GPU-based Split algorithm for Large-Scale CVRPSD

Abstract: Dynamic programming (DP) is a cornerstone of combinatorial optimization, yet its inherently sequential structure has long limited its scalability in scenario-based stochastic programming (SP). This paper introduces a GPU-accelerated framework that reformulates a broad class of forward DP recursions as batched min-plus matrix-vector products over layered DAGs, collapsing actions into masked state-to-state transitions that map seamlessly to GPU kernels. Using this reformulation, our approach takes advantage of massive parallelism across both scenarios and transitions, enabling the simultaneous evaluation of \emph{over one million uncertainty realizations} in a single GPU pass -- a scale far beyond the reach of existing methods. We instantiate the framework in two canonical applications: the capacitated vehicle routing problem with stochastic demand and a dynamic stochastic inventory routing problem. In both cases, DP subroutines traditionally considered sequential are redesigned to harness two- or three-dimensional GPU parallelism. Experiments demonstrate near-linear scaling in the number of scenarios and yield one to three orders of magnitude speedups over multithreaded CPU baselines, resulting in tighter SAA estimates and significantly stronger first-stage decisions under fixed time budgets. Beyond these applications, our work establishes a general-purpose recipe for transforming classical DP routines into high-throughput GPU primitives, substantially expanding the computational frontier of stochastic discrete optimization to the million-scenario scale.