## Limitations

The limitations of the graphical method are basically the size of the bar chart paper and therefore the number of activities. Most programmes are drawn on either A1 or A0 size paper and the number of different activities must be compressed into the 840 mm width of this sheet. (It may, of course, be possible to divide the network into two, but then the interlinking activities must be carefully transferred.) Normally, the divisions between bars is about 6 mm, which means that a maximum of 120 activities can be analysed. However, bearing in mind that in a normal network 30% of the activities are dummies, a network of 180 to 200 activities could be analysed graphically on one sheet. Briefly, the mode of operation is as follows:

1 Draw the network in arrow diagram or precedence format and write in the activity titles (Figures 21.9 and 21.10). Although a forward pass has been carried out on both these diagrams, this is not necessary when using the graphical method of analysis.

2 Insert the durations.

o ? io i5* i? 2i o ? !io is \ i? !2i o 8 io¿ i3 \. i5 2i¿ 23

Figure 21.9 AoA Network

 o e e e 2 B B 3 11 A B C 4 4 1o 1o 4 12 12 4 1S
 o ? ? ? 3 1o 1o S 1S 1S 2 1? 1? 4 21 D E F G H —1 o o ? ? o 1o 1o o 1S —1 1S o 1? 1? o 21
 o B B B 1 9 1o 3 13 13 1 14 1S 4 19 21 2 23 J K L M N P 4 4 12 12 4 13 13 3 16 16 3 1? 1? 2 21 21 o 23

Figure 21.10 AoN Network

Figure 21.10 AoN Network

3 List the activities on the left hand vertical edge of a sheet of graph paper (Figure 21.11) showing:

(a) Activity title.

(c) Node no. (only required when using these for bar chart generation).

4 Draw time scale along the bottom horizontal edge of the graph paper.

5 Draw a horizontal line from day 0 of the first activity which is proportional to the duration (using the time scale selected) e.g. 6 days would mean a line 6 divisions long (Figure 21.11). To ease identification an activity letter or no. can be written above the bar.

6 Repeat this operation with the next activity on the table starting on day 0.

7 When using arrow (AoA) networks, mark dummy activities by writing the end time of the dummy next to the start time of the dummy e.g. 4 ^ 7 would be shown as 4,7 (Figure 21.13).

8 All subsequent activities must be drawn with their start time (start day no.) directly below the end time (end day no.) of the previous activity having the same time value (day no.).

Days

A

6

B

2

C

3

D

7

E

3

F

5

G

2

H

4

J

8

K

1

L

3

M

1

N

4

P

10 L 113 FF

13 M 114

15 FF

Free float

21 P 123

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Days

Figure 21.11 Bar chart

Free float

9 If more than one activity has the same end time (day no.), draw the new activity line from the activity end time (day no.) furthest to the right.

10 Proceed in this manner until the end of the network.

11 The critical path can now be traced back by following the line (or lines) which runs back to the start without a horizontal break.

12 The break between consecutive activities on the bar chart is the Free Float of the preceding activity.

13 The summation of the free floats in one string, before that string meets the critical path is the Total Float of the activity from which the summation starts, e.g. in Figure 21.11 the total float of activity K is 1 + 1 + 2 = 4 days, the total float of activity M is 1 + 2 + 3 days and the total float of activity N is 2 days.

The advantage of using the start and end times (day nos.) of the activities to generate the bar chart is that there is no need to carry out a forward pass. The correct relationship is given automatically by the disposition of the bars. This method is therefore equally suitable for arrow and precedence diagrams.

An alternative method can however be used by substituting the day numbers by the node numbers. Clearly this method, which is sometimes quicker to draw, can only be used with arrow diagrams as precedence diagrams do not have node numbers. When using this method, the node numbers are listed next to the activity titles (Figure 21.13) and the bars are drawn from the starting node of the first activity with a length equal to the duration. The next bar starts vertically below the end node with the same node number as the starting node of the activity being drawn.

As with day no. method, if more than one activity has the same end node number, the one furthest to the right must be used as a starting time. Figure 21.12 shows the same network with the node numbers inserted and Figure 21.13 shows the bar chart generated using the node numbers.

Node no.

A

1-2

B

2-3

C

3-4

D

1-5

E

5-S

F

6-7

G

7-8

H

8-9

J

1-10

K

10-11

L

11-12

M

12-13

N

13-14

P

10 K 111

12 M 113

Free float

0 1 2 3 4 5 S 7 B 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Days

Figure 21.13 Bar chart

Figure 21.14 shows a typical arrow diagram and Figure 21.15 shows a bar chart generated using the starting and finishing node numbers. Note that these node numbers have been listed on the left hand edge together with the durations to ease plotting.

### Time for analysis

Probably the most time-consuming operations in bar chart preparation is the listing of the activity titles, and for this there is no short cut. The same time, in fact, must be expended typing the titles straight into the computer. However, in order to arrive at a quick answer it is only necessary at the initial stage to insert the node numbers, and once this listing has been done (together with the activity times) the analysis is very rapid. It is possible to determine the critical path for a 200-activity network (after the listing has been carried out) in less than an hour. The backward pass for ascertaining floats takes abut the same time.

Drains 1

Foundations Brickwork Ground slab

Windows Doorframes

Carpenter Roofing

Plumber

Electrician

Joiner Finishes

Evacuate ^ trench ^

Concrete bed

Evacuate 7

Concrete floors

Rrickwork "

10 Brickwork 15 17 Ground 20 Brickwork 30 33 Brickwork 40

33 ^.--"38 Floor boards/ 42 Joists ---50 Decking Felt

Deliver 30^ Jdsts gg Floor boards timber /TA 1st floor . /TTV—"" stairs

Deliver plumb, fittings

Deliver elect, fittings

50 54 60 70

Clear site

Figure 21.14 Arrow diagram of house

Critical activities -w

Dummy activities---

Time periods in work days

 Activity S F Time Dummies Floats 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 Excavate trench Concrete bed 2 2 3 6 2 3 3 I r~i Lay and joint pipes Test Excavate foots 4 1 6 7 8, 3 3 0 r~ 1 1 n Concrete foots Brickwork to d.p.c 6 7 8 3 7 0 0 Hardcore Ground slab Brickwork g -1 10 10 13 2 3 10 16, 20, 17, 14, 0 0 0 Windows delivered Fix frames g. fl. 1 11 12 4 2 13, 14, 16, 17, 20, 24 8 I zn ( )ritica 1 acti\ ityra Deliver timber Joists 1st fl. Brickwork 1 - r 14 16 15 19 3 3 7 16, 21, 23, 17, 24, 27 0 0 I i F :loat I i Fix frames 1st fl. Deliver plumb, ftgs 17 1 20 2 5 19, 24, 39 i— i Plumber g. fl. Deliver elec. ftgs Electric g. fl. 20 1 21 26 21 22 5 3 5 23, 28 30 0 I 1 i Floor boards stair Joists roof 24 25 4 3 26, 28, 30, 33 0 0 ^BS Plumber 1st fl. Electr. 1st fl. Decking roof 26 28 30 27 29 31 5 5 2 30, 33 4 0 0 1 BBS Felt roof Joiner 1st fix ho 2 3 34, 0 1 1 1 Plasterer Joiner 2nd fix Painter 36 37 6 10 10 0 0 0 Clear site 37 38 3 0

Figure 21.15 Bar chart of house

Figure 21.15 Bar chart of house