This paper focuses on minimizing the energy consumed by vehicles for parts supplying to workstations in mixed-model assembly lines. The parts are assumed to be packed in bins (or pallets). The bins are shipped from a so-called “supermarket” and delivered periodically to the workstations using tow trains with wagons. For each time period, depending on the production plan, a workstation has a specific demand of parts expressed as a portion of a bin. The problem is to define the sequence of workstations to be visited by the tow train at each time period, as well as the number of bins to be delivered at each stop, so as to avoid any material shortage. This paper provides an analysis of the computational complexity related to this problem and proposes two original mixed integer linear programming formulations. We also provide computational analysis and experiments that put the efficiency of one particular formulation into evidence and show the conditions under which energy-efficient supplying is not in contradiction with economic efficiency.