Deterministic inventory model for items with linear demand, variable deterioration and partial backlogging

A deterministic inventory model is developed for a deteriorating item having linear demand and variable deterioration rate. Shortages are allowed and partially backlogged. In developing the model we have assumed that the rate of backlogging is variable and dependent on the waiting time for the next replenishment. The objective of the model is to develop an optimal policy that minimises the total average cost. Suitable numerical example has been discussed to understand the problem. Sensitivity analysis has been carried out to show the effect of changes in the parameter on the optimum total average cost.