Private and public clouds are good means for getting on-demand intensive computing resources. In such a context, selecting the most appropriate clouds and virtual machines (VMs) is a complex task. From the user’s point of view, the challenge consists in efficiently managing cloud resources while integrating prices and performance criteria. This paper focuses on the problem of selecting the appropriate clouds and VMs to run bags-of-tasks (BoT): big sets of identical and independent tasks. More precisely, we define new mathematical optimization models to deal with the time of use of each VMs and to jointly integrate the execution makespan and the cost into the objective function through a bi-objective problem. In order to provide trade-off solutions to the problem, we propose a lexicographic approach. In addition, we introduce, in two different ways, capacity constraints or bounds on the number of VMs available in the clouds. A global limit on the number of VMs or resource constraints at each time period can be defined. Computational experiments are performed on a synthetic dataset. Sensitivity analysis highlights the effect of the resource limits on the minimum makespan, the effect of the deadline in the total operation cost, the impact of considering instantaneous capacity constraints instead of a global limit and the trade-off between the cost and the execution makespan.