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

Explanation:

Economic order quantity is that size of the order which helps in minimizing the total annual cost of inventory in the organization.

When the size of order increases, the ordering costs (cost of purchasing, inspection, etc.) will decrease whereas the inventory carrying costs (costs of storage, insurance, etc.) will increase.

Economic Order Quantity (EOQ) is that size of order which minimizes total annual costs of carrying and cost of ordering.

It is evident from above that the minimum total costs occur at a point where the ordering costs and inventory carrying costs are equal.

Concept:

The PERT (Project Evaluation and Review Technique) technique is used, when activity time estimates are stochastic in nature. For each activity, three values of time (optimistic, most likely, pessimistic) are estimated.

• Optimistic time (to) estimate is the shortest possible time required for the completion of the activity
• Most likely time (tm) estimate is the time required for the completion of activity under normal circumstances
• Pessimistic time (tp) estimate is the longest possible time required for the completion of the activity

In PERT expected time of an activity is determined by using the belowgiven formula:

\({t_E} = \frac{{\left( {{t_o} + 4{t_L} + {t_p}} \right)}}{6}\)

Concept:

In CPM:

The standard deviation of the critical path:

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

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

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

Calculation:

Given:

σ1, σ2, ...., σ8, σ9 = 3

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

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

σcp = \(\sqrt {9 \times 9} \) = 9

∴ the standard deviation of the critical path is 9.

PERT Network Analysis

In PERT (Program Evaluation and Review Technique) network analysis, the duration of an activity is considered as a random variable. The technique is used to represent and analyze the tasks involved in completing a project. To model the uncertainty in activity durations, PERT uses a specific type of probability distribution.

Analyzing the Given Options

1. Option 1: Chi-square distribution (Incorrect)

   Chi-square distribution is primarily used in hypothesis testing and in construction of confidence intervals. It is not suitable for representing the distribution of activity durations in PERT.

2. Option 2: Beta distribution (Correct)

   PERT assumes that the activity durations follow a Beta distribution. This distribution is flexible and can take various shapes depending on the values of its parameters. It is particularly useful for modeling the uncertain nature of activity durations in project management.

3. Option 3: Alpha distribution (Incorrect)

   Alpha distribution is not a standard term in probability and statistics. There is no well-defined distribution known as the Alpha distribution, making this option incorrect.

4. Option 4: Gamma distribution (Incorrect)

   Gamma distribution is used in various fields for modeling positively skewed data, but it is not specifically used in PERT for activity duration estimation.

Explanation:

Activity A → B: Solid arrow means B can only start after A ends ⇒ B is dependent on A.

Activity C → D: Solid arrow means D can only start after C ends ⇒ D is dependent on C only.

Dummy C → B: Dummy arrow shows logical dependency ⇒ B is also dependent on C.

(i) Activity B is controlled by activity A – Correct

(ii) Activity D is controlled by both A and C – Incorrect (only C controls D)

(iii) Activity B is independent of activity C – Incorrect (dummy from C to B shows B depends on C)

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:

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,   

 \(E=\frac{9+4\times10+12}{6}= \frac{61}{6}\) = 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.

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:

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.

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.