Session guide: Network techniques

This is a technique-oriented session, and best handled by working through an illustration. In order to be ready with all the calculations, the resource person should beforehand have worked through the example given in EXHIBIT 3.

Initiate discussion by asking participants whether they have been able to draw a project graph for the relationships presented in Table 1. Chances are that some of them may have drawn fairly neat graphs while others may have graphs which are difficult to read since lines cross each other blurring the relationships between various activities. At this stage, introduce the concept of network.

Show EXHIBIT 1, explain what a network is, and discuss the components of a network. A network is composed of activities and events. Show EXHIBIT 2. Activities represent a definite stage of work for the project. They have to be sequenced in order of given technical or other relationships. Activities may be real or dummy. Dummy activities are used solely to establish relationships and are of no consequence in terms of time or resources. Each activity consists of a beginning and an end. Events represent a definite point in a total project. Events occur instantaneously and have no duration. They consume neither time nor resources. Draw diagrams of activities and events to illustrate these concepts. Observe that while activities are denoted by arrows, events are shown by circles in a project network.

Using the concepts of activities and events, draw a network for the illustration¹ given as EXHIBIT 3. It is preferable to draw the network in stages, encouraging class participation. Once the network has been drawn (EXHIBIT 4), observe that it:

· shows all the stipulated sequential relationships;
· has a beginning and an end; and
· there are various ways to traverse it from beginning to the end.

1. The example and its solution are taken from pages 141-151 in: Gupta, V.K., Asopa, V.N., Gaikwad, V.R., & Kalro, A.H. No date. Planning Rural Development Projects in Laos: A Guide. New Delhi: ILO-ARTEP.

Observe that several activities can be conducted simultaneously, allowing project duration to be reduced. One does not have to wait for one activity to be completed before initiating another activity unless there is a predecessor relationship. Besides, different times taken by various activities may provide some advantages.

Discuss the need for estimating time for each activity. Note that we may have either a definite knowledge of the time required for an activity or only an estimate of time. Introduce the concepts underlying Critical Path Method (CPM) and the Programme Evaluation and Review Technique (PERT) models. Observe that PERT incorporates uncertainty and controls cost through control of time. In contrast, CPM brings costs into direct consideration. CPM is more suited for institute management and can be used as a planning, monitoring and controlling tool. In contrast, PERT is more appropriate for scientific research projects which involve a high level of uncertainty concerning activity times. Depending on whether PERT or CPM is being used, we can estimate time for each activity. For the PERT model we first obtain optimistic, pessimistic and most likely time estimates, and then compute an expected time, as discussed in the note. Since the discussion in the session concentrates on CPM, we have assumed normal time estimates.

Incorporate into the network the time estimates for the individual activities given in EXHIBIT 5. Show EXHIBIT 6, which is the network with time estimates. Now ask participants how many routes are there from event 1 to event 9. This is tantamount to completing the entire project through all its activities. Let them work through the various paths. There are six different paths (EXHIBIT 7) and the longest one has a total time of 36.2 months. This is called the critical path. Discuss the important features of the critical path. Observe that, while activities on the critical path are being completed within the stipulated time, activities on the other paths (called slack paths) will also be pursued simultaneously and completed during that period. Since the critical path is the longest path, it represents the minimum time required for completing the project. If a project network is modified, the critical path may also change.

Show EXHIBIT 8 and introduce the concept of earliest start and finish times. Note that we compute these in order to gain a better understanding of the interrelationship between various project activities and to try to reduce or control project duration.

Earliest start and finish times are calculated using a forward computation method. Earliest start time is the earliest time that a project activity can be initiated. Obviously, this will depend on completion of the predecessor activities. Add to the earliest start time the time required to complete that particular activity. This gives the earliest finish time. Using the relationships shown in EXHIBIT 8, compute earliest start and finish time for individual activities in the network.

Show EXHIBIT 9 and introduce the concept of latest start and finish times. These are calculated using backward computation: we start with the completion time of objective event (9) for last activity i (8, 9) and work backward. Using the relationships shown in EXHIBIT 9, compute the latest start and finish times for the network. Note that one may compute either the earliest or the latest time estimates. Both need not be computed. The resource person should do these calculations on the board, activity by activity, for the entire network. Show EXHIBIT 10, where these values are tabulated.

Show EXHIBIT 11 and introduce the concept of slack time. Slack may be total or free. Total slack is the difference between the latest and earliest start times of an activity. It can also be calculated as the difference between the latest and earliest finish times. Free slack is the difference between the earliest finish time of an activity and the earliest of the early start times of all its immediate successors. Illustrate the calculation using the partial network in EXHIBIT 12. Use the data on early and late start and finish times given in EXHIBIT 10 and calculate total and free slacks. Incorporate these estimates in the network, as shown in EXHIBIT 13. Note that activities on the critical path will have no slack time. It follows then that activities which are not on the critical path probably have some slack time. Knowing this helps when scheduling activities. The strategy should be to concentrate on activities on the critical path by taking advantage of the knowledge of slack available on activities which are not on the critical path.

Discuss the need for reducing project duration. At this' stage, it would be useful to discuss time and cost relationships as a prelude to crashing the network. Recall that the CPM model has definite time estimates for each activity. In some cases this time can be reduced by providing more support and resources. This is called crashing. Show EXHIBIT 14 and use the data on crashing time and cost to illustrate the process of crashing stage by stage. This should be done with the help of EXHIBIT 15. Observe that, for obvious reasons, only the activities on the critical path will be considered for crashing. Thus, only activities e, h and a should be crashed. We will begin with the activity which has the smallest cost per unit of time. Stage-by-stage crashing should be shown and discussed. As EXHIBIT 15 shows, we begin with the original network (Chart I) and then crash activity e from 4.1 to 2.1 weeks at a cost of Rs 240 per week. This reduces the project duration or the length of the critical path from 36.2 to 34.2 months (Chart II in EXHIBIT 15). Next, we crash activity h from 5 to 4 weeks at a cost of Rs 300 per week; this further reduces the length of the critical path by another week, from 34.2 to 33.2 months (Chart III in EXHIBIT 15).

Finally, we crash activity a from 8 to 6 weeks at a cost of Rs 450 per week and that reduces the project duration to 31.2 weeks (Chart IV in EXHIBIT 15).

Before concluding the session, ask participants whether there are limits to crashing. Obviously, the cost of crashing imposes a limit. In addition, technical requirements may also limit the potential for time reduction.

EXHIBIT 1

THE CONCEPT OF A NETWORK

A network diagram is a graphical representation of all the activities of a project, placing them in their proper sequence and with all interdependencies clearly established. The network diagram provides a complete picture of the project.

EXHIBIT 2

ACTIVITIES & EVENTS

Activities · Real or dummy · Predecessor-successor relationship · Represented by arrows

Events
· Instantaneous occurrence
· Denotes the beginning or end of an activity
· Represented by circles
· Burst or merge events
Event	Activity a ®	Merge event	Burst event

EXHIBIT 3

Illustration: ACTIVITIES AND EVENTS IN A PROJECT PLAN

Stage of work	ACTIVITY			EVENT
	Identification	Predecessor	Successor	Identification	Predecessor	Successor
1	a	-	b, d	(1,2)	2	2
2	b	a	c	(2,3)	2	3
3	c	b	e	(3,4)	3	4
4	d	a	e	(2,4)	2	4
5	e	c, d	f, g, h	(4,5)	4	5
6	f	e	j	(5,6)	5	6
7	g	e	k	(5,7)	5	7
8	h	e	I	(5,8)	5	8
9	i	h	-	(8,9)	8	9
10	j	f	i	(6,8)	6	8
11	k	g	i	(7,8)	7	8

Source: pp. 141-151 in: Gupta, V.K., Asopa, V.N., Gaikwad, V.R., & Kalro, A.H. No date. Planning Rural Development Projects in Laos: A Guide. New Delhi: ILO-ARTEP.

EXHIBIT 4

NETWORK FOR EXHIBIT 3

Figure

EXHIBIT 5

Illustration: TIME ESTIMATES FOR ACTIVITIES

Job identification	Activities predecessor successor		Normal time (months)
a	-	b, d	8.0
b	a	c	8.6
c	b	e	6.3
d	a	e	14.7
e	c, d	f, g, h	4.1
f	e	i	1.1
g	e	i	3.7
h	e	i	5.0
i	h	-	4.2

For PERT:

Expected time (t_e) = (t_o + 4t_m + t_p)/6

where:

t_o = most optimistic time estimate
t_m = most likely time estimate
t_p = most pessimistic time estimate

EXHIBIT 6

ILLUSTRATION INCORPORATING TIME ESTIMATES IN THE NETWORK

Figure

EXHIBIT 7

Illustration: DIFFERENT PATHS THROUGH THE NETWORK

Path	Time for completion (events 1 to 9)
	(months)
1-2-4-5-6-8-9	32.1
1-2-4-5-7-8-9	34.7
1-2-4-5-8-9	36.0
1-2-3-4-5-6-8-9	32.3
1-2-3-4-5-7-8-9	36.2

· Identify the critical path.
· Why is it the critical path?
· What about other paths?

EXHIBIT 8

CALCULATING EARLIEST START AND FINISH TIMES

Earliest start (ES) time Earliest possible time an activity can begin is the latest of the earliest finish (EF) times of the proceeding activities Thus ES (3,4) = EF (2,3) = 16.6 months

Earliest finish time Sum of the earliest time an activity can begin and the time (t) required to complete the activity Thus EF (2,3) = ES (2,3) + t(2,3) = 8 + 8.8 = 16.6 months EF (3,4) = ES (3,4) + t(3,4) = 16.6 + 6.3 = 22.9 months

EXHIBIT 9

CALCULATING LATEST START AND FINISH TIMES

Latest start (LS) time The latest time an activity can be started without delaying completion of the project

Latest finish (LF) time Sum of the latest start time of an activity and the time (t) taken to complete it

Examples LS i (8,9) = 36.2 - 4.2 = 32 months LF i (8,9) = 32 + 4.2 = 36.2 months LS f (5,6) = 32-1.1 = 30.9 months LF f (5,6) = 30.9 +1.1 = 32 months LS a (5,7) = 32 - 3.7 = 28.3 months LF a (5,7) = 28.3 + 3.7 = 32 months

EXHIBIT 10

EARLIEST AND LATEST TIME ESTIMATES

Activity	Earliest		Latest		Slack
	Start	Finish	Start	Finish	Start	Finish
a	0.0	8.0	0.0	8.0	0.0	0.0
b	8.0	16.6	8.0	16.6	0.0	0.0
c	16.6	22.9	16.6	22.9	0.0	0.0
d	8.0	22.7	8.2	22.9	0.2	0.2
e	22.9	27.0	22.9	27.0	0.0	0.0
f	27.0	28.1	30.9	32.0	3.9	3.9
g	27.0	30.7	28.3	32.0	1.3	1.3
h	27.0	32.0	27.0	32.0	0.0	0.0
i	32.0	36.2	32.0	36.2	0.0	0.0

EARLIEST AND LATEST TIME ESTIMATES FOR NA PHOK SEED PROJECT

EXHIBIT 11

TOTAL AND FREE SLACK TIME

Total slack Difference between late start and early start times or Difference between latest finish and earliest finish times

Free slack Difference between early finish time of an activity and the earliest of the early start times of all its immediate successors

EXHIBIT 12

Illustration: PARTIAL NETWORK OF NA PHOK SEED FARM

EXHIBIT 13

SLACK TIME ESTIMATES

Activity	Slack
	Total	Free
a	0.0	0.0
b	0.0	0.0
s	0.0	0.0
d	0.2	0.2
e	0.0	0.0
f	3.9	3.9
g	1.3	1.3
h	0.0	0.0
i	0.0	0.0

TOTAL AND FREE SLACKS

EXHIBIT 14

TIME AND COST ESTIMATES

Job	Activities		Normal time (months)	Crash time (months)	Crashing cost (Rs)
	Predecessor	Successor
a	-	b, d	8.0	6.0	450
b	a	c	8.6	6.6	240
c	b	e	6.3	2.3	72
d	a	e	14.7	14.7	-
e	c, d	f, g, h	4.1	2.1	240
f	e	i	1.1	1.1	-
g	e	i	3.7	2.7	900
h	e	i	5.0	3.0	300
i	h	-	4.2	2.0	-

EXHIBIT 15

Figure