زمان پرداخت بهینه برای یک خرده فروش تحت تاخیر مجاز پرداخت توسط عمده فروش

The retailer (buyer) is usually allowed a permissible credit period to pay back the dues without paying any interest to the wholesaler (supplier). In this problem the retailer can pay the wholesaler either at the end of credit period or later incurring interest charges on the unpaid balance for the overdue period. This research develops a retailer's model for optimal cycle and payment times for a retailer in a deteriorating-item inventory situation where a wholesaler allows a specified credit period to the retailer for payment without penalty. Under these conditions, this wholesaler-and-retailer system is modeled as a cost minimization problem to determine the optimal payment time under various system parameters. The model is solved through an iterative search procedure and the overall findings indicate that the retailer has always an option to pay after the permissible credit period depending on interest rates, unit purchase and selling price, and the deterioration rate of the products.

In a typical buyer–seller situation, an inventory model considers a case in which depletion of inventory is caused by a constant demand rate, but in real-life situations there is inventory loss by deterioration also. This paper considers a retailer's model in which the deterioration rate is constant, and the retailer has an option to fix the payment period instead of settling the account with the wholesaler (supplier) at a particular allowable time frame. In today's competitive business transactions, it is common to find that the retailers (buyers) are allowed some credit period before they settle the account with the wholesaler. This provides a very big advantage to the customers, due to the fact that they do not have to pay the wholesaler immediately after receiving the product, but instead, can delay their payment until the end of the allowed period. The customer pays no interest during the permissible time for payment, but interest will be charged if the payment is delayed beyond that period. A lot of work has been done on deteriorating inventory systems [1], [2], [3], [4], [5], [6] and [7]. Heng et al. [5] integrated Misra's [1] and Shah's [2] models to consider a lot-size, order-level inventory system with finite replenishment rate, constant demand rate, and exponential decay. Su et al. [8] considered an inventory under inflation for stock dependent consumption rate and exponential decay while Hariga [6] and [9] developed models for deteriorating items with time-dependent demand. Kim et al. [10] developed an optimal credit policy to increase wholesaler's profits with price-dependent demand functions. Goyal [11] developed an economic order quantity under the conditions of permissible delay in payments for an inventory system. Aggarwal and Jaggi [12] developed a model to determine the optimum order quantity for deteriorating items under a permissible delay in payment. Hwang and Shinn [13] modeled an inventory system for retailer's pricing and lot sizing policy for exponential deteriorating products under the condition of permissible delay in payment. Other researchers also considered similar issues relating to payment period or lot sizing [14], [15], [16], [17], [18] and [19].

This research addresses a retailer's model for optimal strategy for payment time. Here we developed a model for optimal cycle and payment times for a retailer in an inventory situation with deteriorating products, where a wholesaler allows a speci"ed credit period to the retailer (buyer) for A.M.M. Jamal et al. / Int. J. Production Economics 66 (2000) 59}66 65 payment without penalty. Order quantity and other schedules for the inventory system are easily obtained when the optimal cycle time is known. Test results show that the total inventory cost decreases and the optimal payment period becomes shorter as the unit selling price increases relative to the unit cost * which means that the retailer should settle his account relatively sooner. It may be also noted that the payment time reduces in general as the di!erence between payable and earned interest rates increases. However, the total inventory cost in this case increases. It is further noted that both cycle time and payment period become shorter as the product deteriorates faster, resulting in higher total inventory cost. It is to the advantage of the retailer that he should be prepared, in this case, to pay for his inventories sooner as well. Overall, the retailer has the freedom to adjust his payment depending on interest rates, unit purchase and selling price of the products, and the product deterioration rate. This retailer's model has wide range of applications in wholesale-retail business where the competition is sti!, especially in storage and warehousing since many competitive products are pushed to the market by o!ering greater advantage and pro"t margin to the retailers.