Optimal replenishment and optimal pricing decisions when a retailer sells new and old generation products together

For the demands of new and old generation products existing together, the optimal decisions problem for two generations production need be considered by retailer. New generation product can satisfy the demand for old generation production, but retailer need decide the substitution price. When the demand is stochastic, for maximizing expectation profits, the optimal replenishment quantity and optimal price need be determined. A single period stochastic inventory model was formulated. The uniqueness and existence of optimal decisions were proved, and the conditions that the optimal decisions should satisfy were obtained. The final, the expressions of the optimal condition under the uniform distribution were given.