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In this example, we use sparse derived sets with an explicit listing. When we use this technique to define a sparse set, we must explicitly list all members belonging to the set. This will usually be some small subset of the dense set resulting from the full Cartesian product of the parent sets.
For our example, we will set up a PERT(Project Evaluation and Review Technique) model to determine the critical path of tasks in a project involving the roll out of a new product. PERT is a simple, but powerful, technique developed in the 1950s to assist managers in tracking the progress of large prodects. PERT is particularly useful at identifying the critical activities within a project, which, if delayed, will delay the project as a whole. These time critical activities are referred to as the critical path of a project. Having such insight into the dynamics of a project goes a long way in guaranteeing it won't get sidetracked and become delayed. In fact, PERT prove so successful, the Polaris project, on which it was first used, was completed 18 months ahead of schedule. PERT continues to be used successfully on a wide range of prjects. For more information on PERT, and a related technique called CPM (Critical Path Method), please refer to Schrage(19997) or Winston(1995).
In this model, Wirless Widgets is about to launch a new product--the Solar Widget. In order to guarantee the launch will occur on time, WW wants to perform a PERT analysis of the tasks leading up to the launch. Doing so will allow them to identify the critical path of tasks that must be completed on time in order to guarantee the Solar Widget's timely introduction. You have a list of tasks to be accomplished and their anticipated times for completion. Also, certain tasks must be completed before others can commence. The goal is to construct a PERT model for the Solvar Widget's introduction in order to identify the tasks on the critical path.