This work presents an efficient mathematical formulation for the optimal planning of multiproduct assembly lines. The aim is to establish a cyclic production agenda that minimizes the sum of inventory holding and transition costs per unit time. Besides, carbon footprint of assembled products is tracked along the line while optimally determining task times and operating modes. Batch sizing and sequencing in synchronous assembly lines have been typically addressed through discrete-time approaches that imply significant computational burden. In contrast, our novel representation resembles continuous-time pipeline scheduling models that permit to obtain optimal solutions in reasonable times. Results show the capabilities of the optimization approach to solve large instances of the problem, also demonstrating how task times and operating modes can be handled to reduce carbon footprint with no loss of productivity.