Present value optimization of two-echelon supply chains with trade credit and lot-splitting under a discounted cash flow framework

Tien-Yu Lin; Xiu-Hua Wei; Yun-Feng Zheng; Tien-Yu Lin; Xiu-Hua Wei; Yun-Feng Zheng

doi:10.3934/jimo.2026085

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 5: 2319-2346. doi: 10.3934/jimo.2026085

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Research article

Present value optimization of two-echelon supply chains with trade credit and lot-splitting under a discounted cash flow framework

1.
Qiaoxing College of Economics and Management, Fujian Polytechnic Normal University, No. 1, Campus New village, Longjiang Street, Fuqing City, Fujian Province 350300, China
2.
China–Indonesia Industrial Cooperation Research Center, Fujian Polytechnic Normal University, No. 1, Campus New village, Longjiang Street, Fuqing City, Fujian Province 350300, China

Received: 16 October 2025 Revised: 16 March 2026 Accepted: 16 March 2026 Published: 14 April 2026
90B05, 91B06, 90B30

This study develops a rigorous discounted cash flow (DCF) framework for optimizing replenishment decisions in two-echelon supply chains with trade credit and lot-splitting. Traditional models rely on single-cycle present value, which does not provide a theoretically consistent basis for evaluating replenishment policies in an infinite-horizon setting and may bias decisions toward unrealistically short cycles. To address this limitation, this paper formulates the infinite-horizon present value of a stationary replenishment policy and converts it into a discounted cost-rate objective. Within the unified DCF structure, all major cost components are valued according to their exact timing, allowing the model to jointly determine the optimal cycle length and shipment frequency. Numerical experiments show that discounting has a strong influence on optimal policies, that lot-splitting becomes more beneficial when discounted holding costs dominate, and that trade credit significantly reshapes the joint optimality of replenishment timing and shipment frequency. Overall, the study provides a theoretically consistent DCF-based two-echelon inventory model, offering both theoretical refinement and practical guidance for firms operating under capital constraints and time-sensitive replenishment environments.
- inventory strategy,
- present value optimization,
- discounted cash flow,
- supply chain management,
- trade credit,
- lot-splitting
Citation: Tien-Yu Lin, Xiu-Hua Wei, Yun-Feng Zheng. Present value optimization of two-echelon supply chains with trade credit and lot-splitting under a discounted cash flow framework[J]. Journal of Industrial and Management Optimization, 2026, 22(5): 2319-2346. doi: 10.3934/jimo.2026085

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Abstract

This study develops a rigorous discounted cash flow (DCF) framework for optimizing replenishment decisions in two-echelon supply chains with trade credit and lot-splitting. Traditional models rely on single-cycle present value, which does not provide a theoretically consistent basis for evaluating replenishment policies in an infinite-horizon setting and may bias decisions toward unrealistically short cycles. To address this limitation, this paper formulates the infinite-horizon present value of a stationary replenishment policy and converts it into a discounted cost-rate objective. Within the unified DCF structure, all major cost components are valued according to their exact timing, allowing the model to jointly determine the optimal cycle length and shipment frequency. Numerical experiments show that discounting has a strong influence on optimal policies, that lot-splitting becomes more beneficial when discounted holding costs dominate, and that trade credit significantly reshapes the joint optimality of replenishment timing and shipment frequency. Overall, the study provides a theoretically consistent DCF-based two-echelon inventory model, offering both theoretical refinement and practical guidance for firms operating under capital constraints and time-sensitive replenishment environments.

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