Project Management Institute

A risk analytic treatment of CPM/PERT type networks using linear programming methodology

Although critical path method (CPM) and program evaluation and review technique (PERT) are powerful tools that can help project managers effectively plan, control, monitor, and audit large and multi-activity networks, these programs cannot provide project managers with the best project solution. Optimizing a CPM/PERT network demands that project managers introduce more complex analytical techniques involving mathematical programming, the simplest of which is linear programming (LP). This article examines how project managers can apply an LP algorithm to find the optimum solution for any project network. It identifies three tasks that LP accomplishes, the last of which involves determining the risk associated with optimum solutions, a task that this article describes in-depth. In doing so, it details the process of calculating and analyzing project risk. It also defines the purpose of using LP, identifies its variables, and outlines its system of linear equations.
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