Dynamic pricing, advertising and inventory optimization for perishable products under trade credit

Yan Shi; Xiang Liu; Konstantina Skouri; Yan Shi; Xiang Liu; Konstantina Skouri

doi:10.3934/jimo.2026148

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 9: 4231-4257. doi: 10.3934/jimo.2026148

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Research article

Dynamic pricing, advertising and inventory optimization for perishable products under trade credit

1.
School of Economics and Management, Guangxi University of Science and Technology, Liuzhou, Guangxi 545006, China
2.
Guangxi Research Center for New Industrialization, Liuzhou, China
3.
Department of Mathematics, University of Ioannina, Ioannina, Greece

Received: 23 May 2026 Revised: 03 August 2026 Accepted: 04 August 2026 Published: 11 August 2026
90B05

This paper develops a continuous-time model for expiration-sensitive products to jointly determine optimal dynamic pricing, advertising investment, and inventory decisions under trade-credit financing. Demand depends on both selling price and advertising-generated goodwill, with goodwill following Nerlove–Arrow dynamics, whereas inventory availability is subject to sales depletion and age-dependent deterioration over time. The trade-credit mechanism introduces regime-switching dynamics based on the relationship between the credit period and the replenishment cycle, leading to a hybrid optimal control problem analyzed using Pontryagin's Maximum Principle. A post-solution approximation of the goodwill trajectory is proposed that preserves the structure of the original optimality conditions while providing semi-closed-form expressions for the optimal policies. Numerical experiments demonstrate that the approximation closely reproduces the exact optimal trajectories and objective values. The results further show that trade credit enhances retailer profitability by relaxing liquidity constraints, thereby enabling lower inventory levels, stronger advertising investment, smoother pricing policies, and higher goodwill, particularly for products with longer expiration periods. The proposed framework provides a decision-support tool for jointly coordinating operational, marketing, and financial decisions in expiration-sensitive supply chains.
- trade credit,
- deteriorating products,
- dynamic pricing,
- goodwill,
- advertising investment,
- optimal control
Citation: Yan Shi, Xiang Liu, Konstantina Skouri. Dynamic pricing, advertising and inventory optimization for perishable products under trade credit[J]. Journal of Industrial and Management Optimization, 2026, 22(9): 4231-4257. doi: 10.3934/jimo.2026148

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Abstract

This paper develops a continuous-time model for expiration-sensitive products to jointly determine optimal dynamic pricing, advertising investment, and inventory decisions under trade-credit financing. Demand depends on both selling price and advertising-generated goodwill, with goodwill following Nerlove–Arrow dynamics, whereas inventory availability is subject to sales depletion and age-dependent deterioration over time. The trade-credit mechanism introduces regime-switching dynamics based on the relationship between the credit period and the replenishment cycle, leading to a hybrid optimal control problem analyzed using Pontryagin's Maximum Principle. A post-solution approximation of the goodwill trajectory is proposed that preserves the structure of the original optimality conditions while providing semi-closed-form expressions for the optimal policies. Numerical experiments demonstrate that the approximation closely reproduces the exact optimal trajectories and objective values. The results further show that trade credit enhances retailer profitability by relaxing liquidity constraints, thereby enabling lower inventory levels, stronger advertising investment, smoother pricing policies, and higher goodwill, particularly for products with longer expiration periods. The proposed framework provides a decision-support tool for jointly coordinating operational, marketing, and financial decisions in expiration-sensitive supply chains.

References

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