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In this paper, we study an inventory control model, which is analyzed by means of a difference equation. This model is applied to study the stock of a polyester company. In this company, two types of polyester are manufactured, and it is considered a stochastic demand. In the paper, an optimal policy of production is determined, which minimizes the total expected discounted cost. The one-step cost function is integrated with the following components: production, storage and sale lost. The methodology consists on applied the dynamic programming approach and some results of convex analysis to determine a (R, Q)-optimal policy, where R and Q are positive numbers. R represents the maximum level of production and Q is the minimum stock. Finally, with a company database of monthly sales, we adjust a probability distribution and present a numerical implementation of the optimal. Furthermore, simulations to observe the asymptotic behavior of the stock are illustrated. |
