This paper is proposing a novel machine scheduling model for the unrelated parallel machine scheduling problem without setup times to minimize the total completion time, also known as “makespan”. This problem is a NP-complete problem, and to date, most approaches for real-life situations are based on the operator’s experience or simple heuristics. The new model based on the Memetic Algorithm, which was proposed by P. Moscato in 1989, is a hybrid algorithm that includes genetic algorithm and local search optimization. The new model is tested on randomly generated datasets, and is compared to optimal solution, and four scheduling models; three rule-based heuristic algorithms, and a genetic algorithm based scheduling model from literature; the test results show that the new model performed better than scheduling models from literature.