Virtual machine allocation is a core problem in cloud computing. Most cloud computing platforms allow users to submit one requirement, which does not satisfy the diversity of user demands and also reduces the incomes of the platform. We propose a novel model, called multi-choice virtual machine allocation (MCVMA) with time windows, where the users can enter and leave the system at any time and submit multiple requirements. We design an optimal algorithm based on dynamic programming and a heuristic algorithm based on the resource scarcity and density for the MCVMA problem with time windows. We experimentally analyze both algorithms in terms of social welfare, execution time, resource utilization and users served.