A Multi-Criteria Decision Analysis Technique for Stochastic Task Criticality in Project Management

Abstract

Inherent in project management is the risk that a project fails to meet planned completion deadlines due to delays experienced in individual tasks. As such, certain critical tasks may be candidates for risk management (e.g., the allocation of additional resources such as labor, materials, and equipment) to prevent delays. A common means to identify such critical tasks is with the critical path method (CPM), which identifies a path of tasks in a project network that, when delayed, result in project delays. This work offers a complementary, stochastic approach to CPM that ranks tasks according to their effect on the project completion time distribution, when the distributions of task completion time are delayed. The new hybrid approach is based on the use of a Monte Carlo simulation and a multi-criteria decision analysis technique. Monte Carlo simulation allows for approximating the cumulative distribution function of the total duration of the project, while the multi-criteria decision analysis technique is used to compare and rank the tasks across percentiles of the resulting project completion time distributions. Doing so allows for different percentile weighting schemes to represent decision maker risk preferences. The suggested approach is applied to two project network examples. The examples illustrate that the proposed approach highlights some tasks as risky, which may not always lie on the critical path as identified by CPM. This is valuable for practicing managers as it allows them to properly consider their risk preferences when determining task criticality based on the distribution of project completion time (e.g., emphasizing median vs. upper tail completion time).