As for all kind of software, customers expect to find business process execution provided as a service (BPMaaS). They expect it to be provided at the best cost with guaranteed SLA. From the BPMaaS provider point of view it can be done thanks to the provision of an elastic cloud infrastructure. Providers still have to provide the service at the lowest possible cost while meeting customers expectation. We propose a customer-centric service model that link the BP execution requirement to cloud resources, and that optimize the deployment of customer’s (or tenants) processes in the cloud to adjust constantly the provision to the needs. However, migrations between cloud configurations can be costly in terms of quality of service and a provider should reduce the number of migrations. We propose a model for BPMaaS cost optimization that take into account a maximum number of migrations for each tenants. We designed a heuristic algorithm and experimented using various customer load configurations based on customer data, and on an actual estimation of the capacity of cloud resources.