Chapter 9 : Project management

9.1

The PERT method (Program, Evaluation and Review Technique)

This method can also be applied to carry out studies or projects. It was perfected in 1958 for the setting-up of the POLARIS programme that was to coordinate the activities of several thousands of organizations. It has since then been a great success and is now used in a lot of firms, small or big, private or public. At the same period, other methods appeared such as the Critical Path Method (CPM) and the potentials method. All these methods have a lot in common. In our course, we will only focus on the PERT method. 9.1.1 Definition of the method The PERT method is a scheduling method or a programming and control technique ; it enables to schedule and control the carrying out of a number of activities leading to the realization of a determined project according to a fixed objective. The problem in project scheduling is to determine when each activity must begin or end so that the entire project can be completed in time. Examples : building a new hospital, development of advertising campaigns, and so on. In this context, to programme or to schedule means to draw up a detailed timetable concerning the beginning and the end of the different activities and, of course, the beginning and the end of the whole project. To control means to monitor the carrying out of this programme, to modify it according to the real evolution of the project and to draw interesting conclusions. These programming and control activities are done according to a determined objective or to a criterion we have to optimize. This criterion may be -

the time : we have to minimize the global lead time of a project. the resources : we have to minimize the necessary resources by balancing the loads. the costs : we have to minimize the global cost of the operation (PERT COST).

In a general way, we will first try to optimize the global lead time and from that programme, we will examine the other criteria. 9.1.2

Network representation

9.1.2.1 Preliminary convention The problem elements are of two types : -

The tasks or activities are the elements that take some time, consume time.

-

The events are the elements that do not consume time. They indicate a stage in the project realization.

As the model used in this method is graphic, it is important to agree upon the used graphic symbols : -

the events are represented by nodes, they are identified by a number or a letter.

-

the activities are represented by arrows, the length of which has no significance. They are identified by a number or a letter.

9.1.2.2 First stage : problem analysis – identification of the factors As we have to develop a programme of activities, the first stage consists in identifying all the tasks we have to carry out in order to meet the objective. We thus draw a list of all the necessary tasks. Practically, this problem is not as simple as it seems to be. Any omission at that level may completely modify the solution. 9.1.2.3

Second stage : data quantification and network development

(a) data quantification, that is to say research concerning the lengths of the activities. We try to determine the length of each identified task in the first stage. The way we can determine the length depends on the field of the problem : -

determined field : if we deal with an activity that has a precise operating mode with a standard time, we know the length : t.

-

predictable field : some activities of a repair shop have predictable lengths (ex : the repairing of a crankshaft depends on the number of fissured bearings we find when we dismantle it). We can give a statistical estimate of the length : L(t).

-

uncertain field : the length of some works (research works, works influenced by meteorological conditions, and so on.) cannot be determined, even in a predictable way. We can then proceed by giving 3 estimates as regards the length :

-

optimistic estimate (t0) : we assume that all circumstances are favourable ;

-

pessimistic estimate (t p ) : we assume that all circumstances are unfavourable ;

-

average estimate (t m) : we assume that everything happens as usual : some circumstances being favourable, others not.

These estimates are at least partially subjective. We then combine these 3 estimates by the following formula in order to find out the length of the task : t 0 + 4t m + t p t= 6 (b) network development In this case, the network is a logical representation of the sequence of activities. This representation is given the form of a chart. We talk about PERT diagram or network. We can find out these relations by asking the 3 following questions for each activity : What are the activities that must be carried out before the one I consider ? What are the activities that immediately follow the one I consider ? What are the activities that can be carried out at the same time as the one I consider ? Actually, these 3 questions are 3 different ways of formulating the same question. (c) let us take a simple example We have identified 7 tasks for which we have estimated the length ; we have asked the above questions for each one of them. All answers and data are to be found in the following table : We notice that the task n°5, that lasts 5 days, must be preceded by the tasks n°1 and 4 and followed by the task n°6. We also notice that the process starts with the carrying out of the tasks n°1 and 2, and ends with the carrying out of the tasks n°6 and 7. Task n°

Length (days)

1 2 3 4 5 6 7

5 4 3 2 5 8 5

Tasks that must Tasks that must precede follow 2 2 1,4 3,5 3

5 3,4 6,7 5 6 -

Let us represent all these elements as a diagram.

5

C

1

E

t=5

6

t=5

t=8

A

t=2

4

F

t=0

7

2 t=4

3

B

t=5

D

t=3

The event A, beginning of the operations, indicates the beginning of the carrying out of the tasks 1 and 2 that are not preceded by any other one. In the nodes that represent the events, we should leave spaces where we can write the time data. A pragmatic work method for the representation is the following : Start with the start and end events with the arrows that respectively go from them and come to them. 1

6 F

A

7

2

Then draw intermediate nodes with the arrows that come to them and those that go from them. 4

2 B

3

Try to make the ends and arrows meet by eventually moving the nodes so that these arrows do not cross each other.

If we follow the inferior arc of the scheme, we notice that the task 2 is followed by the task 3, being itself followed by the end task 7. Just as on the superior arc, the task 1 is followed by the task 5, followed itself by the task 6. But the task 5 must also be preceded by the task 4 that follows the task 2. So we imagine a fictitious task of no length between the events D and E in order to express the relation between the tasks 6 and 3. In order to indicate that the task 6 can only begin if the task 3 is completed : we divide the first node of the preceding drawing in two with an arrow between the two (well-oriented !).

5

E

6 F 7

3

D

Finally, we write its length on each arc. 9.1.2.4

Third stage : network exploitation

We will describe the network exploitation using the example above. We must though choose a criterion : let us assume that our problem consists in carrying out the 7 tasks in a minimum time. (a) For each event A, B, C, we determine the earliest start time (ST) of happening. -

event A : it is the beginning of the operations, so it can happen at the time 0. We write 0 in the left space of the node.

-

event B : it is the end of the task 2, the beginning time of the tasks 3 and 4, it can happen at the time 0 + 4 D. The earliest finishing time is actually equal to the earliest beginning time + the activity length.

-

event C : it is the end of the tasks 1 and 4, the beginning of the task 5, it can happen at the earliest after 6 D because, although the task 1 only lasts 5 days, the task 4 that follows the task 2 can only be completed after 4 + 2 = 6 D. Both activities must be completed. And so on, we then know that the whole operation cannot be completed in less than 19

days. It is a first result but maybe not the most interesting one.

(b) Let us once again consider the events one by one, starting with the last one, and calculate the latest start time (LS) of happening or, in other words, the moment when it can still happen so that the whole operation is all the same completed in 19 days. The event F can and must be completed in 19 D, we write 19 in the middle space of the node. In order to have completed F in 19 D, -

the event E must happen at the latest after 11 D, we write 11 in the middle space ; the event D must happen at the latest after 14 D as the activity 7 lasts 5 days but we must not forget that D must also precede E that can at the latest happen after 11 D. Thus, the latest time for D is also 11 ; the event B must happen at the latest after the shortest of the 2 times given by the arrows that go from it, that is to say 11 – 3 = 8 or 6 – 2 = 4, so after 4 D ; the event A must happen at the latest after the shortest of the 2 times given by 4 – 4 = 0 and 6 – 5 = 1, that is to say 0 D.

C 1 t=5

6 6

E

5 0

t=5

t=8

A 1 0 0

6

11 110

F t=2

4

0 2 t=4

t=0

7 B 4 4

3 0

t=3

D

19 190

t=5

7 110

(c) We notice that for some events, the earliest and latest times are the same. There is no slack for these events : they are critical. Any delay in a critical event automatically leads to a delay in the carrying out of the whole operation. A task may be considered critical if it meets these 3 conditions : -

the start event is critical ; the end event is critical ; the difference of time between its end event and its start event must be equal to its carrying out length. The whole of the critical activities constitutes the critical path of the project.

As regards the carrying out of the non-critical activities, we have a slack. In the example, the activity 3 lasts 3 days. It can begin at the earliest after 4 D and end at the latest after 11 D, we thus have a slack of 4 D.

C 1 t=5

6 6

E

5 0

t=5

11 11 0

t=8

A 1 0 0

F t=2

4

0

t=0

7

2

B

t=4

4 4

9.1.2.5

6

3 0

t=3

D

19 19 0

t=5

7 11 4

Fourth stage : solution analysis

(a) The developed network provides us with management information: - the minimum necessary time to carry out the whole project ; - the critical path. The model is thus a control tool. It indicates the critical activities, that is to say those that require a particular attention. It also indicates the moment when each activity of the critical path is to begin or to end. (b)

As regards the non-critical activities, it is interesting for the person who organizes the production to know the slacks, as they indicate the limits of his freedom to act regarding the carrying out of the project. We therefore have to distinguish 3 slacks. If we consider an activity ij limited by the events i and j, we have :

i

j

1 ti Ti 0 0 The total slack = mt

mt

t = tij

1 tj Tj 0

= Tj - ti - tij

The free slack : is the maximum delay we can accept for an activity, assuming that it has begun at the earliest, without preventing the beginning at the earliest of the following activities : mf = tj - ti - tij

The independent slack : is the maximum delay we can accept for an activity, assuming that it has begun at the latest, without preventing the beginning at the earliest of the following activity : mind = tj - Ti - dij

If we consume the total slack, it influences the two events i and j and can lead to the appearance of a new critical path or to the modification of the critical path. It is thus the coordinator of the different activities who can handle the total slacks. The free slack does not influence the following activities but it is only completely available if the preceding activity is carried out in time in order to enable ij to begin at the earliest. The independent slack completely belongs to its activity and is not influenced by the preceding or following activities. It thus constitutes a freedom of action that may entirely be given to the person in charge of the carrying out of an activity. Slack calculation is as important for the planning of a project as for identifying the critical path. A judicious study of the slacks will enable an optimal use of the available means. During the carrying out, the person in charge knows where the reserves that can be directed towards the critical areas are. The model also shows us how we can modify the problem data in order to improve the global result. For instance, if we allocate more resources to a task of the critical path by removing them from another non-critical task, we can maybe shorten the length of the whole operation. 9.2 GANT's diagram 9.2.1 Description When we have finished calculating the PERT network, it is interesting to show our results in the form of a diagram representing the activities according to time. The time is represented on the horizontal axis, the activities on the Y-axis. The diagram indicates the beginning at the earliest, the length and the end at the latest of each activity. The following diagram represents the activities of our example.

Tasks\Time

1 2 3 4 5 6 7

1 2 3 4

9.2.2

Optimization of the use of resources

GANT's diagram is a real timetable of the activities and is thus a very practical means to control the carrying out of a project. But it is even more a tool enabling the optimization of the use of resources by balancing the loads (workforce, machines, transport means, and so on.).

EXAMPLE -

Summary table of the tasks Task 1 2 3 4 5 6 7 8 9

Length 6 4 5 3 7 4 4 6 2

Preceded by 2 1, 5 2 1, 5 3,4 6, 7 3, 4

Followed by 4, 6 3, 5 7, 9 7, 9 4, 6 8 8 -

-

PERT diagram

C 1

E

6

11 11 0

t=4

18 18 0

t=6

t=6

A 1 0 0

t=7

5

0

8 F

4 t=3

t=4

7

24 24 0

9

2

3

B

t=4

4 4

t=5

0

D

t=2

14 14 0

Minimum length of the project : 24 days. Critical path : task 2, 5, 4, 7, 8. -

GANT's diagram

Let us assume that the staff is able to carry out any of these tasks, the problem is to spread these tasks over the time in order to minimize the necessary number of persons, enabling a continuous rotation and respecting the fixed global lead time. GANT's diagram will help us to solve this problem. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1 2 3 4 5 6 7 8 9 Task: 2

5

4

7

8

The activities of the critical path can follow one another on one time axis (1). Concerning the other activities, we have to make them slide between the earliest and latest moments in order to minimize the maximum number of activities on a same vertical, that is to say to minimize the number of activities that must take place at the same time or, in other words, minimize the number of teams. In this example, we have been able to limit the number of teams to 2. 9.3 Extension of the method : PERT-COST In the examples we have up to now seen, we have agreed that time was the criterion. We may though choose other criteria and thus extend the application field of the method. To minimize the costs is often an essential objective and many variants of the PERT method also aim at this objective. We will quickly describe the principle of a PERT-COST : (a)

As in the PERT method, we first assess all the necessary tasks.

(b)

We then quantify by estimating the length of each identified task. Moreover, for each task, we try to determine the relation between the cost of the task and its carrying out length. In most cases, this curve looks like the one below.

Cost

Length A length that is too short implies the use of numerous resources and expensive means (overtime hours or shifts). A length that is too long brings about a bad use of resources and waste. There is usually an optimal length to which a minimal cost corresponds.

(c)

We then establish the model as in the PERT method by selecting the optimal lengths (except if there is a constraint for one length). By doing that, we already have the minimum cost for all the tasks that belong to the critical path, as they are carried out one after the other in their optimal length.

We then analyse the other tasks step by step in order to reduce the total cost. Conclusion The PERT method is a planning tool (setting-up of a programme of activities and determination of the lead times), an organization tool (allocation and minimization of the resources), a coordination tool (underscoring of the relations between the activities), a control tool (assessment of the project progress in practice) and a management tool.

Project management : exercises

1.

Give the main characteristics of the PERT method.

2.

What is a critical activity ? What are the conditions for a task to be critical ?

3.

With the graphic method of the CPM, find out the minimum length of the project having the following tasks : Task 1 2 3 4 5 6 7 8 9 10

Length 5 4 3 5 6 2 3 4 5 4

Precedence 1 2 2 3, 4 3, 4 5 6 7, 8

Draw GANT's diagram and the critical path. 4.

During the carrying out of a project, what does happen if a machine that is necessary for a task of the critical path breaks down ? What are your solutions ?