Demand for computing capacity in the cloud is generally not easily forecast; however, sub-optimal pricing and mis-allocation of cloud computing resources both have negative consequences for users and providers of cloud computing. This thesis approaches pricing and capacity allocation in cloud computing through the lens of stochastic mixed integer programming (SMIP), which provides a particularly useful framework for solving large, complex decision-making problems under uncertainty.

Often, the uncertainty inherent to SMIPs manifests in the right-hand side (demand) vector. Thus, it is important to have a framework by which to assess a mixed integer programming (MIP) model’s quality over unknown or stochastic right-hand sides. As such, this thesis explores both theoretical and practical applications of SMIPs and MIPs with unknown right-hand sides. In particular, this thesis develops theoretical evaluative metrics for MIPs over multiple right-hand sides via gap functions, presents several stochastic optimization approaches to optimal pricing in the cloud, and formulates waste-minimizing (revenue-maximizing) SMIP models that optimize capacity allocation in the cloud.