In this paper, we study the problem of finding optimal mappings for several independent but concurrent workflow applications, in order to optimize performance-related criteria together with energy consumption. Each application consists in a linear chain application with several stages, and processes successive data sets in pipeline mode, from the first to the last stage. We study the problem complexity on different target execution platforms, ranking from fully homogeneous platforms to fully heterogeneous ones. The goal is to select an execution speed for each processor, and then to assign stages to processors, with the aim of optimizing several concurrent optimization criteria. There is a clear trade-off to reach, since running faster and/or more processors leads to better performance, but the energy consumption is then very high. Energy savings can be done at the price of a lower performance, by reducing processor speeds or enrolling fewer resources.. We consider two mapping strategies: in one-to-one mappings, a processor is assigned a single stage, while in interval mappings, a processor may process an interval of consecutive stages of the same application. For both mapping strategies and all platform types, we establish the complexity of several

A large class of applications need to execute the same workflow on different data sets. Efficient execution of such applications necessitates intelligent distribution of the application components and tasks on a parallel machine, and orchestrating the execution by utilizing task-, data-, pipelined-, and replicated-parallelism. The scheduling problem that encompasses all of these techniques is called pipelined workflow scheduling, and has been widely studied in the last decade. Multiple models and algorithms flourished to tackle various programming paradigms, constraints, machine behaviors or goals. This paper surveys the field by summing up and structuring known results and approaches.