Computing offloading and scheduling are emerging, accompanied by smart city services, Internet of Things, and other rich cloud services. Cloud-assisted mobile edge computing provides malleable resources but introduces considerable overhead. Due to the geographical distributions and distances of the edge, cloud, and mobile terminal, promoting cost efficiency and reducing the makespan of applications are urgent targets. For multiple mobile applications, the soft deadline constraint for each application is common in the edge-cloud environment. When multiple users initiate application requests, scheduling on the target offloaded platform commences. Some workflows, especially newly arrived workflows, might suffer from “starving to death,” which has the risk of being missed. This article describes a dynamic, multiworkflow offloading, and scheduling, adaptive heterogeneous earliest-finish-time-based algorithm, which can lightly run on a distributed network. We explore an innovative model composed of a multiobjective makespan and cost for a soft deadline constraint optimization problem. Abundant data are adopted to test the offloading and scheduling effect on a variety of platform parameters, and comparative experiments demonstrate the validity and efficiency of the adaptive system.