Capacity Expansions with Bundled Supplies of Attributes : An Application to Server Procurement in Cloud Computing

The recent trend of a surge in demand for cloud services has posed a challenging capacity expansion problem for the cloud providers: while the growths of demand for different capacity attributes (e.g., CPU and RAM) are time-varying and disproportionate, replenishments of these attributes are often in packages (e.g., server clusters) of pre-determined configurations; the ratio of supply in a specific package does not match with the ratio of demand of the capacity attributes. We develop a model, where demand growths of two attributes are considered, and focus on a class of policies consisting of multiple capacity expansion cycles, where capacities are added through sequential replenishments of two given cluster-types and excess capacities of both attributes are required to reach a desired minimum level at the start and the end of each cycle. For the linear demand growths, we identify the optimal policy in closed-form, and for the exponential demand growths, we devise a dynamic-programming-based algorithm, as well as a forward-looking heuristic based on minimization of the total cost rate of each cycle, to determine the optimal cycle lengths. Moreover, we examine how to efficiently choose the two cluster-types, statically or adaptively, in the presence of many options, and we propose a cluster-selection heuristic, which indicates to select the leading cluster that would cause the minimal excess capacity and the following cluster that would deplete the excess capacity the fastest. Finally, we conduct a numerical study of the performance of the proposed policies and heuristics