Purchasing Inventory Models for Deteriorating Items with Linear Demand and Shortages - in Third Order Equation

In this paper, a purchasing inventory model for deteriorating items is developed with a linear, positive trend in demand, allowing inventory shortages and backlogging. It is assumed that the goods in the inventory deteriorate over time at a constant rate . Two models are developed for two operational policies. The first policy covers the case that the inventory model with linear demand for deteriorative items and the second policy covers the case that the inventory model with linear demand for deteriorative items and shortages. Mathematical model is developed for each model to reduce the third order equation and the optimal cycle time and inventory lot size which minimizes the total cost is derived. Illustrative example is provided for each model. In each model, sensitivity analysis is performed to show how the optimal values of the policy variables in the model change as various model parameters are changed. The validation of result in this model was coded in Microsoft Visual Basic 6.0.