Cloud computing is an emerging paradigm that provides hardware, platform and software resources as services over the internet in a pay-as-you-go model. It is being increasingly used for hosting and executing service-based business processes. These business processes are exposed to dynamic evolution during their life-cycle due to the highly dynamic evolution of cloud environments. The main adopted technique is to couple cloud computing with autonomic management in order to build autonomic computing systems. Almost all the existing approaches on autonomic computing have been focused on modeling and implementing autonomic mechanisms without paying any attention to the optimization of the autonomic management cost. Therefore, in this paper, we propose a novel approach based on binary linear program for determining the optimal allocation of cloud resources to manage a service-based business process which guarantees the specific requirements of customers and minimizes the management monetary cost. Then, to validate our approach under realistic conditions and inputs, we extend the CloudSim simulator to model and simulate the behaviour of business processes and their management in a cloud environment. Experiments conducted on two real datasets highlight the effectiveness of our approach.