Decaying inventory model with stock-dependent demand and shortages under two-level trade credit

Abstract

In the present day, competitive marketplace, offering delay payments, has become a commonly adopted method. Previous inventory models under permissible delay in payments usually assumed that the demand of the items was either constant or merely dependent on the retailing price. This paper deals with a lot-sizing model for deteriorating items with stock-dependent demand and delay in payments. In the model, shortages are allowed to occur and demand during the stockout period is partially backlogged. In this study, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to his customer in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. That is, the retailer can accumulate revenue and earn interest during this period with rate Ie under the condition of trade credit. At the end of the trade credit period offered by the supplier, the account is settled and the retailer starts paying the capital opportunity cost for the items in stock with an annual rate Ip. The minimization of the total annual cost is taken as the objective function to study the retailer’s optimal ordering policy. Lemmas and Theorem to determine the criterion for the existence and uniqueness of the minimum solution are subsequently developed. We provide an easy and useful computational flowchart and with the help of a computer code using the software Matlab 7.0, the optimal results are determined. A numerical example is included to demonstrate the developed model and the solution procedure. To investigate the effect of changes in some main parameter values on the optimal solution, we conduct a sensitivity analysis and discuss some important managerial insights.