Probabilistic analysis of dynamic inventory models with general demand pattern

This paper discusses a probabilistic inventory model without setup costs and lead times. In the model, partial returns in the case of surplus and additional orders in case of shortage are allowed less than or equal to the maxima permitted, respectively. There are the ordering costs, holding costs and penalty costs in the model. The total expected cost in a single period is not a convex function. Specific values of the variable that minimize the total expected costs in a single period are found and an n-period dynamic model is considered.