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

摘要

This paper develops a deterministic model with time-dependent backlogging rate. 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. It is proved that the optimal replenishment policy not only exists but also is unique. The authors provide simple solution procedures for finding the maximum total profit per unit time. Numerical examples are given to illustrate the model.