt Chart needs amending

17. Decorating & furnishing a spare bedroom Activity No. people 3 Remove old furniture Remove carpet Take down curtains & rail Remove wallpaper 2 1 2 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 1 1 2 2 2 3 1 3 1 Put up posters

18. Resource Histogram 1234567891011121314151617 A BD E GI J L C F H K M Activity No. people 3 Remove old furniture Remove carpet Take down curtains & rail Remove wallpaper 2 2 2 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 1 1 2 2 2 3 1 2 1 Put up posters 1 3 2 4 5 No. people

19. Resource Histogram 1234567891011121314151617 A BD E GI J L C H K M 1 3 2 4 5 5 people are needed to complete this job. Now try and reduce the number of people by levelling the histogram C must be completed by 1.5hrs so drop it into the gap after A K must be completed by 17hrs so drop it into the gap after J M must be completed by 17hrs so drop it down Now 4 people are needed F F Note how F is split so that there are no “holes” in the histogram F