Cloud manufacturing task allocation, routing, and scheduling via scenario-reduced two-stage stochastic programming

Uncertain processing and inter-provider migration times complicate task allocation and scheduling in distributed cloud manufacturing. We formulate a two-stage stochastic mixed-integer model with nonanticipative provider assignments and resource sequencing, followed by scenario-dependent scheduling and tardiness recourse. A 15-scenario hybrid compression procedure combines k-means clustering and backward reduction. Ten independent synthetic instances across three uncertainty regimes were evaluated using 600 training and 5,000 independent test scenarios per condition. In independently reproduced experiments, the hybrid, clustering, forward selection, and a 200-scenario sample average approximation benchmark yielded identical observed test metrics across all 30 conditions. Paired tests identified no significant overall differences but did not establish equivalence. Mean cumulative computation, including scenario selection, model construction, and solver retries, was 1.192 seconds for the hybrid, 1.015 for clustering, and 14.553 for the benchmark. Information-value estimates varied across instances. Findings establish reproducible decision-quality evidence and computational savings relative to the benchmark within small synthetic instances.