Programme Evalution and Review Technique (PERT) and Simulation

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来自 Indian School of Business 的课程

IT Project Management

149 个评分

Indian School of Business

IT Project Management

149 个评分

课程 4（共 6 门，Specialization Business Technology Management）

The concepts and use of project management tools, techniques and methodologies are becoming all pervasive. This course addresses project management in the context of IT projects, including software projects. Using the framework of project life cycle, the course covers various aspects pertaining to (i) project initiation, (ii) project planning and scheduling, (iii) project monitoring and control, and (iv) project termination. For planning and scheduling of projects, the use of project network and estimation of time and cost are covered in detail. Scheduling of projects with resource limitations is covered next. Risk assessment methods including simulation and risk reduction approaches are also be covered. The students will be required to use the software @risk to simulate project completion times. The use of Earned Value Analysis for Project Monitoring and Control is emphasized. For Software Project Management, the Waterfall Model and Agile Project Management are covered in detail.

从本节课中

Resource Scheduling and Risk Management

Activities in a project typically require the use of resources such as people, material, equipment and working capital. The schedule for the activities that we had calculated in the previous module assumes that adequate resources are available as and when required. However, in practice often adequate resources may not be available as required and the schedule may have to be modified. There are two types of problems when resource requirements are considered. One is the Resource Smoothing Problem and the other is the Resource Limitation problem. In the first one, i.e. the Resource Smoothing Problem, although the resources are available as and when required, we would want to find a schedule that “smoothes” the use of resources without delaying the project completion time. Critical Chain Project Management (CCPM) is the next topic dealt with in this module. CCPM has not gained universal acceptance although it is being used by some organizations with positive results. CCPM places a lot of emphasis on aggressive estimation of activity durations and provides for buffers to take care of some delays. With Risk Management, we first define what risk is and then discuss the risk management process including risk identification, risk assessment and various ways of reducing exposure to risk. Risk monitoring and control including change control process are also covered. Finally, the Program Evaluation and Review Technique (PERT) including a simulation approach to finding the distribution of the project completion time is covered as the last topic in this module. As in the previous modules, towards the end of this module, we present some practical aspects pertaining to the concepts covered. This again is done through a Q & A format with Mr. Prashun Dutta, Advisor - Gaiga Smart Cities

Resource Scheduling11:09

Critical Chain Project Management5:19

Risk Management15:30

Programme Evalution and Review Technique (PERT) and Simulation9:12

(Optional Learning) Interview with Prashun Dutta, Gaiga Smart Cities7:30

与讲师见面

M Rammohan Rao
Professor Emeritus
Operations Management

[MUSIC]

In this module, we will discuss program evaluation and

review technique, or PERT as it is typical known as.

PERT typically includes assimilation of the project.

Historically, critical PERT method was developed by DuPont

in the context of preventive maintenance which is carried out on a regular basis.

The work breakdown structure resulted in the identification

of the various activities constituting the preventive maintenance project.

The precedence relationships among the activities leading to the network diagram

and the activity durations which are unknown with a high degree of accuracy.

The requirement was to complete the preventive maintenance as quickly as

possible so as to reduce the downtime of the missionary.

PERT, on the other hand, was developed in the context of an R & D project

where there was considerable uncertainty in many of the activity durations.

But assumes that an activity duration follows a beta distribution,

which is different from a normal distribution

in that the activity duration is always positive.

And there are three parameters, namely optimistic estimate denoted by a,

pessimistic estimate denoted as b, and the most likely estimate denoted as m.

The concept of an optimistic estimate a,

is that there is a chance of 1 in 100 of completing the activity in less than a.

Similarly, the concept of a pessimistic estimate b,

is that there's a chance of 1 in 100 for the activity exceeding the units of time.

The assumptions of a better distribution for

the activity duration implies that the expected or

average duration is equal to a + 4 times the most likely estimate plus b.

The entire thing divided by 6.

As an administration, the better distribution for an activity,

and the distribution of the project completion time, and shown in the diagram.

The variance for the activity duration is given by

somewhat complicated expression as shown in the diagram.

As an illustration, the triangular distribution for

an activity is also shown in the diagram.

Knowing the distribution of the time for each activity,

we would like to find the distribution of the project completion time, so

that we can answer questions such as one, what is the probability of the project

completion time exceeding a specified value?

And two, what are the chances that an activity is on a critical path?

One approach of finding the distribution of project completion time

is to use the expected duration for each activity and find the critical path.

Then assuming independence to the activity durations, the variance or

the length on the duration of the critical path is obtained by adding the variances

of the durations for the activities on the critical path.

The standard deviation of the length of the critical path is,

of course, the square root of the variance.

Finally, assuming the distribution of the project completion time

is a normal distribution, one can find the probability of the project completion time

exceeding a specified value.

The above approach is not correct, although it is simple to calculate.

The approach has two flaws.

First, because the uncertainty in activity durations, the same path my not

be critical in different realizations in the activity durations.

The same path is always the critical path only in very rare instances where

the critical path is the dominant path in the sense that the length is always

greater than the length of the other paths in all realizations of activity durations.

Second, the assumption or normality of the distribution of project completion time

would be valid only if the critical path has a large number of activities.

Because the Central Limit Theorem which states that the sum of a large number of

independent identically distributed random variables is approximately normal,

is valid in most instances only if large is at least 25 to 30.

Except possibly when the distribution of this activity duration is a uniform

distribution, in which case the number may be as low as 12 to 15.

The correct approach to finding a distribution of the completion time is to

use simulation.

It is a mathematical model that's an abstraction of the real world.

And the model is run typically on the computer, and

not in the real world, to find out the possible outcomes.

And arrive at appropriate actions as necessary to

be implemented in the real world.

The user simulation in PERT is [INAUDIBLE] through a simple example.

We consider a project where we have ten activities denoted as a, b,

c, d, e, f, g, h, i, and j respectively.

The president's relationship among the activities are shown in the table.

The three estimates, minimum, mostly, and maximum estimates for

the duration of each activity are also shown in the same table.

The duration of each activity is seen to follow a triangular distribution

with the associated three parameters for that activity.

The associated network is shown in the diagram.

Assuming a triangular distribution for each activity, the expected durations and

the variances are shown in the next table.

Each trial's simulation approach is to generate a random value for

each activity duration from its assumed distribution.

There are different approaches to generate random variants from an astute

distribution.

And these approaches do not cover,

are available in most of the books on simulation.

With the general directive activity durations, we find the critical part, and

note the project completion time and the particular activities.

Then, we repeat the drive safer about 10,000 times and

find 10,000 project completion times which gives us a of all the completion times.

In Azure, we also get the number of times an activity is on the critical part.

The proportion of trials in which an activity is on the critical path

is referred to as the criticality index for that activity.

The summary statistics for

1,000 simulation runs using the software @RISK are shown in the table.

The criticality index for each activity is shown in the next table.

And this example if you use the expected duration of each activity the critical

that is activity BG and I.

The expected completion time for the project is 44 and

the variance for completion time is 44.67.

Currently the standard deviation is equal to square root 44.67 equal to 6.68.

The table below gives the probability of the project completion time less than or

equal to specified value as calculated by the incorrect approach of assuming

of a normal distribution, the distribution of the length of the same critical path

consisting of activities B, G, and I.

The same table gives that correct values obtained by a simulation approach

using the software @RISK.

Note that the incorrect or the estimates required probabilities

because in some realizations of the activity do, then the part B, G,

I has a length less than or equal to specified value.

Some other part may have lengths greater than the specified value.

You briefly outline the simulation approach,

when there are resources limitations.

In this case, as the project progresses,

decisions must be made as to which activities take priority.

It should be noted the realizations or

the duration of the activities to be done in the future are not known currently, and

will be known only in the future, perhaps after the activity is completed.

With resource limitations, each trial and

simulation of the project must be done starting from the beginning.

And incrementing the crop but

unilateral time in the activity durations are measured.

When one of the activity is completed,

a decision has to be made as to which of the succeeding activities maybe started

if the resources required exceed availability.

A heuristic as discussed in the module and resource should be used.

The duration for the activities that had to be

started immediately must be generated from their respective distributions.

The clock is then incremented by a day and

the process is continued until the project is completed.

One try the simulation is completed then the project is completed.

The activity that constitute the critical change should be noted.

The entire process is then repeated for the remaining times of simulation

then by generating say 10,000 values for the project completion time.

This would give the distribution of the project completion time and

the criticality index for each activity can be calculated.

This completes the module on PERT.

[MUSIC]

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