A business process is a combination of structured and related activities that aim at fulfilling a specific organizational goal for a customer or market. An important measure when developing a business process is the degree of parallelism, namely, the maximum number of tasks that are executable in parallel at any given time in a process. This measure determines the peak demand on tasks and thus can provide valuable insight on the problem of resource allocation in business processes. This paper considers timed business processes modeled in BPMN, a workflow-based graphical notation for processes, where execution times can be associated to several BPMN constructs such as tasks and flows. An encoding of timed business processes into Maude's rewriting logic system is presented, enabling the automatic computation of timed degrees of parallelism for business processes. The approach is illustrated with a simple yet realistic case study in which the degree of parallelism is used to improve the business process design with the ultimate goal of optimizing resources and, therefore, with the potential for reducing operating costs.