#OperationsResearch #Math #Statistics #PERT #CPM #Network #Crashing #TimeCostRelationship #FreeLecture #FreeStudy #Solution #VideoLecture
(1) Crashing the project means crashing a number of activities to reduce the duration of the project below its normal time.
(a) Crashing an activity means performing it in the shortest possible time by allocating to it necessary additional resources.
(b) Crashing an activity means taking special costly measures to reduce the duration of an activity below its normal time.
Activity: 1 – 2 1 – 3 1 – 4 2 – 4 2 – 5 3 – 6 4 – 6 5 – 6
Time(Days): 6 8 5 3 5 12 8 6
Time (Days): 4 4 3 3 3 8 5 6
(Rs/Day): 80 90 30 — 40 200 50 —
There is a penalty clause in the contract and it provides for a penalty of is Rs. 100 per day for the project completion time over 17 days. The direct cost of completing all the activities is Rs. 6,500. The overheads amount to Rs. 160 per day.
(1) Draw a network and find out normal duration of the project, its cost and critical path.
(2) Calculate and plot on a graph the cost-time function for the project and state –
(i) the lowest cost and associated time
(ii) the shortest time and associated cost
Summarized steps involved in Crashing (Time-Cost Trade-Off Procedure:
Step – 1:
Determine the normal project completion time and associated critical path.
(a) When all activities are completed with their normal time. The critical path with normal time provides the starting point of the crashing analysis.
(b) When all activities are crashed. The critical path with crash time provides the end/stopping point for crashing analysis.
Step – 2:
Identify the critical activities with normal time and find out ‘crash cost per unit of time’ for each activity.
Sometimes the crash cost per unit of time can be found out by the following formula also:
Crash cost per unit of time =
(Crash Cost – Normal Cost)/(Normal Time – Crash Time)
This crash cost per unit of time is also known as ‘Cost slope’ and it indicates the direct extra cost per unit of time required to reduce the duration of an activity.
Step – 3:
For the purpose of reducing the total project completion time, identify and crash an activity time on the critical path with the lowest ‘crash cost per unit of time to the point where
(i) the activity has been crashed to its lowest possible time; OR
(ii) another path in the network becomes critical.
Sometimes two or more paths become critical with equal length of time simultaneously and, then, we need to crash one activity from each of such critical paths simultaneously.
Step – 4:
If the critical path under crashing is still critical, repeat Step-3. However, if, due to crashing of an activity time in step-3, other path(s) in the network also become critical, then identify and crash the activities on each of the critical paths with the minimum joint crash cost. For this purpose we can have one or more combinations of activities for crashing simultaneously and out of them we select the combination with the lowest possible joint crash cost.
Step – 5:
Terminate the procedure when all critical activities activity on any one (or more) critical path(s) have been crashed to their lowest possible time. Determine the total project cost (= Direct Costs + Indirect Costs) corresponding to each of the different project duration.
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