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As known, it is not possible to develop an algorithm that can compute the exact value of the minimum makespan on identical parallel machines in polynomial time. Therefore heuristic methods are convenient to find near optimal solutions. In this thesis, it is aimed to compose a new heuristic algorithm to minimize the makespan on identical parallel machines. This algorithm can present better solutions than LPT (Longest Processing Time) algorithm in general. The computer models of the proposed and LPT algorithms are developed. 1640 different problems are solved using the two models to compare the performances of the algorithms. Numbers of jobs, numbers of machines or the mean of processing times are changed one at a time, while keeping the rest constant and, the variation in the makespan is observed. Finally it is concluded that there is sufficient evidence that the proposed algorithm provides better solutions than LPT in the light of the data collected from the uniform distribution. The proposed algorithm is also modified to the probabilistic cases.
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