Deteriorating inventory model for time dependent demand and holding cost with partial backlogging

In most of the deteriorating items inventory model the holding cost and demand rate has considered as a constant function. But in realistic situation these cost varying according to time. So in this paper, we developed a deterministic deteriorating inventory model in which demand rate and holding cost both is linear function of time, deterioration rate is constant, backlogging rate is variable and depend on the length of the next replenishment, shortages are allowed and partially backlogged. The model is solved analytically by minimizing the total inventory cost. The model is tested for a set of parameter and results indicate that the model is quite stable. The model can be applied for optimizing the total inventory cost of deteriorating items inventory for a business enterprise where demand and holding cost both is linear function of time.