PERT and CPM MCQ Quiz - Objective Question with Answer for PERT and CPM - Download Free PDF

Explanation:

Critical Path Method (CPM):

• The Critical Path Method (CPM) is a project management technique used to determine the sequence of activities that directly affect the project completion time. It identifies the longest path of dependent activities in the project schedule, known as the critical path. The duration of this path determines the shortest possible project completion time.

Critical Path and Slack:

• The critical path in a project is defined as the sequence of tasks where any delay in one task would directly result in a delay in the overall project completion. The slack (or float) is the amount of time an activity can be delayed without affecting the project’s completion date. For activities on the critical path, the slack is zero because there is no flexibility to delay these activities without impacting the entire project.

Why Slack on the Critical Path is Zero:

• The critical path represents the longest duration path in the project network. If any activity on this path is delayed, the entire project completion time will also be delayed.
• Slack is calculated as the difference between the latest allowable finish time (LF) and the earliest finish time (EF) of an activity:
  Slack = LF - EF
• For activities on the critical path, the LF equals EF because they determine the project’s end date. Therefore, their slack is zero.

Explanation:

Critical Path Method (CPM):

Definition: The Critical Path Method (CPM) is a project management technique used to analyze and schedule tasks within a project. It identifies the longest sequence of dependent tasks (known as the critical path) that determines the shortest possible project duration. Any delay in the tasks on the critical path will directly impact the overall project completion time.

How to Identify the Critical Path:

• List all the tasks required to complete the project.
• Define dependencies between tasks (i.e., which tasks must be completed before others can start).
• Determine the duration of each task.
• Calculate the earliest start (ES) and finish (EF) times for each task by performing a forward pass through the network diagram.
• Calculate the latest start (LS) and finish (LF) times for each task by performing a backward pass through the network diagram.
• Identify the tasks with zero slack (i.e., tasks where ES = LS and EF = LF). These tasks form the critical path.

To identify the critical path, we analyze the given network diagram and follow these steps:

• Step 1: List all paths in the network diagram and calculate the total duration for each path.
• Step 2: Identify the path with the longest duration. This is the critical path because it governs the minimum time required to complete the project.

Based on the given data:

• Path 1: 1-2-3-7
  • Total duration = Sum of durations of tasks along this path.
• Path 2: 1-2-4-5-6-7
  • Total duration = Sum of durations of tasks along this path.
• Path 3: 1-2-4-5-6
  • Total duration = Sum of durations of tasks along this path.
• Path 4: 1-2-4-7
  • Total duration = Sum of durations of tasks along this path.

From the calculations, Path 2 (1-2-4-5-6-7) has the longest duration. Therefore, it is the critical path.

Explanation:

CPM & PERT:

• CPM (Critical Path Method) and PERT (Program Evaluation and Review Technique) are both project management techniques used to plan, schedule, and control complex projects. They are essential tools for project managers to ensure that projects are completed on time and within budget. Understanding the key concepts and terminology associated with CPM and PERT is crucial for effective project management.
• Earliest Start Time (A): This is the earliest time at which a task can begin without any delay in the project. It is determined by the completion times of preceding tasks.
• Latest Start Time (B): This is the latest time a task can start without delaying the project. It is calculated by working backward from the project's end date.
• Total Float (E): This is the amount of time that a task can be delayed without affecting the overall project timeline. It is calculated as the difference between the latest start time (B) and the earliest start time (A).

Therefore, the correct formula to calculate the total float (E) is:

E = B - A

Explanation:

Program Evaluation and Review Technique (PERT) Activity Relation:

Definition: The Program Evaluation and Review Technique (PERT) is a project management tool used to schedule, organize, and coordinate tasks within a project. It is particularly useful for projects where the time required to complete different tasks is uncertain. PERT involves the identification of the critical path and the calculation of various time estimates for activities in a project.

Time Estimates: PERT uses three different time estimates to determine the expected duration of a project activity:

• Optimistic Time (B): The minimum possible time required to complete an activity, assuming everything proceeds better than is normally expected.
• Pessimistic Time (C): The maximum possible time required to complete an activity, assuming everything goes wrong (but excluding major catastrophes).
• Most Likely Time (D): The best estimate of the time required to complete the activity, assuming everything proceeds as normal.

Expected Time (A): The expected time for an activity in PERT is calculated using a weighted average of these three-time estimates. The formula for the expected time (A) is given by:

Formula:

A = (B + 4D + C) / 6

In this formula:

• B is the Optimistic Time.
• C is the Pessimistic Time.
• D is the Most Likely Time.

⇒ \(D=\frac{6 A-C-B}{4}\)

Concept: 

The critical path is the sequence of activities that represents the longest path through a project. It determines the shortest possible project duration.

The critical path can be easily determined with the help of total float calculations. The activities on the critical path are those activities that have total float equal to zero

i.e. TF = 0.

Total float:

• The time span by which starting or finishing time of an activity can be delayed without affecting the overall completion time of the project.
• It refers to the amount of time by which completion of activity could be delayed beyond the earliest expected completion time without affecting overall project time.
• Total Float is given by
• TF = LFT – EFT (or) LST – EST

Where,

EST = Earliest start time, LST = Latest Start time

EFT =  Earliest finish time, LFT = Latest finish time

tij is activity duration from (Activity ‘i’ to Activity ‘j’)

Ei = EST, Ej = EFT = EST + tij

Lj = LFT, Li = LST = LFT - tij

For critical activity TF = 0

i.e. LST – EST = 0

LFT - tij – EST = 0 i.e. LFT – EST = tij

Free Float:

• It refers to the amount of time by which completion of an activity can be delayed beyond the EFT without affecting the EST of a subsequent succeeding activity.
• It is given by FF = TF – Sj
• i.e. TF = FF + Sj
• If Sj = 0 → FF = TF = 0
• If Sj ≠ 0 FF < 0
• Where Sj is slack of Head event

Independent Float

• It refers to the amount of time by which the start of an activity is can be delayed without affecting EST of any immediately following activity
• It is given by IF = FF – Si  
• i.e. FF = IF + Si
• If Si = 0 → FF = IF = 0
• If Si ≠ 0 FF > IF

Concept:

In CPM:

The standard deviation of critical path:

σ_cp = \(\sqrt {Sum\;of\;variance\;along\;critical\;path} \)

σ_cp = \(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

Where, σ₁, σ₂, ...., σ₈, σ₉ are the standard deviation of each activity on the critical path   

Calculation:

Given:

σ1, σ2, ...., σ8, σ9 = 3

σcp = \(\sqrt {σ _1^2 + σ _2^2 + \ldots + σ _8^2 + σ _9^2} \)

σ_cp = \(\sqrt {3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2 + 3^2} \)

σ_cp = \(\sqrt {9 \times 9} \) = 9

∴ the standard deviation of the critical path is 9.

Explanation:

A project may be defined as a combination of interrelated activities which must be executed in a certain order before the entire task can be completed.

The aim of planning is to develop a sequence of activities of the project so that the project completion time and cost are properly balanced.

To meet the objective of systematic planning, the management has evolved several techniques applying network strategy.

PERT (Programme Evaluation and Review Technique) and CPM (Critical Path Method) are network techniques which have been widely used for planning, scheduling and controlling the large and complex projects.

• PERT (Project Evaluation and Review Technique) approach takes account of the uncertainties. In this approach, 3-time values are associated which each activity. So it is probabilistic.

• CPM (Critical Path Method) involves the critical path which is the largest path in the network from starting to ending event and defines the minimum time required to complete the project. So it is deterministic.

Difference between PERT and CPM (Critical Path Method)

Concept:

Project Evaluation and Review Technique (PERT) is probabilistic in nature and is based upon three-time estimates to complete an activity.

Optimistic Time (to): It is the minimum time that will be taken to complete an activity if everything goes according to the plan.

Pessimistic Time (tp): It is the maximum time that will be taken to complete an activity when everything goes against the plan.

Most likely time (tm): It is the time required to complete a project when an activity is executed under normal conditions.

Average or most expected time is given by \({t_E} = \left( {\frac{{{t_p}\; + \;4{t_m}\; + {t_o}}}{6}} \right)\)

The variance gives the measure of uncertainty of activity completion. The variance of the activity is given by 

Variance, \(V = {\left( {\frac{{{t_p} - {t_0}}}{6}} \right)^2}\)

Standard duration, \(\sigma = \sqrt {variance} \)

Calculation:

Given:

t_p = 10 days, t_o = 4 days

\({\rm{V}} = {\left( {\frac{{{{\rm{t}}_{\rm{p}}} - {{\rm{t}}_{\rm{o}}}}}{6}} \right)^2} = {\left( {\frac{{10 - 4}}{6}} \right)^2} = 1\)

The variance of the activity is 1.

Explanation

Slack or Event Float

• Slack corresponds to the event in PERT.
• Float corresponds to activity in CPM.

Slack

• It is defined as the amount of time by which an event can be delayed without delaying the project schedule.
• Slack of an event = Latest Start Time – Earliest Start Time OR Latest Finish Time – Earliest Finish Time

There are three types of floats.

Explanation:

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

Difference between PERT and CPM (Critical Path Method)

PERT does take uncertainties involved in the estimation of times, therefore three-time estimates have been taken for the calculation project duration. They are optimistic (t_o), pessimistic (t_p), and most likely (t_m).

\(T_e=\frac{t_o\;+\;4t_m\;+\;t_p}{6}\)

Therefore, the option 2 is the incorrect statement among the given options.

Explanation:

PERT stands for Program Evaluation and Review Technique and was developed to address the needs of projects for which the time and cost estimates tend to be quite uncertain.

It has a probabilistic approach and hence suitable for the projects which are to be conducted for the first time or projects related to research and development.

PERT uses 3 cases:

• Optimistic time ⇒ estimates the shortest possible time required for the completion of the activity.
• Most likely time ⇒ estimates the time required for the completion of activity under normal circumstances.
• Pessimistic time ⇒ estimates the longest possible time required for the completion of the activity.

Explanation:

CPM does not directly model uncertainty.

PERT was developed to address the needs of projects which are being done for the first time – a challenge to estimate activity duration.

PERT (Program Evaluation and Review Technique) uses 3 cases:

• Most Optimistic
• Most Pessimistic
• Most likely durations

PERT determines the probability for each duration, whereas CPM considers the most likely duration.

In the standard PERT analysis, the distribution assumed for the activity times is a Beta distribution.

Concept:

Optimistic time (to), Pessimistic time (tp), Most likely time (tm):

Expected time: \({t_E} = \frac{{{t_o} + 4{t_m} + {t_p}}}{6}\)

Standard deviation: \(\sigma = \frac{{{t_p} - {t_o}}}{6}\)

For a PERT network,\(\;{\sigma ^2} = {\left( {\frac{{{t_p} - {t_o}}}{6}} \right)^2}\)

The variance is given by:

\(V = {\sigma ^2} = {\left( {\frac{{{t_p} - {t_o}}}{6}} \right)^2}\)

Calculation:

Given:

t_o = 6, tm = 9, tp = 12

Standard deviation: \(\sigma = \frac{{{t_p} - {t_o}}}{6}\)

\(\sigma = \frac{{{12} - {6}}}{6}=1\)

Explanation :

A critical path is a sequence of interdependent activities or tasks that must be finished before the project can be finished. It is the longest path (i.e. path with the longest duration) from project start to finish.

The path which moves along the activities having total float zero.

A. Critical Path Method
1. The critical path method (CPM) is a project modelling technique that's used by project managers to find important deadlines and deliver a project on time.

2. In a project, the critical path is the longest distance between the start and the finish, including all the tasks and their duration.

3. Once a critical path is determined, you'll have a clear picture of the project's actual schedule.

4. To find this, project managers use the CPM algorithm to find the least amount of time necessary to complete each task with the least amount of slack.
5. Once done by hand, nowadays, the critical path is calculated automatically by the project scheduling software. That makes the whole method a lot easier.

B. Critical Path Analysis
1. As mentioned, the purpose of a critical path is to find the least amount of time you'll need to complete a task.

2. Critical path analysis furthers your ability to make better estimates for scheduling because you're mapping out every important task that must be done for a successful project.

C. Critical Path Example

Explanation:

Total float: 

Total Float/Slack = Latest Finish time (LF) - Earliest Start time (ES) - (Earliest Finish time EF - Earliest Start time ES  )or Total Float/Slack = Latest Finish time (LF) - Earliest Finish time (EF) OR = Latest start time (LS) - Earliest start time (ES)

If we use the  formula with the given values, we get:

Total Float = LS - ES = 45 - 15 = 30 OR  45 - 15 = 30