Mohammad Reza Nemati - MSc., Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran
Mehrdad Kargari - Associate Professor, Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran
Ehsan Nikbakhsh - Assistant Professor, Faculty of Industrial and Systems Engineering, Tarbiat Modares University, Tehran, Iran

Decision-making to determining the composition of the product by identifying the products and determining their types and quantities, considering the limited resources, is one of the most important effective decisions of the production units. The purpose of determining the optimal product mix is to find a production plan in such a way that the amount of profit obtained is maximized and the constraints of resources, market, sales, etc. are considered. In the literature, various models have been presented to solve this problem in different industries and it is always of great importance. The proposed model in this research is based on the basic model available in the literature is used and according to the constraints of the real environment, including market share limitations, a multi-period and multi-product model with an inventory and shortage system has been studied. Finally, with the real data of a lubricant company, the results of the model show improvement compared to the actual profitability of the company

product mix, optimum production, inventory system, shortage, lubricant industry.