Resource Loading And Smoothing.docx

Project Planning, Gantt chart representation, Scheduling, Resources Loading and Resource Smoothing in network analysis Example: The data about a small project is given below: Activity A B C D E F G H I

Representation by tail and head event 12 13 111 28 37 38 78 711 811

Duration in weeks

Predecessor activity

Manpower requirement

16 20 30 15 15 10 3 16 12

A B B E E D, F and G

2 6 4 3 2 5 2 4 4

Given that the availability of manpower per week is limited to 10 only for the entire project. Solution: (i) Project Planning:

Steps of preparing the analysis table: First calculate the earliest

event

times E and latest

event times L by forward and backward passes respectively. Then, a) b) c) d) e) f)

Fill in activity numbers and their duration times in the analysis table. Write down start time of activities Early from the analysed network, using the E of the tail events. Write down finish time of activities Late also from the analysed network, using the L of the head events. Calculate start time of activities Late from above by subtracting duration time from finish time Late. Calculate finish time of activities Early from above by adding duration time to finish time Early. Calculate total float of activities by subtracting finish time Early from finish time Late.

Event slack for any event i = difference between the latest time i L and earliest time iE for the event.

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Analysis Table Activity

1-2 1-3 1-11 2-8 3-7 3-8 7-8 7-11 8-11

A B C D E F G H I

Dura tion

Start Time of activities

Finish Time of activities

Float

Early

Late

Early

Late

Total

Free

Indepe ndent

D

= Earliest time of tail event, iE

= (Latest time of head event, jL – D)

= (Earliest time of tail event, jE + D)

= Latest time of head event, jL

[jL – iE – D]

[jE – iE –D]

[jE – iL –D]

16 20 30 15 15 10 3 16 12

0 0 0 16 20 20 35 35 38

8 0 21 24 20 29 36 35 39

16 20 30 31 35 30 38 51 50

24 20 51 39 35 39 39 51 51

8 0 21 8 0 9 1 0 1

0 0 21 7 0 8 0 0 1

0 0 21 0 0 8 0 0 0

The critical path is 1---3---7---11 i.e. (B-E-H) and the project completion time is 51 days. (i) Gantt chart: In this chart the length represents time and the chart itself can be used to record the progress of work. a) b) c) d) e) f)

List activities in order of increasing head numbers. Where two or more activities have the same head number, arrange these in order of increasing tail numbers. Construct a Gantt chart framework with time scale along the top, head numbers down the left-hand side. Set off the first activity in the above list, putting its left-hand end on the 0 week column Mark the tail and head numbers at the beginning and end of the bar. Set off the second activity on the list, aligning the tail number with the head number of the previous activity, provided these numbers are same. If they are not, then align the tail number with the preceding tail number with which it coincides. Repeat steps three and four for all the activities in turn, aligning tail numbers with previous head numbers where possible, alternatively tail numbers with previous tail numbers. Simple rule: “Match the tail number with that same number which is farthest to the right”. Any dummies must be included as single upright lines.

This will result in the Gantt chart shown below, prepared on the basis of earliest start time of activities. Determining the critical path from the Gantt Chart: Starting with the farthest right-hand point (11) of 7-11, draw a line upwards from (7) until it meets the farthest right-hand point matching the left-hand number on the first activity i.e. 7 in this case. Here, the farthest righthand number matching the first left-hand number (7) is the 7 in activity 3-7. The critical path then lies along 3-7. Again starting with 3, draw a line upwards to meet the next right-hand (3) which is farthest to the right – in this case (3) in activity 1-3. The critical path then lies along activity 1-3. So the complete critical path is 13711. Resources Loading: The manpower resource loading is shown by the following histogram. Resource Smoothing: The manpower loading revealed by the histogram is not acceptable. For 30 weeks, the load exceeds the capacity, which can have only one result, namely that activities will take longer than planned, and the overall project time will increase. For 21 weeks, capacity exceeds the loading and this will mean that men are idle. Clearly it is desirable to try to shift some of the earlier over-load into the later under-load. If this could be completely done, then the load would be “smoothed”. Smoothing should be attempted by delaying some non-critical

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activities which have some floats. Activity 1-11 possesses the greatest float, and it should therefore be examined first. This is an trial and error method utilising the floats.

Resource Loading Histogram

The dotted line shows the manpower capacity and the over- and under-loading of manpower.

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