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The finite horizon should be considered for products with a limited lifecycle. To introduce this possibility, multiple orders and partial backlogging policies are established under trade credit in an inventory model, where demand is a time-varying function and the backlogging rate is a decreasing function about a customer's waiting time. This paper presents lemmas and theories to determine optimal replenishment time and backlogging time to maximize total profit for the retailer. A search algorithm to solve the optimal order strategy is proven based on the theoretical results. Numerical examples are presented, and the optimal order strategy is obtained. A sensitivity analysis of the main parameters is carried out. The effects of total profit on the main parameter of trade credit are analyzed from both macroscopic and microscopic perspectives.

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