Performance Optimizations for a Parallel, Two Stage Stochastic Linear Program A Case Study of the Military Aircraft Allocation Problem

The US air fleet is tasked with the worldwide movement of cargo and personnel. Due to a unique mixture of operating circumstances, it faces a large scale and dynamic set of cargo movement demands with sudden changes almost being the norm. Airfleet management involves periodically allocating aircraft to its myriad operations, while judiciously accounting for this uncertainty to minimize operating costs. We have formulated this allocation problem as the optimization of a stochastic two-stage integer program. Our work aims to enable rapid decisions via a scalable parallel implementation. We present the design of our parallel solution that applied a well-known masterworker approach to solving the undecomposed linear programs underlying the formulation. This paper presents a narrative of the issues encountered and solutions that we developed to combat these. We believe these techniques may be generally applicable in other contexts where a parallel solution of stochastic optimization is of interest.