Inventory model for deteriorating items with time-dependent partial backlogging rate and inventory-level-dependent demand rate

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In this paper,a more general inventory model for deteriorating items with partial backlogging rate was developed,and the deterioration rate changed as the time was running on.When the inventory level was positive,the demand rate depended on the selling price;but when the inventory level was negative,some customers were more impatient to wait,therefore the sale opportunity was reduced and a bigger shortage led to a larger loss.With some analysis,the necessary condition for the existence of optimal solution to the general model was derived.The necessary conditions of the existence and uniqueness of the optimal solutions were introduced.At last,a case study was provided for the proposed model.