An inventory model for non-instantaneous deteriorating items with credit period and carbon emission sensitive demand: a signomial geometric programming approach

This study considers sustainability issues and default risks in the context of joint inventory control and trade credit financing for Non-Instantaneous Deteriorating Items (NIDIs) in a supplier-retailer-customer system, in which the supplier offers an upstream full trade credit to the retailer and the retailer, in turn, provides a downstream partial trade credit to her/his customers. Demand rate is sensitive to the amount of carbon emissions, the length of the credit period suggested by the retailer to its customers and selling price. The main objective of this study is to optimize credit period, order quantity, and replenishment cycle time in order to maximize retailer's total profit and minimize carbon emissions at the same time. For solving the proposed problem, we apply an approximation method to simplify the profit function and transform the problem into a constrained Signomial Geometric Programming (SGP) problem, then a global optimization approach is used for solving the model.Finally, a numerical illustration and sensitivity analysis are performed to demonstrate the problem and the solution procedure. Some useful managerial insights are obtained from computational results. The results show that the retailer will increase its total profit by considering trade credit policy and non-instantaneous deteriorating phenomenon.