Let's create a sample model to explain the methodology of project management:
- Assume that you have five mile stones to achieve A, B, C, D and E.
- Milestone A is your starting point
- Milestone B is dependent on A and requires 2 hours of work to achieve
- Milestone C is also dependent on A and requires 4 hours of work
- Milestone D is dependent on Milestone B and take 5 hours of work
- Milestone E is dependent on Milestone B and requires 2 hours of work, requires 1 hour of work after Milestone C and finally requires 3 hours of work after Milestone D.
- A --> B (2 hours)
- B --> D (5 hours)
- D --> E (3 hours)
However, this becomes more complicated if resources can be moved from one task to another to influence (shorten) the job time. In this case it is possible to use graph theory and Dijkstra's algorithm to determine which paths are relatively over capacity (shortest paths) so that they can contribute resources to the critical path to reduce over all project time.
In the example above, resources could be taken from the following tasks and reallocated to the slowest task (B --> D) with the goal being to reduce systematic slack time across any path to 0.
- A --> C
- C --> E
- B --> E
SAT Based Example: It takes 4 people 1 hour to paint a house. How many man hours are required for 16 people to paint 8 houses?
Answer: 1 house takes 4 people one hour so each house is 4 man hours of work. 8 houses would be 32 man hours (4 man hours per house x 8 houses) of work.
32 man hours divided amongst 16 people evenly is 2 hours.
Obviously, the examples provided in this post assume that workers are interchangeable, that there are no diminishing returns of labour etc. However, even without these assumptions, if there are large unbalances in the project paths, there is an obvious benefit to moving resources from one area to another to improve the overall project completion time.
1 comment:
The concept is relatively simple to understand but it is a critical Project Management tool for scheduling (Critical Path Method) and to apply the utilization of resources to complete major projects. The system can be fully computerized and run on real time basis to predict/react to delays, cost over-runs, etc.
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