This study presents a comparative study to determine ideal stock levels of a multi-national tire manufacturing company. The conventional inventory models can not be sufficient to optimize the production, the inventory quantity and the backorder simultaneously. Therefore, it is not possible to obtain a production policy by considering these objectives for all produced parts concurrently. In this paper, a production problem with three objectives is solved with mathematical modeling, greedy algorithm and genetic algorithm considering production constraints of a company. While existing inventory models based on conventional methods were applied for safety stock level determination, our proposed model uses the mathematical programming based optimization methods based on mathematical programming. Furthermore, the production planning policy is obtained with the optimum production amount and the stock is determined by considering the constraints defined by the firm. Finally, in our numerical results, we compare each solution methodology with respect to each objective criteria. (C) 2015 Elsevier Inc. All rights reserved.