We consider the problem of scheduling independent jobs that are generated by processing units at the edge of the network. These jobs can either be executed locally, or sent to a centralized cloud platform that can execute them at greater speed. Such edge-generated jobs may come from various applications, such as e-health, disaster recovery, autonomous vehicles or flying drones. The problem is to decide where and when to schedule each job, with the objective to minimize the maximum stretch incurred by any job. The stretch of a job is the ratio of the time spent by that job in the system, divided by the minimum time it could have taken if the job was alone in the system. We formalize the problem and explain the differences with other models that can be found in the literature. We prove that minimizing the max-stretch is NP-complete, even in the simpler instance with no release dates (all jobs are known in advance). This result comes from the proof that minimizing the max-stretch with homogeneous processors and without release dates is NP-complete, a complexity problem that was left open before this work. We design several algorithms to propose efficient solutions to the general problem, and we conduct simulations based on real platform parameters to evaluate the performance of these algorithms.