Project Crashing

In the event of the project's expected time of completion being more than the desired time, an attempt is made to reduce the time involved in some of the activities so that the project is completed on time. This process of reducing the time of the project by reducing the scheduled time of some of the activities is called crashing. Project crashing is accomplished by subcontracting, overtime, extra shifts, increasing the number of workers, additional capacity installation, etc. The key objective is to reduce the project time as much as possible with minimal expenditure. As these approaches have significant cost implications, operations managers analyze the time-cost trade-offs and reduce the project duration with minimal increase in costs. The steps involved in this project crashing are described below:

1. First, identify the normal cost (estimated cost requirement for finishing activity in normal time) and crash cost and time (estimated cost requirement for finishing activity in crash time or reduced time).

2. Identify the critical path and calculate new time-cost ratio for each activity based on the crash time and cost. Though the relationship is not linear, we assume a linear relation for simplicity and calculate the per unit crash cost as

     3. Highlight the activities on the critical path with the smallest time-cost ratio and crash those activities. Crash the        selected activity to the maximum possible extent until one of the conditions given below is satisfied.

• The activity time is at its minimum possible value.
• The time reduced is equal to the smallest slack value of the non-critical activities.
• The reduced time is equal to the desired project completion time.
• After crashing, if the critical path changes, then the crash time is calculated based on the new critical path.

     4. Repeat the steps 2-3 till the project duration is crashed to the desired new level.                  

Problem 

Based on the information given in the following table, identify the number of days by which the project can be crashed and the total cost of crashing.

Solution

1. Draw a network diagram using the normal time and calculate earliest and latest  times. From the Figure (a) we can see activities 1-3 and 3-4 are on the  critical path.

Figure a

1. Calculate the time cost ratio of each activity.

Time cost ratio =

Activity 1-2 cannot be crashed.

Time cost ratio (1-3) = (3500-3000)/(4-3) = 500

Time cost ratio (2-4) = (6000-4000)/(4-2) = 1000

Time cost ratio (3-4) = (3000-2000)/(3-2) = 1000

1. The critical path activity with smallest time cost ratio is selected and crashed. The activity 1-3 on the critical path has the smallest time cost ratio and it can be crashed by a day. This crashing will increase the project cost by Rs 500 and reduce the project duration from 7 days to 6 days.

2. The network diagram for the new schedule is given in Figure b. As a result of the crashing, we now have two critical paths 1-2, 2-4 and 1-3, 3-4. As activities 1-2 and 1-3 cannot be crashed further, we have to crash the activities 2-4 and 3-4. Activity 3-4 can be crashed by a day and activity 2-4 can be crashed by two days. As crashing activity 2-4 by two days will not affect the project duration, both activities 3-4 and 2-4 are crashed by one day each.

Figure b                  

      5. The final network diagram is shown in Figure c. The final project duration is reduced to 5 days and the total cost of crashing = 500 +1000 +1000 = 2500.  

Figure c                

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