Inventory Model for Perishable Items with Variable Holding Cost and Partial Backlogging

In the traditional inventory models,there exists a common assumption that the holding cost is constant.In the paper,we relax this assumption and two possibilities are considered :(i)A non-linear function of the length of time the item;(ii) A non-linear function of the amount of on-hand inventory.we develop two inventory models for deteriorating items with stock-dependent demand in which shortages are allowed to occur and partial backlogged.The proofs are provided for the existence and uniqueness of optimal replenishment schedule a certain condition.