An inventory model for time varying holding cost and price discount on backorders in stock dependent demand environment

In this paper, an inventory model for deteriorating items is studied with stock dependent demand rate where holding cost is expressed as linearly increasing function of time. The study includes some features that are likely to be associated with certain types of inventory in real life, like inventory of seasonal fruits and vegetables. When shortage occurs, only a fraction of unmet demand is backlogged, and the inventory manager offers a discount on it. Conditions of permissible delay in payments are also taken into account. The optimum ordering policy and the optimum discount offered for each backorder are determined by minimizing the total cost in a replenishment interval. Sensitivity analysis is also performed by changing (increasing or decreasing) the parameters and taking one parameter at a time, keeping the remaining parameters at their original values.