Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs

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.