Inventory and preservation investment for deteriorating system with stock-dependent demand and partial backlogged shortages

Our model deals with the stock-dependent demand as exhibiting huge volume of commodities leads to more costumers and augment the trading of the goods. As some goods like vegetables, fruits, medicines deteriorate after a period of time, resulting in economical and financial losses, we took this factor into consideration and included a constant deterioration rate, controlled by suitable preservation technologies. Preservation technology investments are made for the valuable business as it helps to decrease the rate of deterioration. Our model allows shortages, and back-ordering is permissible to manage the loss that occurs due to perishable objects and shortages. The objectives are to find the optimal cycle time, preservation technology cost, and positive inventory time. The paper also proves the convexity of total cost through graphs with respect to decision variables. A sensitivity analysis of decision variables with respect to different inventory parameters is carried out.