Cloud computing has given enterprises the opportunity to acquire computing resources cost effectively and yet benefit from other key cloud features that include scalability, instant provisioning, and virtualized resources. Cloud service providers enable businesses to acquire resources by offering different cloud deployment, service, and pricing models. A major challenge for cloud users is to determine the amount of resources to be provisioned that meet their expected needs over the planning horizon, the deployment models to opt for, and the pricing models to adopt to minimize cost. Research in cloud economics has focused on building analytical optimization models that require the representation of the expected demand pattern over the planning horizon as a probability density function amenable to mathematical analysis. In this work, however, we have built a computational model based on simulation and genetic programming to compute the optimal combination of own-private and public cloud resources that satisfy a given pattern of demand as well as the optimal contract guaranteed service level. The model incorporates into the optimization process the different price subscription models offered by cloud providers. The distinguishing features of our model is that it can handle any theoretical or empirical demand probability distribution. In addition, our computational scheme allows for any random variation in any of the parameters affecting the total cost of cloud resources consumed as long as this variation can be described by a theoretical or an empirical density function. The accuracy and correctness of the model was tested against results obtained from mathematical models based on normally and exponentially distributed demand patterns with almost identical results. Thus, our computational model provides a valuable decision tool to help identify the most cost-effective way of provisioning computing resources. Results of experiments conducted in this work indicate that it is more cost effective to use a mixed strategy rather than depend entirely on own-private capacity or on-demand public cloud computing resources alone irrespective of the level of variation in demand; the optimal level of ownprivate computing capacity is affected by the shape of the demand curve, level of variations in demand, guaranteed service level, and the cloud price subscription model adopted. Future work will extend the computational model to optimize the cost of using cloud storage and networking services. Future work will extend the model to include the cost optimization of using cloud storage and networking services.