With software services becoming ever more ubiquitous, organizations are increasingly relying on interconnected business processes that orchestrate the interplay of individual services. The virtually unlimited computing resources available in cloud environments facilitate rapid, on-demand deployment of elastically scaling processes. Yet, due to the load fluctuations typically encountered in volatile process landscapes, optimal resource allocation and process scheduling are complex tasks. In this work, we address the challenge of cost-optimized process execution in scalable environments, leveraging techniques from the fields of elastic processes, operations research, and cloud computing. Based on previous work that uses Virtual Machines (VMs) as scheduling units, this thesis presents a novel optimization approach that allows for auto-scaling over four dimensions: vertically and horizontally, for both VM and container instances. Our solution enables allocation of services to lightweight containers, leading to more fine-grained control over resources for process executions. We define the optimization problem as a Mixed Integer Linear Programming (MILP) model, and apply heuristics that reduce the search space while still considering all resource, cost, and quality constraints, as well as VM and container characteristics of the underlying system. The approach is implemented using an off-the-shelf solver, and the optimization result is executed as part of a newly designed container-based middleware. We additionally introduce a time discretization framework that allows us to simulate long-running, realistic scenarios. Our extensive experimental evaluation under various configurations shows substantial cost savings and better resource utilization as compared to recently proposed VM-based approaches, without sacrificing adherence to service level agreements (SLAs).