Inventory model for the growing items with price dependent demand, mortality and deterioration

Growing items like livestock, chicks, etc. gain weight in the growing phase but some of them are lost due to mortality. In the selling phase, some inventory is lost due to deterioration. Such aspects make procurement decisions quite difficult for these items. In the light of such aspects, we developed an inventory model for the growing items with price dependent demand, mortality and deterioration. Shortages are partially backlogged. Our aim is to optimise the total cost by determining the optimal ordered quantity and total cycle length. Convexity of the cost function with respect to the decision variables has been discussed analytically. Solution procedure along with numerical example at different percentage of backlogged quantity is provided to show the applicability and validity of our model. Sensitivity analysis shows that total cycle length is the most sensitive among all the decision variables and parameters.