Different aspects of assembly line optimization have been extensively studied. Part feeding at assembly lines, however, is quite an undeveloped area of research. This study focuses on the optimization of part feeding at mixed-model assembly lines with respect to the Just-In-Time principle motivated by a real situation encountered at one of the major automobile assembly plants in Spain. The study presents a mixed integer linear programming model and a novel simulated annealing algorithm-based heuristic to pave the way for the minimization of the number of tours as well as inventory level. In order to evaluate the performance of the algorithm proposed and validate the mathematical model, a set of generated test problems and two real-life instances are solved. The solutions found by both the mathematical model and proposed algorithm are compared in terms of minimizing the number of tours and inventory levels, as well as a performance measure called workload variation. The results show that although the exact mathematical model had computational difficulty solving the problems, the proposed algorithm provides good solutions in a short computational time.