We study time-of-use pump scheduling to deliver a required volume using a finite set of pump combinations with empirical flow–power performance, subject to per-shift caps on pump switches. We prove a structural theorem: partitioning the horizon into maximal intervals with constant tariff and shift (atoms), there always exists an optimal schedule with at most one internal switch in at most one atom, with all other switches at atom boundaries. This insight yields an exact mixed-integer linear program with atom-level variables and without time discretization.