The Study Of Stochastic Inventory Model

With the developing of market economy, the inventory problem is more important than ever. Many inventory models have been studied. The market and service are changing now and then, so are the inventory models.In this article, we start from the easiest model-----newspaper vendor model, then the two-product inventory model with substitution. At last we discuss the many-product inventory model with substitution. In the market, many same or products of similar nature can substitute for each other and excess demand for products can also be met by reorder. Our purpose is to find how the substitution and reorder influence inventory from the retailer's viewpoint, by this we get the condition the optimal order quantities subject to. And we present the sufficient conditions for the objective function to be concave.This paper contains five parts. The background of stochastic inventory model and domestic and foreign research present situation are presented in the first part. The second part is the two-period model; we have proved-the optimal order volume existence and shown the formula. In the third part, we discussed the two-product model with substitution, proved the optimal solution is existence and the expression of optimal solution. In the forth part, we discussed the many-product model with substitution, and proved that the optimal solution is not always existence. In the fifth part, we discussed the demand-time-continue model, and gave the optimal cycle length.The changing of real life requested us to keep pace with times in stock modeling. More and more people join in studying the inventory problem, the theoretically achievement inevitably played a great role in instructing practice.