Actual trend today is towards a macro economy based on the OPEX costing model. This trend is the solution proposed for dealing with a large population sharing a limited number of resources on this planet. Cloud Computing is one of the consequences of this tendency. It promises access to a large number of services in an on-demand manner. This raises the problem of finding the best strategy to migrate on premise resources in the cloud. Despite the popularity of the subject, none of the existing papers treats directly the migration period when cost increases and solutions have to be found to limit the expenses and diminish the risk of service interruption. In this paper we propose a methodology of modeling a migration in the cloud that aims achieving lower costs or minimal time, depending on which constraint is needed first. Through a realistic experiment we show the migration of a web system using the proposed methodology. We also see a lot of possible developments and generalizations of the method in similar IT projects of transitioning from CAPEX to OPEX