To determine the total crash cost required to complete a project in a reduced time (e.g., crashing by 1 time unit or more), the following steps and concepts are essential:
Key Concepts in Project Crashing
- Project crashing is a technique to shorten the project duration by adding resources or increasing costs on critical path activities to reduce their time
- The critical path is the longest sequence of activities determining the shortest possible project duration; crashing focuses on activities on this path
- Crash cost per time unit for each activity is calculated as:
Crash cost per time unit=Crash cost−Normal costNormal time−Crash time\text{Crash cost per time unit}=\frac{\text{Crash cost}-\text{Normal cost}}{\text{Normal time}-\text{Crash time}}Crash cost per time unit=Normal time−Crash timeCrash cost−Normal cost
- The activity with the lowest crash cost per time unit on the critical path is chosen to be crashed first to minimize additional cost
Example Calculation (Based on Provided Data)
Consider a project with activities having normal and crash times and costs:
Activity| Normal Time| Crash Time| Crash Cost per Period
---|---|---|---
A| 10| 8| $120
B| 12| 11| $300
C| 11| 10| $150
D| 26| 8| $230
E| 5| 3| $260
Calculate crash cost per time unit:
- A: $120 / (10-8) = $60
- B: $300 / (12-11) = $300
- C: $150 / (11-10) = $150
- D: $230 / (26-8) = $10.36
- E: $260 / (5-3) = $130
Activity D has the lowest crash cost per time unit ($10.36). Therefore, crashing the project by 1 time unit should be done by crashing Activity D, costing $10.36 for that unit of time reduction
Total Crash Cost to Complete Project in Reduced Time
- If the project needs to be crashed by more than one time unit, repeat the process by crashing the lowest cost per time unit activities on the critical path until the desired duration is achieved.
- The total crash cost is the sum of the additional costs incurred by crashing the chosen activities.
- For example, if crashing by 3 weeks, as in one case study, the project cost increased from $94,000 to $97,000, implying an additional $3,000 due to crashing
Summary
- Identify critical path activities.
- Calculate crash cost per time unit for these activities.
- Select activities with the lowest crash cost per time unit to reduce project duration.
- Sum the additional costs of crashing these activities to find the total crash cost.
- For a 1 time unit crash, the total crash cost equals the crash cost per time unit of the chosen activity (e.g., $10.36 for Activity D in the example).
- For multiple units, sum accordingly based on activities crashed and their costs
This approach ensures the project is completed faster with the minimum increase in cost.
