سیاست های اعتباری تجارت مطلوب و "تعیین اندازه دسته تولید" در مدل مقدار تولید اقتصادی با یادگیری منحنی هزینه های تولید

In reality, a seller (e.g., a supplier or a manufacturer) frequently offers his/her buyers trade credit (e.g., permissible delay in payment). Trade credit reduces the buyer's holding cost of inventory and hence attracts new buyers who consider it to be a type of price reduction. On the other hand, granting trade credit also increases the seller's opportunity cost (i.e., the loss of capital opportunity during the credit period) and default risk (i.e., the event in which the buyer will be unable to make the required payments on his/her debt obligation). In addition, it is a well-known fact of learning-by-doing that production cost of a new product declines by a factor of from 10 to 50 percent each time the accumulated production volume doubles. Therefore, we propose an economic production quantity model from the seller's prospective to determine his/her optimal trade credit period and production lot size simultaneously in which (i) trade credit increases not only sales but also opportunity cost and default risk, and (ii) production cost declines and obeys a learning curve phenomenon. Then the necessary and sufficient conditions to obtain the seller's optimal trade credit and order quantity are derived. Finally, we use some numerical examples to illustrate the theoretical results and to provide some managerial insights.

In 1913, Harris proposed the classical economic order quantity (thereafter, EOQ) model by assuming that a buyer must pay for the items as soon as receiving them (Harris, 1913). In practice, a seller frequently offers his/her buyers a permissible delay period (i.e., credit period) for settling the amount owed to him/her. Usually, there is no interest charge to the buyer if the outstanding amount is paid within the permissible delay period. However, if the payment is not paid in full by the end of the permissible delay period, then the seller charge the buyer interest on the outstanding amount. Granting a permissible delay period attracts new buyers who may consider it to be a type of price reduction. Hence, from a seller's prospective, granting a permissible delay period increases sales. On the other hand, granting a permissible delay period increases not only the seller's opportunity cost but also the seller's default risk because the longer the permissible delay period, the higher the opportunity cost as well as the default risk. Consequently, it is an important and relevant issue for the seller to find an optimal trade credit such that the sales increase induced by trade credit can significantly overcome the cost increase of opportunity cost and default risk.

How to determine the optimal length of trade credit for the seller has received relatively little attention by the researchers. In this paper, we have originally developed an EPQ model to reflect the facts: (1) the total unit production cost declines by a factor of from 10 to 50 percent each time the accumulative production volume doubles due to learning by doing, (2) trade credit reduces the buyer's inventory holding cost and attracts new buyers, and (3) the longer the credit period, the higher the opportunity cost and default risk. Then we have derived the necessary and sufficient conditions to obtain the optimal solution. In addition, we have characterized the influence of the parameters to the optimal solution. For example, if the learning coefficient l is higher, then the production cost is lower, and the seller can afford to offer a longer credit period M⁎ (i.e. more sales), and hence produce larger lot-size Q⁎, and obtain higher annual total profit Π⁎(M⁎, Q⁎). Finally, we have provided numerical examples and sensitivity analysis to illustrate the proposed model and understand managerial insights. Hence, we have made some innovational and significant contributions for a seller to determine his/her optimal trade credit and lot size simultaneously.