Prioritization via stochastic optimization
We take a novel perspective on real-life decision making problems involving binary activity-selection decisions that compete for scarce resources. The current literature in operations research approaches these problems by forming an optimal portfolio of activities that meets the specified resource constraints. However, often practitioners in industry and government do not take the optimal-portfolio approach. Instead, they form a rank-ordered list of activities and select those that have the highest priority.
The academic literature tends to discredit such ranking schemes because they ignore dependencies among the activities. Practitioners, on the other hand, sometimes discredit the optimal-portfolio approach because if the problem parameters change, the set of activities that was once optimal no longer remains optimal. Even worse, the new optimal set of activities may exclude some of the previously optimal activities, which they may have already selected. Our approach takes both viewpoints into account. We rank activities considering both the uncertainty in the problem parameters and the optimal portfolio that will be obtained once the uncertainty is revealed.
We use stochastic integer programming as a modeling framework. We develop several mathematical formulations and discuss their relative merits, comparing them theoretically and computationally. We also develop cutting planes for these formulations to improve computation times. To be able to handle larger real-life problem instances, we develop parallel branch-and-price algorithms for a capital budgeting application. Specifically, we construct a column-based reformulation, develop two branching strategies and a tabu search-based primal heuristic, propose two parallelization schemes, and compare these schemes on parallel computing environments using commercial and open-source software.
We give applications of prioritization in facility location and capital budgeting problems. In the latter application, we rank maintenance and capital-improvement projects at the South Texas Project Nuclear Operating Company, a two-unit nuclear power plant in Wadsworth, Texas. We compare our approach with several ad hoc ranking schemes similar to those used in practice.