Algorithm of determining Product's Batch Size and Sequence of the Operations of n Job on m Machine

In this paper, a heuristic algorithm has been presented with the aim of determining the quantity of a best batch size for minimizing the makespan of a production system in order to meet the demands of a specified period for a product. This algorithm calculates the time required for fulfilling each of the requisite operations for producing a batch size by taking into account the standard time for fulfilling the operations, number of similar parts used in one unit of a product, the machinery setup time, scrap percentage of each operation on the relevant machinery and the quantity of that batch size. This algorithm allots the requisite operations to the machinery for producing the total demand of a specified period by making use of the calculated information, SPT1 rule, the specified conditions in the algorithm and the quantity of the production in each batch size. Then, with respect to the quantity of this batch size, the aggregate of the setup and idle times of machinery is calculated for the whole period. Afterwards, the quantity of the optimum batch size which minimizes the aggregate of these times is obtained by calculating the aggregate of these times for the different quantities of the batch sizes and comparing them. Some examples have been presented for comparing this algorithm with Ho & Chang, Johnson, and Palmer's algorithms. The results show that this algorithm presents a better makespan in comparison with the aforementioned algorithms.