Optimal dynamic trade credit and preservation technology allocation for a deteriorating inventory model

Abstract

In this paper, we examine an optimal dynamic decision-making problem for a retailer selling a single deteriorating product, the demand rate of which varies simultaneously with time and the length of credit period that is offered to the customers. The deterioration rate is time dependent and can be reduced by an investment in preservation technology. In addition, the risk of default increases with the credit period length. A generalized model is presented to determine the optimal trade credit, preservation technology investment and replenishment strategies that maximize the retailer’s total profit after the default risk occurs over a finite planning horizon. Under certain conditions, we first establish a single period deteriorating inventory model, and then provide a comparative statics analysis that characterizes the impacts of key parameters on the retailer’s optimal trade credit and preservation technology investment decisions by using the properties of the supermodular function. Dynamic programming is then used to solve the proposed model by employing the obtained theoretical results. At the end of this paper, some numerical examples and the results of a sensitivity analysis are used to illustrate the features of the proposed model; we then offer our concluding remarks.