In this paper, we study the problem of finding optimal mappings for several independent but concurrent workfl ow 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 multi-criteria optimization problems, whose objective functions combine period, latency and energy criteria. In particular, we exhibit cases where the problem is NP-hard with concurrent applications, while it can be solved in polynomial time for a single application. Also, we demonstrate the difficulty of performance/energy trade-offs by proving that the tri-criteria problem is NP-hard, even with a single application on a fully homogeneous platform.