Distributionally Robust Dynamic Resource Provisioning Under Service-Level Agreement

We consider a dynamic resource provisioning problem for a supplier in which the availability of the provisioned resource is subject to random disruptions whose distribution is only indirectly observable through samples. To signal its commitment to service quality, the supplier adopts a service level agreement contract that specifies both the target service level and the associated penalty for violation over a finite contract period. The supplier needs to dynamically determine resource provisioning decisions with the objective of minimizing operational costs and penalties incurred due to service-level agreement violations. We construct a Wasserstein-based distributionally robust dynamic programming framework to model and solve the dynamic resource provisioning problem under a service-level agreement. In particular, we provide a convexification algorithm that enables us to solve the nonconvex robust dynamic programming problem in a backward manner. We further examine a special case where service shortages depend linearly on the provisioned resources, enabling the problem to be reformulated into a sequence of linear programs. This linear shortage model naturally connects to residual-based robust formulations, which facilitate us to accommodate nonlinear relationships between resource provisioning and service shortages. We propose several approximation algorithms to improve computational efficiency. To mitigate the possibly over-conservativeness, we explore radius adjustment strategies based on sample size, state, stage, and cumulative cost information, which yield consistent out-of-sample performance. We perform a case study of a cloud computing example to demonstrate the effectiveness of the proposed solution approach and elicit managerial insights. The results suggest that suppliers should provide fewer backup servers when cumulative downtime is low or when approaching the end of the planning horizon. The dynamic resource provisioning policy significantly reduces the total cost compared to the best static policy. Furthermore, applying appropriate radius adjustments can further enhance the out-of-sample performance.