A configurable process model is a generic model from which an enterprise can derive and execute process variants that meet its specific needs and contexts. With the advent of cloud computing and its economic pay-per-use model, enterprises are increasingly outsourcing partially or totally their process variants to cloud providers, and recently to cloud federations. A main challenge in this regard is to allocate optimally cloud resources to the process variants' activities. More specifically, an enterprise may be interested in outsourcing only those that result in an optimal deployment. Due to the diversity of the enterprise QoS requirements, the heterogeneity of resources offered by the cloud federation and the large number of possible configurations in a configurable process model, finding the optimal process variant deployment becomes a highly challenging problem. In this paper, we propose a novel approach to solve this problem through a binary/(0-1) linear program with a quadratic objective function under a set of constraints pertinent to both the enterprise and cloud federation requirements. Our prototypical implementation demonstrates the feasibility and the results of our experiments highlight the effectiveness of our proposed solution