Pipelined workflows are a popular programming paradigm for parallel applications. In these workflows, the computation is divided into several stages, and these stages are connected to each other through first-in first-out channels. In order to execute these workflows on a parallel machine, we must first determine the mapping of the stages onto the various processors on the machine. After finding the mapping, we must compute the schedule, i.e., the order in which the various stages execute on their assigned processors. In this paper, we assume that the mapping is given and explore the latter problem of scheduling, particularly for linear workflows. Linear workflows are those in which dependencies between stages can be represented by a linear graph. The objective of the scheduling algorithm is either to minimize the period (the inverse of the throughput), or to minimize the latency (response time), or both. We consider two realistic execution models: the one-port model (all operations are serialized) and the multi-port model (bounded communication capacities and communication/computation overlap). In both models, finding a schedule to minimize the latency is easy. However, computing the schedule to minimize the period is NP-hard in the one-port model, but can be done in polynomial time in the multi-port model. We also present an approximation algorithm to minimize the period in the one-port model. Finally, the bi-criteria problem, which consists in finding a schedule respecting a given period and a given latency, is NP-hard in both models.