## Chapter

(a) Activity D dangles, giving the project two 'end events'. This network should 6.1 Errors drawing be drawn as below. To aid comparison with the original, the nodes have not activity networks been renumbered, although we would normally do so.

(b) Once again, this network has two end nodes, but in this case the solution is slightly different since we should introduce a dummy activity if we are to follow the standard CPM conventions.

(c) Either this one has a dangle (although, because of the way it is drawn, it is less obvious) or activity E has its arrow pointing in the wrong direction. We need a bit more information before we can redraw this one correctly.

(d) Strictly speaking, there is nothing wrong with this one - it is just badly drawn and the nodes are not numbered according to the standard conventions. It should be redrawn as in the follow ing example.

In this diagram the nodes have retained their original numbers (to aid identification) although they should of course be renumbered sequentially from left to right.

(e) This one contains a loop - F cannot start before G has finished. G cannot start before E has finished and E cannot start before G has finished. One of the arrows is wrong! It is probably activity F that is wrong but we cannot be sure w ithout further information.

6.2 Drawing Brigette's activity network as a CPM network

6.3 Drawing a CPM network

### 6.4 Calculating activity floats

Brigette's payroll CPM network should look like the diagram below. If your diagram is not exactly the same as this check that it is logically the same.

Figu re F.6 Brigelte 's CPM netw ork.

A solution is given in Figure 6.3. If your solution is not exactly the same as this do not worry. Just check that it is logically the same and that it follows the CPM conventions of layout and node numbering etc.

Free float and interfering float for each of the activities are shown in Table F.9 below. Note that activity A has no free float since any delay in its completion will delay the start of activity C. Activity C, however, has a 2-week free float so long as activity A keeps to time. Moat must be regularly monitored as a project progresses since a delay in any activity beyond its free float allowance will eat into the float of subsequent activities.

Table F.9 Activity floats

Activity Total float Free float Interfering float

6.5 Shortening a project duration

Shortening activity F to 8 weeks will bring the project completion dale forward to week 11 - that is, it will save 2 weeks on the duration of the project. However, there are now two critical paths. I -5-6 and I -2-4-6, so that reducing the duration of activity F any further will not shorten the project duration any further. If we wish to complete the project earlier than week 11 we must save time on path 1-5-6 and path 1-2-4-6.

Figure F.7 illustrates a precedence network for Amanda's project showing an 6.6 Theprecedence earliest completion date of day 96. network

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7.1 Brigette's Among the factors that she might consider are the following,