Expanding the cloud: An integrated optimization framework for distributed infrastructure scaling under uncertainty

With the continuous surge in computing demand, cloud service providers (CSPs) are aggressively expanding their data center (DC) infrastructures across diverse geographical regions. Considering the substantial capital investments and extended planning horizons, it is crucial to account for operational uncertainties throughout the expansion process. This study introduces a joint optimization model integrating DC site selection, resource provisioning, network configuration, and demand assignment. Long-term uncertainties in demand and electricity price growth are modeled with robust sets, while short-term uncertainties in availability, demand, and electricity price are captured by representative scenarios. To address the resulting mixed-integer nonlinear programming problem, we develop a hybrid Benders decomposition method that merges classical and logic-based Benders cuts. Numerical experiments validate the scalability and computational efficiency of the proposed approach, demonstrating that it achieves a computational speedup of around 100x compared to standard commercial solvers on large-scale instances. Results indicate that short-term demand volatility dominates cost impacts, whereas long-term uncertainties accelerate facility deployment. The findings also show that, compared to rigid static strategies, adopting dynamic service commitments significantly reduces cumulative costs by up to 11.25%. This study also investigates interactions between service commitments and budget limits. Theoretical contributions include advanced uncertainty quantification and algorithmic design, while practical implications guide CSPs in balancing cost-efficiency with service commitments.