Inventory model with nonlinear price-dependent demand for non-instantaneous decaying items via advance payment and installment facility

Determining the joint pricing and ordering policy is a challenging task for policy-makers dealing with perishable items. This research deals with the inventory coordination for a decaying commodity under a non-linear price-sensitive demand structure where the policy-maker completes the payment partially in advance, exploiting the multiple installments facility to control supply disruptions. Moreover, an inventory-out situation is incorporated to make the model more representative; shortages are backlogged partially through a variable rate in exponential form, depending on the customer waiting times. Though the formulated inventory coordination creates a highly complex optimization problem, the existence of the joint optimal pricing and ordering policy is explored by developing several theoretical outcomes. Three numerical illustrations are adopted to ensure the effectiveness of the model in providing the joint optimal pricing and ordering policy for the decision manager. Furthermore, to visualize the concavity of the average profit of the policy manager, as well as to demonstrate the adequacy of the optimum condition, MATLAB software was utilized. Finally, sensitivity studies for known key parameters are done using graphic presentation and a few supportive guidelines for the manager are also shown. The inventory manager should motivate the supplier to allow a higher installment frequency to implement the prepayment regulation, thus reducing the capital cost against the prepayment amount.