(Critical path method (CPM

The critical path method (CPM) is a step-by-step project technique for process planning that defines critical and non-critical tasks with the goal of preventing time-frame problems and process bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that interact in a complex manner.
In applying the CPM, there are several steps that can be summarized as follows:
1. Define the required tasks and put them down in an ordered (sequenced) list.
2. Create a flowchart or other diagram showing each task in relation to the others.
3. Identify the critical and non-critical relationships (paths) among tasks.
4. Determine the expected completion or execution time for each task.
5. Locate or devise alternatives (backups) for the most critical paths


Simplex Method
The Simplex Method is "a systematic procedure for generating and testing candidate vertex solutions to a linear program.
The Simplex Method selects the variable that will produce the largest change towards the minimum (or maximum) solution. That variable replaces one of its compatriots that is most severely restricting it, thus moving the Simplex Method to a different corner of the solution set and closer to the final solution. In addition, the Simplex Method can determine if no solution actually exists. Note that the algorithm is greedy since it selects the best choice at each iteration without needing information from previous or future iterations. This method will give the following benefits
1. Provides an efficient procedure for solving such large problems
2. It uses methods from linear algebra
3. The study of systems of linear equations
4. Using matrices