Despite the prevalence of cloud and edge computing, ensuring the satisfaction of time-constrained business processes, remains challenging. Indeed, some cloud/edge-based resources might not be available when needed leading to delaying the execution of these processes' tasks and/or the transfer of these processes' data. This paper presents an approach for specifying, verifying, and deploying time-constrained business processes in a mono-cloud, multi-edge context. First, the specification and verification of processes happen at design-time and run-time to ensure that these processes' tasks and data are continuously placed in a way that would mitigate the violation of time constraints. This mitigation might require moving tasks and/or data from one host to another to reduce time latency, for example. A host could be either a cloud, an edge, or any. Finally, the deployment of processes using a real case-study allowed to confirm the benefits of the early specification and verification of these processes in mitigating time constraints violations.