Warehouse inventory model for deteriorating items of a supply chain with nonlinear demand function and permissible delay in payment under inflation

Abstract

Warehouse inventory problems have consistently gained importance and drawn the attention of world-wide researchers during the past few decades. Reasons such as meeting the demand of seasonal products, enjoying discounts for bulk purchase, etc. have necessitated the purchase of goods in excess of the capacity of Owned Warehouse (OW). Moreover, the trade credit period provided by suppliers motivates the retailer to purchase a quantity that exceeds the Owned Warehouse capacity. In the present study of warehouse inventory model for deteriorating items of a supply chain with nonlinear ramp functions and permissible delay in payment under inflation, two models Shortages Followed by Inventory (SFI) and Inventory Followed by Shortages (IFS) have been formulated. Both the models consist of ordering cost, unit cost, deterioration cost, shortage cost and holding cost with replenishment where delay in payments is allowed. The development of these models is to minimize the total average cost per unit time. In order to validate the models, numerical examples have been considered. Then the sensitivity of several major parameters of exponential and quadratic functions is analyzed using MATLAB. The optimal solutions with the effects of major parameters have been represented graphically and in tabular form. From the numerical results of SFI model, it is clear that when the values of parameters of the exponential function as well as holding cost per unit time increase, the cost per unit time decreases. Similarly, if the values of parameters of the quadratic function as well as ordering cost and shortage cost increase, the cost per unit time increases respectively. Consequently, from the numerical results of IFS model, it is evident that when the values of parameters of the exponential function as well as ordering cost and shortage cost increase, the cost per unit time increases. Similarly, if the values of parameters of the quadratic function as well as holding cost increase, the cost per unit time decreases. Finally, comparison between SFI model and IFS model has been carried out. For both cases, it is observed that IFS model is better than SFI model up to a certain level.