AUTHOR=Li Zhonghui , Chamchang Panida , Niu Lili , Mo Jiangtao TITLE=A multi-cycle inventory control model for deteriorating items with partial backlogging under trade credit JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=Volume 8 - 2022 YEAR=2022 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2022.1005509 DOI=10.3389/fams.2022.1005509 ISSN=2297-4687 ABSTRACT=The finite horizon should be considered for products with limited life cycle. To introduce this possibility, multiple orders and partial backlogging policies are established under trade credit in an inventory model, where the demand is a time-varying function and the backlogging rate is a decreasing function about the customer’s waiting time. This paper presents lemmas and theories to determine the optimal replenishing time and the backlogging time to maximize the total profit for the retailer. A search algorithm for solving the optimal order strategy is proved on the basis of the theoretical results. Numerical examples are presented and the optimal order strategy is obtained. Sensitivity analysis of the main parameters is carried out. The effects of total profit on main parameter of trade credit is analysed from macroscopic and microscopic perspectives.