Other Scheduling Methods

Dr. Ayham Jaaron

04.04.2011Chapter 11

PERT and CPMthese are quite similar to each other, and they are often combined.

PERT: (Program Evaluation and Review Technique) it is an event-oriented network analysis technique used to estimate project duration when individual activity duration estimates are highly uncertain. PERT is considered a probabilistic, or stochastic, method.

CPM: (Critical Path Method) it is used to determine critical activities, it is also used when the cost aspect of the project is to be evaluated.

Calculating activity time: (Three time estimates)

so far in our previous problems we have used a single time estimate for each activity duration. These estimates are developed intentionally in the project planning phase.

As a matter of fact, there are several uncertainties with most projects in general. One way of resolving the uncertainty problem is to develop three time estimates for each activity in the project.

When these estimate are used on a project, the resultant network is said to have used PERT technique.

Three time estimates

1) Optimistic Time (a):

This estimate of an activity time is the minimum time an activity would take, if everything goes well. Here consider normal level of efforts and resources, and will not consider crashing the activity.

Three time estimates...cont’d

2) Pessimistic time (b):

It is the maximum time an activity could take, if bad Luck was encountered at every stage of performing the activity. This time estimate takes into account problems in development, fabrication, execution...etc. But not weather and environmental snags.

Three time estimates..cont’d.

3) Most Likely time (m):

This is the normal time necessary to complete the activity, and is the time that would occur most frequently if the activity would be repeated several times. In reality, this would be the time required where trivial obstacles (e.g. Arriving 15 minutes later than schedule) could occur that could be easily skipped.

Three time estimates..cont’d.

• The preceding values are estimated by the scheduler or project manager, who uses his or her experience and good judgment to do so.

• The mean weighted value for these three durations is called the expected duration (Te)

Three time estimates

• Once we have the above three estimates for each activity, we shall do the following:

1- calculate the expected mean time for each activity.

Te= (a+4m+b)/6

2- calculate the variance of the activity times.

Variance= (b-a/6)2

3- Make statistical inferences about project completion time.

Problem• Calculate the expected time required to complete

each of the following activities and construct the network using the AON technique?

Activity

Predecessor Optimistic time

Pessimistic time

Most likely time

A --- 10 22 22

B --- 20 20 20

C --- 4 16 10

D A 2 32 14

E B,C 8 20 8

F B,C 8 20 14

G B,C 4 4 4

H C 2 16 12

I G,H 6 38 16

J D,E 2 14 8

Uncertainty of project completion time

• When discussing project completion dates with senior management, the PM should be able to determine the probability that a project will be completed by the suggested deadline.

• To find this probability, a variance can be used to measure the dispersion of population and these are elicited from the activities on the critical path.

Uncertainty of project completion time

• Once we have the three time estimates for each activity, we shall do the following:

1- calculate the expected mean time for each activity.

Te= (a+4m+b)/6

2- calculate the variance of the activity times.

3- Make statistical inferences about project completion time.

Uncertainty of project completion time

• Variance describes how far values lie from the mean.

Variance= Б2 = (b-a/6)2

Where: Б= standard deviation• Remember, it is the critical path that determine

the expected duration of the project. For this reason, the means and variances of activities on critical path is of great importance in finding uncertainty of project completion time.

Uncertainty of project completion time

The distribution of the project duration times, is often approximated as a normal distribution. Therefore, we calculate the standard normal variable as:

Z = (Ts-Te) / √ σm2

where: Ts = Scheduled project completion time (determined by contract)

Te = expected duration of the project.

σm2 = sum of variances on the critical path.

Cumulative standard normal distribution for Z-values

Problem

• For the following project whose information are provided in the table below, your manager is concerned whether the project will be completed in 50 days as agreed on contract. Can you provide a probability measure to meet your manager inquiry?

Activity Predecessor Optimistic time

Pessimistic time

Most likely time

Te

A --- 10 22 22 20

B --- 20 20 20 20

C --- 4 16 10 10

D A 2 32 14 15

E B,C 8 20 8 10

F B,C 8 20 14 14

G B,C 4 4 4 4

H C 2 16 12 11

I G,H 6 38 16 18

J D,E 2 14 8 8

Continued...

• After drawing the network, the critical path can be identified to be: a-d-j and the total project time is 43 weeks.

• Therefore, we are interested in variances for these three activities to find total variances on critical path.

Problem 2

• In you previous problem, what scheduled deadline is consistent with a manager desire of having a 95% probability of on-time completion?

Problem 3

• For the following project information, find the probability that the project will be completed in 26 days. Also, determine the completion time corresponding to 98% probability of on-time completion?

Activity

Predecessor

Optimistic time

Pessimistic time

Most likely time

Te Variance (b-a/6)2

A --- 1 7 4 4 1

B --- 2 2 2 2 0

C A 2 8 5 5 1

D A 3 5 4 4 0.11

E C, B 4 8 6 6 0.44

F C,B 2 2 2 2 1

G D,E 3 9 6 6 1

Continued...

• After making the network, the critical Path is: A-C-E-G and has a total duration of 21 weeks.

• Total variances on CP= 3.44

• Z = (Ts-Te) / √ σm2 = 2.695

• The probability is 99.64%