Robust Capacity Planning for Project Management

We consider a significant problem that arises in the planning of many projects. Project companies often use outsourced providers that require capacity reservations that must be contracted before task durations are realized. We model these decisions for a company that, given partially characterized distributional information, assumes the worst-case distribution for task durations. Once task durations are realized, the project company makes decisions about fast tracking and outsourced crashing, to minimize the total capacity reservation, fast tracking, crashing, and makespan penalty costs. We model the company's objective using the target-based measure of minimizing an underperformance riskiness index. We allow for correlation in task performance, and for piecewise linear costs of crashing and makespan penalties. An optimal solution of the discrete, nonlinear model is possible for small to medium size projects. We compare the performance of our model against the best available benchmarks from the robust optimization literature, and show that it provides lower risk and greater robustness to distributional information. Our work thus enables more effective risk minimization in projects, and provides insights about how to make more robust capacity reservation decisions. Summary of Contribution: This work studies a financially significant planning problem that arises in project management. Companies that face uncertainties in project execution may need to reserve capacity with outsourced providers. Given that decision, they further need to plan their operational decisions to protect against a bad outcome. We model and solve this problem via adjustable distributionally robust optimization. While this problem involves two-stage decision making, which is computationally challenging in general, we develop a computationally efficient algorithm to find the exact optimal solution for instances of practical size.