Optimal payment time for retailer's inventory system

A retailer's inventory control system for the optimal delay in payment time for initial stock-dependent consumption rate when a wholesaler permits delay in payment is developed. Shortages are not allowed in the inventory system. The effect of inflation rate, deterioration rate, initial stock-dependent consumption rate and a wholesaler's permissible delay in payment is discussed. A mathematical model is derived when a wholesaler permits that the credit period is less than or equal to the retailer's optimal payment time, and that the retailer's optimal payment time is less than or equal to the cycle time for settling the account. Besides, an expression for a retailer's inventory system's total cost derived for this case and five special cases will be discussed. Moreover, a computational procedure is proposed to obtain the optimal cycle time, retailer's payment time and order size. The results could help retailer's managers to determine the optimal total cost and strive for the wholesaler's permission to delay the payment period. Thus, a retailer can attempt to gain two very big advantages: (I) that the retailer will have more money to run in that period because of the extension of the optimal payment lime and (2) that extra interest will be earned in that period. Finally, a numerical example demonstrates the applicability of the proposed model and a sensitivity analysis is also discussed.