Ordering or returning policies in single period stochastic inventory with uniform distributed demand

This paper presents an optimal inventory policy under a given stochastic demand such as uniformly distributed demand, single-item, single period review inventory system. The optimal inventory control policy obtained in this paper is called four-point policy, that is, when inventory level of the entity is below an ordering point, the entity orders the stock level up to a fixed level (second point); when the inventory level of the entity is over a return point (third point), returns the stock level down to a fixed level (fourth point); otherwise, nothing should be done. Moreover, the optimal inventory decision functions have the continuous order property and continuous return property. We also analyze the (S, K)-convex properties of the cost function of the inventory.