Optimal lot size for an item with partial backlogging rate when demand is stimulated by inventory above a certain stock level

In this paper, a deterministic inventory model with time-dependent backlogging rate is developed. The demand rate is a power function of the on-hand inventory down to a certain stock level, at which the demand rate becomes a constant. We prove that the optimal replenishment policy not only exists but also is unique. Furthermore, we provide simple solution procedures for finding the maximum total profit per unit time. Numerical examples have also been given to illustrate the model and we conclude the paper with suggestions for possible future research.