Non-instantaneous deterioration effect in ordering decisions for a two-warehouse inventory system under advance payment and backlogging

The process of deterioration may not start immediately after the consignment reaches the go down; there generally occurs a delay. In certain cases, deterioration might begin after a certain period which may further prolong due to the introduction of better methods of inventory management. To take into cognizance of these situations, in contrast to the ordinary assumption in the existing models, we have considered that the decay in owned warehouse begins earlier than that in case of rented warehouse as the latter always provides for better inventory management and facilities. Applying these phenomena, a two-storage inventory model has been formulated with advance payment under three different situations according to different possibilities of starting times of deterioration in both warehouses. In this model, demand depends upon the selling price wherein shortages are considered partially with fixed backlogging rate. Analyzing and investigating the proposed problem, three different optimization problems are formulated and the optimality of these problems is proved theoretically. To solve the model, an algorithm is proposed. Then, to illustrate the model numerically, an example is considered and solved. Finally, post optimality is performed in order to investigate the effects of changes of different system parameters.