PERT MCQ Quiz in বাংলা - Objective Question with Answer for PERT - বিনামূল্যে ডাউনলোড করুন [PDF]

Concept:

Expected time: It represents a particular time of an activity that has 50% chances of being met and 50% chances of being exceeded.

The expected time (te) is given as:

\({{\rm{t}}_{\rm{e}}} = \frac{{{{\rm{t}}_0} + 4{{\rm{t}}_{\rm{m}}} + {{\rm{t}}_{\rm{p}}}}}{6}\)

Also, Standard deviation (σ) is given by \(\frac{{{{\rm{t}}_{\rm{p}}} - {{\rm{t}}_0}}}{6}\)

 Variance (σ ²) is given by \(σ^2 = {\left( {\frac{{{t_p} - {t_o}}}{6}} \right)^2}\)

Where, tp = Pessimistic time, t0 = Optimistic time, tm = Most likely time

Calculation

Given:

 t0 = 2 weeks, tm = 4 weeks, tp = 9 weeks

\(∴ {{\rm{t}}_{\rm{e}}} = \frac{{2\ + \ 4 \times 4 \ + \ 9}}{6}\)

 t e = 27/6 = 4.5 weeks

Standard deviation is given by

 \({\rm{σ }} = \frac{{\left( {9 - 2} \right)}}{6} = 7/6\)

 ∴ Variance = σ ² = (7/6)² = 49/36

Concept:

Critical time:

• In project management, the critical path is the longest sequence of tasks/activities, that must be completed to successfully conclude the project, from start to finish.
• So, it is also the minimum possible time, in which the project is said to be completed and hence also called project completion time.

Calculation:

Given:

T_A = 8 Days, T_B = 11 Days, T_C = 6 Days, T_D = 12 Days, T_E = 7 Days, T_F = 16 Days, T_G = 9 Days

∴ The duration of project completion is 40 days ie along the critical path A - B - D - G

Explanation:

Bar chart (Gantt chart):

(i) It is a pictorial chart.

(ii) It has two coordinate axes, the horizontal axis (coordinate) represents the elapsed time and the vertical axis represents the job or activity to be performed.

From the above Gantt chart, it is clear that horizontal lines, which are blue in color show the activity of the project

(iii) The beginning and end of each bar represent starting and finishing times of a particular activity respectively.

(iv) The length of the bar shows the time required for completion.

Limitation of a bar chart:

(i) Lack of degree of detail.

(ii) A bar chart does not show the progress of work and hence it can not be used as a control device.

(iii) A bar chart is unable to depict the interdependencies of various activities clearly.

(iv) No provision to account for time uncertainties.

(v) Bar chart can not distinguish between critical and non-critical activities and hence resource smoothening and resource-leveling can not be done.

Concept:

PERT stands for "Programme Evaluation and Review Technique​". This network model is used for project scheduling.

Difference between PERT and CPM (Critical Path Method)

Concept-

Probability factor \(z = \frac{{x - \overline x }}{\sigma }\)

Where x̅ = mean, σ = std. deviation.

For z = 0, P(z) = 50%

For z < 0, P(z) < 50%

For z > 0, P(z) > 50%

In this probability distribution, the curve is symmetric about mean that is

The area covered under the entire curve is 1 unit. So area covered upto a point which is less than mean will be less than 50%.

Explanation:

Mile Stone chart:

• It is a modification over the original Gantt chart (Bar Chart). MIlestone is key events of main activities represented by the bar. Therefore they give an idea about the completion of sub-activities.
• Controlling can be better achieved with the help of milestone charts. But still, activity interrelationship and accountability of time uncertainty can not be depicted which can be overcome in-network technique. 

Important Points

Work break down structure:

• These are incremental and hierarchical the composition of the project phases. It is a tree-like structure and it shows the description of the job for completion of the project from top to bottom.
• The main jobs are broken down into the number of small manageable units depending upon the size, time or efforts require for completion.

Bar chart (Gantt chart):

• It is a pictorial chart.
• It has two coordinate axes, the horizontal coordinate represents the elapsed time and the vertical coordinate represents the job or activity to be performed.
• The beginning and end of each bar represent starting and finishing time of a particular activity respectively.
• The length of bar shows the time required for completion.

Limitation of bar chart:

• Lack of degree of detail.
• A bar chart does not show the progress of work and hence it can not be used as a control device.
• A bar chart is unable to depict the interdependencies of various activities clearly.
• No provision to account for time uncertainties.
• A bar chart can not distinguish between critical and non-critical activities and hence resource smoothening and resource levelling can not be done.

Concept:

Total float: 

(i) The time span by which starting or finishing of an activity can be delayed without delaying the completion of the project.

(ii) It is the maximum available time in excess of the activity completion time.

Total float is given by,

\({F_T} = \;\left( {T_L^j - T_E^i} \right) - \;{t_{ij}}\)

\({F_T} = \;\left( {T_L^j} \right) - \;\left( {T_E^i + {t_{ij}}} \right)\)

F_T = LFT – EFT

Or, \({F_T} = \;\left( {T_L^j - \;{t_{ij}}\;} \right) - \;T_E^i\)

F_T = LST – EST

Where,

LST = Latest start time = \(\left( {T_L^j - {t_{ij}}} \right)\)

EST = Earliest start time = \(T_E^i\)

EFT = Earliest finish time = \(\left( {T_E^i + {t_{ij}}} \right)\)

LFT = Latest finish time = \(T_L^i\)

Calculation:

Given,

LST = 28 days, EST = 18 days

Total float (TF) = LST – EST = 28 – 18

Explanation:

Free float: It is the portion of total float by which an activity can be delayed without affecting succeeding activity i.e. the successor activity can start at its Earliest Start Time (EST).  But the preceding activities are affected by the free float. 

Free Float = Total Float - Head event Slack

\({F_F} = \left( {T_E^j - T_E^i} \right) - tij\)

Free float is also equal to total float minus head event slack.

\({F_F} = {F_T} - S_j\)

which implies that free float does not affect succeeding activity but affects preceding activities.

• Total Float: It is the maximum delay possible for an activity without considering any delay in its precedence or succeeding activity.
• Interfering Float: Maximum amount by which an activity can be delayed without delaying the project but will cause delay to the Early Start of some following activity. It is given by Total float - Free float.
• Independent float is the maximum delay possible for an activity that used floats of the preceding activity, but we will not affect the float of the succeeding activity.

The correct answer is 7 days.

Key Points To calculate the average time for a project activity using the three-point estimation method, you can use the following formula:

Average Time = (Optimistic Time + 4 * Most Likely Time + Pessimistic Time) / 6

In this case, the optimistic time is 4 days, the pessimistic time is 14 days, and the most likely time is 6 days. Plugging these values into the formula, we get:

Average Time = (4 + 4 * 6 + 14) / 6
Average Time = (4 + 24 + 14) / 6
Average Time = 42 / 6
Average Time = 7

Therefore, the average time for the project activity is 7 days.

Explanation:

Procedure to draw any network diagram:

1. Begin the project with any single milestone and label it start.
2. Find all the activities that have no immediate predecessor ie they start as soon as the project starts. In this case activity, 1 will be our starting activity.
3. Then, find the activities that have a successor of the first activity as their predecessor. In this case, the 2nd activity is the successor of the 1st activity and the predecessor of the 3rd and 4th activity.
4. Repeat the above steps, and by satisfying all the given relationships between various activities, draw the required diagram.
5. Use dummy activity, where ever the above relationship cannot be fulfilled without any error in the network

Errors in networking:

1) Cyclic/ looping error:

2) Dangling error

3) Wagon wheel error