Managing risk-adjusted resource allocation for project time-cost tradeoffs

In the traditional project crashing problem (also known as the time-cost tradeoff problem) associated with a project network, the decision variables are assumed to be continuous, representing the amount of reduction in the duration of the tasks in the project, and the objective is to find the least expensive set of time reductions (“crashing” times) to complete the project within a given time limit (to avoid penalties). We will study a variant of this problem with a combinatorial probabilistic version, where the objective is to find the set of “crashing” choices that minimizes the time reduction cost and the expected penalty risk from tardiness. We show this problem is NP-hard, so we propose efficient heuristics that can provide approximate solutions to this problem. We also extend this problem so that resource assignments can be adjusted following project status reviews several times before reaching the project deadline.