CPM MCQ Quiz in తెలుగు - Objective Question with Answer for CPM - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Concept:

Dummy activity: It is an activity which has zero duration and is created for the sole purpose of establishing the relationship between two activities. It is represented by dashed lines.

Excavate the foundations: This will be an internal activity (a part of project which requires some duration and cost as well to reach the tail event.

Waiting for the arrival concrete materials: It won’t require any cost nor any time hence it can be called as a dummy activity.

Lay the foundation concrete: This is the second stage after the excavation which will require money and time hence not a dummy activity

Cure the foundation concrete: This is the third stage after the lay of concrete which requires minimum 7 days of curing and manpower & resource cost.  

Concept:

• Critical path is the longest path time-wise which can be determined from forward path method only.
• The critical path is the longest path through the network and time along this path gives the project duration. Critical path joins those activities which are critical.
• 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.
• The activities that control the project duration are the ones that have zero total floats and form a continuous chain or path starting at the first node and ending with the last node.

Concept:

In case of project management the followings are definition of various terms:

Duration (D): Duration is the estimated or actual time required to complete a task or an activity.

Earliest start time (ES): It is defined as the earliest possible time at which an activity can start. It is calculated by moving from first to last event in a network diagram.

Earliest finish time (EF): It is the earliest possible time at which an activity can finish.

Relationship between earliest start time, earliest finish time and duration is given by,

Earliest finish time = Earliest start time + duration of that activity

∴ EF = ES + D

EF - ES = D

Latest start time (LS): It is defined as the latest time an activity can start and still allow the project to be completed on estimated project completion time.

Latest finish time (LF): It is the latest possible time at which an activity can finish and still allow the project to be completed on estimated project completion time.

Relationship between latest start time, latest finish time and duration is given by,

Latest finish time = Latest start time + duration of that activity

∴ LF = LS + D

Calculation:

Given,

Activity time (t_ij) = 5 days

Free float = [T_E^j - T_Eⁱ] - t_ij 

⇒ 10 =  [TEj - TEi] - 5 ...................(i)

Total float = 10 days = [T_L^j - T_Eⁱ] - t_ij

⇒ 10 =  [TLj - TEi] - 5 ....................(ii)

From (i) and (ii),

T_E^j = T_L^j .......................(iii) 

Adding (i) and (ii) and putting T_E^j = T_L^j

TLj - TEi = 15 ..................(iv)

∵ We know that, T_Lⁱ = T_L^j - t_ij (By definition) .................(v)

By (iv) and (v) 

T_Lⁱ - T_Eⁱ = 10 days

Maximum delay in the occurance of the preceding event (i) = TLi - TEi = 10 days

Concept:

Slack time 

• It is the amount of time a task can be delayed before the project finish date is delayed. Thus, the slack is the difference between event times denoting the range within which an event time can vary.
• The Earliest Expected Time (TE) is the time when an event can be expected to occur earlier.
• The Latest allowable occurrence time (TE)is the latest time by which an event must occur to keep the project on schedule (without delaying the project).
• Event slack is defined as the difference between the latest event and the earliest event times. i.e. Slack = TL - TE
• Slack is defined as the difference between the latest occurrence time and earliest occurrence time.
• It is also given by the difference between the Latest allowable time and the earliest completion time.

Important Points

Positive slack: When TL > TE. It indicates the project is ahead of schedule meaning thereby the excess resources.

Zero slack: When TL = TE. It indicates that the project is going on schedule meaning thereby adequate resources.

Explanation:

Float:

(i) It is associated with activity times.

(ii) It is analogous to slack of events in PERT.

(iii) It is the range within which start or finish time of an activity may fluctuate without affecting the project completion time.

(iv) Floats are of following types:

(a) 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.

(iii) Total float of activity affects total float of succeeding as well as preceding activities.

(iv) Total float of an activity constrains the finishing of preceding activity and starting of succeeding activity

Total float is given by,

(b) Free float: 

(i) The delay which can be made without delaying succeeding activities.

(ii) It affects only preceding activities.

(iii) In free float, preceding activity is not allowed to occur at its latest time, and hence total float of preceding activity is affected. However, the succeeding activity can start at its earliest start time, and hence its total float is not affected.

Free float is given by,

Where, Sj = Head event slack

(c) Independent float: It is the minimum excess available time that exists without affecting any of succeeding or preceding activities. Independent float is given by

Where, Si = Tail event slack

(d) Interfering float: it is similar to head event slack.

Interfering float is given by

 = S_j

• An activity is a physically identifiable part of a project, which consumes both time and resources.
• Activity is represented by an arrow in a network diagram.
• An event represents the accomplishment of some task. In a network diagram, the beginning and end of an activity are represented as events.
• Each event is represented as a node in a network diagram. An event does not consume any time or resources.
• A dummy activity is represented by a dotted arrow and does not consume any time and resources.

Explanation:

Crashing is the method for shortening the project duration by reducing the time of one or more critical activities to less than their normal time. In crashing if cost increases then time decreases.

Explanation:

Crashing:

• It is the process of reducing the duration of the project at an optimum cost.
• In crashing direct cost increases while indirect cost decreases.
• there are two types of costs and two types of time defined in crashing.
• Normal time: It is the standard time, associated with normal resources of the organisation to perform the activity.
• Crash time: It is the minimum possible time in which an activity can be completed by employing extra resources.
• Normal cost: The expenditure incurred on normal resources for completing an activity in normal time.
• Crash cost: The total expenditure incurred on normal and additional resources for crashing the time.
• The time related to minimum total project cost is between normal time and crash time.
• The time cost relationship is not linear, but the relationship can be approximated by a straight line which is called the ‘cost slope’.

• The cost slope formula can be represented as:

Explanation:

Activity Times in CPM:

1. Earliest start time (EST):  

(i) It is the earliest possible time at which an activity can be started. For an acttivity i - j, earliest event time of event i, i.e.  is EST of activity i - j.

2. Earliest finish time (EFT):

(i) It is the earliest possible time by which an activity can be completed.

For an activity i - j,

EFT = EST + t_ij

3. Latest start time (LST):

(i) This is the latest possible time at which an activity can be started without delaying the overall project.

∴ LST = LFT - Activity duration 

(ii) LST of an activity is to be calculated on the basis of latest occurance time of its head event and not on the basis of latest occurance time of its tail event. So, Latest start of an activity is always greater than or equal to latest event times of all the preceding nodes

4. Latest finish time:

(i) This is the latest time by which an operation or activity must be completed without delaying the project.

For an activity i- j, latest allowable time of head event j, i.e. T_Lj is LFT of activity i - j.

Concept:

From the activity network representation, it can be analyzed that the minimum time to complete the project is the maximum of all paths from start to finish.

So, the longest path will represent the critical path for the network, and it will represent the minimum possible duration required to complete the project.

The critical path will be the longest path in the network requiring the maximum amount of time, but it will represent the minimum duration that is required to complete all the activities i.e. completion of a project.

Example:

TE = Earliest time of an event

TL = Latest time of an event.

Slack (S) = TL - TE

The duration of the project is the sum of duration of each activity along the critical path. Critical path is the path where slack (S) is zero.

Critical path of above network is 1 - 2 - 3- 4 - 5