We consider the Simple Assembly Line Balancing Problem with Power Peak Minimization and Earliest Starting Dates (SALB3PM-ESD), a problem of balancing an assembly line and suitably sequencing its tasks so as to minimize the peak of the electric power consumption associated with them. We propose an ILP-based decoder to optimally split (w.r.t. the power peak) a sequence of tasks over the workstations of the line. The decoder is plugged into a simple local search algorithm to test its effectiveness in quickly computing the optimal split for the solutions encountered in the space of task sequences. Preliminary tests on instances from literature show that the decoder is efficient, and that it seems indeed promising to use it to take advantage of the numerous sequence-based optimization algorithms in the scheduling literature to develop more competitive methods to efficiently tackle the SALB3PM-ESD.