Additive manufacturing (AM) is well known for its potential to facilitate mass customization and low-volume, high-mix production with relatively few geometric constraints. A good example is the Fused Filament Fabrication (FFF) process. However, such AM processes are often considerably slower than traditional manufacturing processes, and this represents one of the most significant barriers to widespread applications of AM. A promising solution is the parallel processing of individual layers. This research investigates a concurrent manufacturing strategy for improving the production speed of the FFF process with multiple extruders working in parallel. To achieve the minimum production time, a scheduling problem is formulated to coordinate the toolpaths of multiple extruders under collision-avoidance constraints. Two heuristic solution algorithms are described, and their performance is compared for various layer profiles. Numerical examples are provided to demonstrate the performance of the two algorithms, and to show a method for determining the optimal number of extruders based on layer characteristics.