Optimal payment time under permissible delay in payment for products with deterioration

A permissible credit period is usually allowed to a retailer to pay back the dues without paying any interest to the supplier. The retailer can pay the supplier either at the end of the credit period or later incurring interest charges on the unpaid balance for the overdue period. The retailer is expected to settle the account at a time before the end of the inventory cycle time because the payable interest rate is generally higher than the earned interest rate. A model for optimal cycle and payment times is developed here for a retailer in a deteriorating-item inventory situation where a supplier allows a specified credit period to the retailer for payment without penalty. Under these conditions, this supplier-and-retailer system is modelled as a cost minimization problem to determine the optimal payment time under various system parameters, An iterative search procedure is applied to solve the problem, and the overall findings indicate that the retailer always has an option to pay after the permissible credit period depending on unit purchase and selling price, the deterioration rate of the products and the interest rate.