Calculating Total Cost After Activity Crashing

In project management, crashing an activity means reducing its duration below the normal duration to potentially shorten the overall project length. This is often done at an increased cost, known as the crash cost. The cost slope represents the additional direct cost incurred for each unit of time the activity duration is reduced.

The total cost of an activity includes both direct cost and indirect cost. Crashing typically increases the direct cost but reduces the indirect cost (because the duration is shorter). The goal is often to find the duration that minimizes the total cost.

Let's break down the calculation based on the information provided:

• Normal Duration ($T_{normal}$) = 24 days
• Normal Cost (assumed to be Total Cost at normal duration) ($C_{normal}$) = Rs. 50,000
• Crash Duration ($T_{crash}$) = 22 days
• Indirect Cost per day = Rs. 1000
• Cost Slope = Rs. 1500 per day

First, let's determine the indirect cost at the normal duration.

Indirect Cost at Normal Duration = $T_{normal}$ × Indirect Cost per day

Indirect Cost at Normal Duration = 24 days × Rs. 1000/day = Rs. 24,000

Assuming the given Normal Cost (Rs. 50,000) is the Total Cost at normal duration, we can find the Normal Direct Cost.

Normal Direct Cost = Normal Total Cost - Indirect Cost at Normal Duration

Normal Direct Cost = Rs. 50,000 - Rs. 24,000 = Rs. 26,000

Now, let's calculate the reduction in duration due to crashing.

Duration Reduction = $T_{normal}$ - $T_{crash}$

Duration Reduction = 24 days - 22 days = 2 days

The cost slope tells us how much the direct cost increases for each day of reduction. Let's calculate the increase in direct cost due to crashing.

Increase in Direct Cost = Duration Reduction × Cost Slope

Increase in Direct Cost = 2 days × Rs. 1500/day = Rs. 3000

Now we can find the direct cost of the activity after crashing.

Direct Cost After Crashing = Normal Direct Cost + Increase in Direct Cost

Direct Cost After Crashing = Rs. 26,000 + Rs. 3000 = Rs. 29,000

Next, we calculate the indirect cost at the crashed duration.

Indirect Cost After Crashing = $T_{crash}$ × Indirect Cost per day

Indirect Cost After Crashing = 22 days × Rs. 1000/day = Rs. 22,000

Finally, the total cost of the activity after crashing is the sum of the direct cost after crashing and the indirect cost after crashing.

Total Cost After Crashing = Direct Cost After Crashing + Indirect Cost After Crashing

Total Cost After Crashing = Rs. 29,000 + Rs. 22,000 = Rs. 51,000

Therefore, the total cost of the activity after crashing will be Rs. 51,000.