Stochastic Optimization Models for Contingency Allocation in Project Management

In many cases, risks that threaten successful project completion can be mitigated (or eliminated) with a proper contingency allocation strategy and exacerbated by an improper one. Yet, despite this importance, there is a dearth of research on the cost contingency allocation problem in academic literature. This thesis looks at the cost contingency allocation problem from two different perspectives and two distinct solutions are introduced: a stochastic linear programming model that addresses a short term strategy and convex-concave utility model that provides a long-term planning solution. The project manager’s ability to approve random requests for contingency is dependent on several constraints, including the amount of funding that is available and the current contingency balance. The stochastic short-term contingency allocation model developed in this thesis delivers, to the decision maker, a single allocation strategy (feasible under all potential futures) where uncertainty is specified via a well-chosen set of scenario paths for the future. Comparison of the model’s solution to that of a typical myopic period-by-period approach shows that the model’s solution is superior to that of the standard practice. This short-term model is then extended to develop a long range contingency allocation plan under the concept of expected utility theory. The hypothesis that the ‘risk-seeking’ and ‘risk-averse’ behaviors modeled by convex and concave utility functions are those exhibited by a project is substantiated by actual project data. These data show that the ‘risk- seeking’ behavior that is an asset at the beginning of a project could lead to over-allocation of contingency early in a project and jeopardize completion if a ‘risk-averse’ behavior is not adopted by the project once the designs and specific project details have been more firmly established. A novel, additive project utility function comprised of performance, scope and schedule utility functions is introduced and the convex-concave utility-based contingency allocation model introduced provides a long term contingency allocation plan that maximizes this utility. Both developed models are empirically validated using data from two Department of Energy projects