Project Planning MCQ Quiz - Objective Question with Answer for Project Planning - Download Free PDF

Concept:

To determine which contractor is more certain, we calculate the standard deviation (σ) for each contractor using the PERT formula:

$\sigma =\frac{t_p-t_0}{6}$

where σ is standard deviation, t_p is pessimestic time, and t₀ is optimistic time.

The smaller the standard deviation, the more certain the estimate is.

Calculation:

Contractor P: ${\sigma }_P=\frac{13-5}{6}=1.33$

Contractor Q: ${\sigma }_R=\frac{12-6}{6}=1.00$

Contractor R: ${\sigma }_R=\frac{14-5}{6}=1.50$

Contractor S: ${\sigma }_S=\frac{13-4}{6}=1.50$

 Contractor Q is most certain about completing the job on time.

Explanation:

CPM (Critical Path Method)

• CPM is an activity-oriented network.

• It focuses on activities that make up a project and identifies the critical path — the sequence of activities that determines the project duration.

• Activities have well-defined, deterministic durations (known in advance).

• Used for projects like construction, maintenance, manufacturing — where activity durations are predictable.

 Additional InformationPERT (Program Evaluation and Review Technique)

• PERT is an event-oriented network, not activity-oriented.

• It focuses on events (milestones) and the probabilities of reaching them.

• It deals with uncertain or variable durations, using probabilistic time estimates (optimistic, most likely, pessimistic).

• Used for research, R&D, or projects with uncertainty in task durations.

Concept:

Probability can be calculated by using probability factor (Z) which is defined as, 

$Z=\frac{T_s-T_e}{\sigma }$

where, T_s = Schedule completion time

T_e = Expected completion time

$\sigma =$ Standard deviation

Z = Probability factor depending on probability

Calculation:

Given: T_e = 20 days, $\sigma =4days$

For 84.13 %, Z = 1

$1=\frac{T_s-20}{4}$

$T_s=20+4=24days$

Explanation:

In PERT (Program Evaluation and Review Technique), the expected time $$
E for an activity is calculated using a weighted average of three time estimates:

• Optimistic time (O): Best-case scenario (shortest possible duration)

• Most likely time (M): Most probable duration under normal conditions

• Pessimistic time (P): Worst-case scenario (longest possible duration)

• The expected time (E) of a PERT activity in terms of optimistic time (O), pessimistic time (P) and most likely time (M) is given by.$\text{E=(O+4M+P)/6}$

 Additional Information

• PERT is a project management tool used to plan, schedule, and control complex tasks where activity durations are uncertain. It is especially useful in research and development or construction projects where time estimates vary.

• PERT helps identify the critical path, which is the longest path of activities that determines the project duration. Delays in critical path activities will delay the whole project.

• It also calculates slack or float time for non-critical activities, helping project managers allocate resources and manage delays more efficiently.

• PERT is probabilistic in nature, unlike CPM (Critical Path Method), which is deterministic. It deals well with projects having uncertain activity durations.

Explanation:

According to the above network following inferences can be drawn:

1. Event 1 is the starting event and Event 8 is the end event.

2. Event 2 precedes Event 3 and Event 4 and follows Event 2.

3. Event 3 precedes Event 5, Event 6, and Event 7 and follows Event 2.

4. Event 4 precedes Event 7 and follows Event 2.

5. Event 5 follows event 3 and precedes Event 6.

6. Event 6 precedes Event 8 and follows Event 5, Event 3, and Event 7.

7. Event 7 precedes Event 6 and follows Event 4 and Event 3.

Additional Information PERT (Program Evaluation and Review Technique)

1. Focus on Uncertainty
   PERT is used for projects where activity durations are uncertain. It uses three estimates: optimistic (O), most likely (M), and pessimistic (P), to calculate the expected duration of each activity.

2. Probabilistic Approach
   PERT is a probabilistic tool that helps in determining the probability of completing the project within a certain time frame. It is suited for research and development projects or new product launches.

3. Event Oriented
   PERT networks are event-oriented, focusing on milestones (events) in the project timeline rather than on individual activities.

4. Emphasis on Time
   The primary goal of PERT is to estimate project duration and manage time-related uncertainties rather than costs.

5. Complex Projects with High Risk
   PERT is typically used for large, complex, and non-repetitive projects where uncertainty and risk are high.

CPM (Critical Path Method)

1. Focus on Activity Duration
   CPM is used for projects with well-known and predictable activity durations. It focuses on determining the critical path, which is the longest sequence of activities in a project.

2. Deterministic Approach
   CPM uses a deterministic model where activity times are assumed to be known and fixed, making it ideal for construction or manufacturing projects.

3. Activity Oriented
   CPM networks are activity-oriented. The focus is on the sequence and duration of tasks required to complete the project.

4. Emphasis on Time and Cost
   In addition to managing project duration, CPM also considers project costs. It helps in optimizing both time and cost through techniques like crashing.

5. Suitable for Repetitive Projects
   CPM is often used in industries like construction, engineering, and production, where projects are repetitive and experience-based.

Concept:

In CPM:

The standard deviation of critical path:

σ_cp = $\sqrt{Sumofvariancealongcriticalpath}$

σ_cp = $\sqrt{{\sigma }_1^2+{\sigma }_2^2+\dots +{\sigma }_8^2+{\sigma }_9^2}$

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

Calculation:

Given:

σ1, σ2, ...., σ8, σ9 = 3

σcp = $\sqrt{{\sigma }_1^2+{\sigma }_2^2+\dots +{\sigma }_8^2+{\sigma }_9^2}$

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:

Errors in network diagram:

(a) Loop error:

• Looping error is also known as cycling error.
• In this error, an endless loop is formed in the network diagram.
• cycling in the network can occur during the development of an activity plan or as a result of a simple error such as attempting to display a repetition of one activity before beginning the next.

(b) Dangling error:

• The project is completed when all its activities are over but the following situation can not arise in any case because a network diagram can not have two end points.

(c) Wagon wheel error:

• This is the most difficult error to spot and this can be found after examining the entire network diagram in detail.
• This is a conceptual error as there may be new event taking place at this point in the following network.

Explanation:

Slack:

(i) Slack is defined as the difference between the latest allowable time and the earliest expected time of an event.

(ii) Slack may be positive, zero, or negative.

(iii) When “slack is greater than zero”. It indicates the project is ahead of schedule and the availability of excess resources Such events are subcritical.

(iv) If slack is zero, it indicates work is on schedule and events are critical. Resources are just adequate.

(v) If slack is negative, it indicates work is behind schedule and may cause a delay in project completion. Events are supercritical. Extra resources are required.

(vi) The path having minimum slack value is the “critical path” which is also the time-wise longest path.

Confusion Points

Slack can be zero or minimum for the case of critical activities.

Since both zero and minimum options are available, we will go for the most appropriate i.e. minimum.

Explanation:

The expected value of a project (E) whose pessimistic estimate is(E_p), optimistic estimate is(E_o) and Most likely estimate is (E_m) is given by :

  $E=\frac{E_o+4E_m+E_p}{6}$

∴ The expected value of the project is,   

 $E=\frac{9+4\times 10+12}{6}=\frac{61}{6}$ = Rs. 10.16 Cr

Explanation:

Barchart or Gantt Chart:

• Bar charts were introduced by Henery Gantt around 1900 A.D., therefore they are also called Gantt charts. 
• A bar chart is a graphical representation of activity v/s time. It provides a visual representation of a project's timeline, showing the start and end dates of various tasks or activities, as well as their dependencies and the overall project schedule.
• Usually horizontal axis represents the time duration and the vertical axis represents activities or jobs to be performed.
• Activities are shown with the help of a bar.
• The beginning and end of each bar show the "time of start" and "time of finish" of the activity respectively.
• Therefore the length of the bar represents the time required for the completion of that activity.
• Gantt charts can show task dependencies, indicating which tasks must be completed before others can begin.
• Illustration is given on how the activities are to be distributed over the project timeline.

Since statement (3) is incorrect about the Gantt chart. Hence option (3) is correct.

Explanation

• Fulkerson’s rule is used for numbering events involved in the project scheduling network.
• Types of network diagram
  • Event on the node ( EON )
  • Activity on the node ( AON )

Important Points

• Hungarian  method – Assignment problems
• Johnson's  rule – scheduling jobs 
• Simplex method -  linear programming

Concept:

​Optimum time:

• We know that Total project cost = Direct cost + Indirect cost.
• If direct and indirect cost varies with time is shown in the figure below, then total project cost versus time curve has the shape as indicated in the figure below

• Such a curve will have a point A where the tangent drawn to the curve would be horizontal.
• The total cost of the project will be minimum at this point which is called as optimum cost of the project and the time corresponding to this point A is called as optimum project duration.
• If the project duration is increased total cost will increase, while if project duration is equal to the crash time, the project cost will be the highest.
• In the process of reducing the project time, efforts should be made to achieve optimum duration such that project cost is min

Additional Information

• Normal time: It is the standard time that an estimator will assign to an activity.

• Crash time: It is the minimum possible time in which an activity can be completed by assigning extra resources.

Explanation:

Dummy Activity.

• A Dummy activity is a type of activity in a project network that neither requires any time nor any resource.
• It is an imaginary activity shown in a project network to identify the dependence among operations.
• An activity followed by a dummy activity can only be completed once the activity or activities preceding the dummy activity is completed.

Additional Information Activity:

• The project can be broken down into various operations, these operations are consuming time or resources is called an Activity.
• Two types of activity (I) Serial Activity and (II) Parallel/concurrent Activity.

Event:

• An event is an instant of time or state at which some specific milestone has been achieved.
• such as the completion of preceding activities and the start of succeeding activities.

Slack:

• This is the time by which an event may be delayed without affecting the completion time of the project. 
• Slack is associated with event. It is an event.
• Slack is used in PERT analysis 

 Float:

• It indicates the time of which, starting or finishing of an activity can be delayed without affecting the project completion time.
• It is use In CPM analysis.

Early Start Time:

• The earliest point in the schedule at which a task can begin.
• EST = $T_E^i$

Early Finish Time:

• The earliest point in the schedule at which a task can finish.
• EFT = $T_E^i$ + t_ij

Latest Start Time:

• The latest point in the schedule at which a task can start without causing a delay.
• LST = $T_L^j$ - t_ij

Latest Finish Time:

• The latest point in the schedule at which a task can finish without causing a delay.
• LFT = $T_L^j$

Types of float:

1) Total float:

• It is the difference between the maximum time available and the actual time required for the completion of the activity. or It is the difference between the time available for an activity performance and the duration of the activity.
• F_T = LST - EST = LFT - EFT = $T_L^j-T_E^i-t_e^{ij}$ 

2) Free float:

• It is the amount of time by which an activity can be delayed without affecting the EST of the succeeding activity.
• F_T = $T_E^j-T_E^i-t_e^{ij}$

3) Independent float:

• It is the excess of minimum available time over the required activity duration
• F_I = $T_E^j-T_L^i-t_e^{ij}$ 

4) Interfering float

• It is the difference between the total float and the free float of an activity.
• F_IN = F_T - F_F

Explanation:

Direct Project cost:

(i) It is the cost that is directly dependent on the amount of resources involved for the completion of activities. It includes labour, materials, plants, and machining.

(ii) To get the same work done in less time, we have to increases the amount of labor, equipment, and time-saving material that too at extra charges which simply means increases indirect cost.

(iii) The project has the highest cost corresponding to the crash duration and has normal cost corresponding to the normal duration.

Normal time:

(i) Normal time is the standard time that an estimator would usually allow for an activity.

(ii) It is the time with which direct cost does not reduce with the increase in time.

Crash time:

(i) Crash time is the minimum possible time in which an activity can be completed, by employing extra resources.

(ii) Crash time is that time, beyond which the activity cannot be shortened by an amount of increases in the resources.