Pricing and sales-cycle optimization for deteriorating fresh agricultural products with live-streaming investment and discounts

Lijun Wu; Xuan Li; Haiping Ren; Lijun Wu; Xuan Li; Haiping Ren

doi:10.3934/jimo.2026171

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 4945-4977. doi: 10.3934/jimo.2026171

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Research article Special Issues

Pricing and sales-cycle optimization for deteriorating fresh agricultural products with live-streaming investment and discounts

School of Business, Jiangxi University of Science and Technology, Nanchang 330013, Jiangxi, China

Received: 12 June 2026 Revised: 02 August 2026 Accepted: 27 August 2026 Published: 11 September 2026
90B05, 90B50, 90C30

Live-streaming e-commerce creates a channel for selling fresh agricultural products, but e-tailers that operate with a fixed order quantity must balance demand conversion, inventory clearance, and deterioration losses. This paper developed a two-stage inventory model with a Weibull time-varying deterioration rate, live-streaming investment, deterioration-stage discounts, and live-streaming sales commission costs. The model jointly determines the regular selling price, sales-cycle length, and live-streaming investment intensity to maximize average profit per unit time. A second-order Maclaurin approximation and a structural solution method are used to identify candidates at the inventory-depletion boundary and exogenous sales-cycle bounds. Results showed that live-streaming investment and deterioration-stage discounts accelerate demand and clearance but do not necessarily increase profit, because their benefits may be offset by investment costs, sales commission costs, lower unit revenue, and deterioration-related costs. The optimal sales cycle is determined by boundary comparison rather than an interior first-order condition. The study provides an integrated basis for coordinated pricing, live-streaming investment, and inventory-clearance decisions in fresh-product e-commerce.
- fresh agricultural products,
- live-streaming investment,
- deterioration-stage discounts,
- weibull deterioration rate,
- sales cycle decisions,
- inventory management,
- average profit optimization
Citation: Lijun Wu, Xuan Li, Haiping Ren. Pricing and sales-cycle optimization for deteriorating fresh agricultural products with live-streaming investment and discounts[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 4945-4977. doi: 10.3934/jimo.2026171

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Abstract

Live-streaming e-commerce creates a channel for selling fresh agricultural products, but e-tailers that operate with a fixed order quantity must balance demand conversion, inventory clearance, and deterioration losses. This paper developed a two-stage inventory model with a Weibull time-varying deterioration rate, live-streaming investment, deterioration-stage discounts, and live-streaming sales commission costs. The model jointly determines the regular selling price, sales-cycle length, and live-streaming investment intensity to maximize average profit per unit time. A second-order Maclaurin approximation and a structural solution method are used to identify candidates at the inventory-depletion boundary and exogenous sales-cycle bounds. Results showed that live-streaming investment and deterioration-stage discounts accelerate demand and clearance but do not necessarily increase profit, because their benefits may be offset by investment costs, sales commission costs, lower unit revenue, and deterioration-related costs. The optimal sales cycle is determined by boundary comparison rather than an interior first-order condition. The study provides an integrated basis for coordinated pricing, live-streaming investment, and inventory-clearance decisions in fresh-product e-commerce.

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