Fresh produce spatial price equilibrium on general networks: Capturing commodity quality deterioration through endogenous transportation time delay functions with capacities

Fresh produce is vital to global food security but is highly vulnerable to transportation delays and capacity disruptions, as in critical links such as the Panama Canal. This paper develops a commodity fresh produce trade equilibrium model under quality deterioration on a general network, allowing for multiple transportation links on a path between supply and demand markets. We extend the Bureau of Public Roads (BPR) congestion function to endogenize time delay as a function of all commodity shipments on a link. By embedding link upper bounds in time delay functions, we capture how upper bounds impact transportation times and fresh produce quality. The spatial price equilibrium conditions are formulated as a variational inequality problem. We also propose commodity quality trade network performance measures, supply-based, demand-based, and network-based, that can be applied for an individual commodity or across all commodities. We apply the model to bananas, a globally popular and nutritious fruit, and its trade from Ecuador and Costa Rica to the European Union, the United States, and Russia, focusing on drought-driven congestion at the Panama Canal. Numerical examples, whose solutions are computed using the modified projection method, show that reductions in transportation link upper bounds and increased free-flow transportation times significantly lower banana shipments, degrade their quality, and shift prices at both supply and demand markets. We include benchmark comparisons with linear congestion and no-congestion specifications to explicitly quantify how nonlinear congestion modeling alters equilibrium flows, prices, transportation times, and quality deterioration. These comparisons reveal that linear and no-congestion specifications can misrepresent congestion effects, particularly when flows operate at moderate-to-high utilization levels. The results align closely with real-world data on banana prices, transportation costs, and export volumes, reinforcing the model’s practical relevance. Our model provides decision-makers with essential insights on the impacts of congestion and increasing transportation times on fresh produce trade and its quality, along with the performance of the trade network.