Inventory model with variable holding cost and lost sales

The holding cost is regarded as constant in the classical economic order quantity(EOQ) models concerning inventory problems.In this paper,firstly,the variable holding cost and the lost sales during the shortage period are studied,and an inventory model is developed for deteriorating items with the partial backlogging and the variable holding cost as the variable holding cost is a function of the length of the holding time,that is h(t).Secondly,through the theoretical analysis,it is proved that the model has a unique optimal integral solution.Finally,for the holding cost function h(t)=τeδt,a numerical analysis of the coefficient of back-orders β and the parameter δ is given by the numerical calculation,and the effect of the change in holding costs and lost sales on the optimal order policy for the inventory system is revealed.