In recent years, part feeding at assembly lines has become a critical issue as the result of a high level of product customization. The assembly line part feeding problem is a complex problem in which a number of decisions should be made in order to select the right quantity of each part to be supplied at the right time under a set of constraints. This study aims to cope with the part feeding problem at assembly lines by introducing a new memetic ant colony optimization-based heuristic algorithm. Due to the novelty of the problem and in order to evaluate the performance of the proposed memetic algorithm, a mathematical formulation is also presented. Case data from an automobile manufacturer and a set of generated instances are used to test both the mathematical model and the proposed memetic algorithm. The results reveal that although it is computationally difficult to solve the problem using the exact mathematical model, the mimetic algorithm was able to find sufficiently good solutions in a short period of time.