Optimizing Nighttime Warming for Solar Greenhouse Cucumber: An Integrated Bio-Economic Framework Combining Non-Linear Cost-Volume-Profit and Data Envelopment Analysis

High energy consumption in winter greenhouses challenges agricultural sustainability. This study integrates nonlinear cost-volume-profit (CVP) and data envelopment anal-ysis (DEA) to balance cucumber yields with energy costs in Northern China. Results show that while a 19°C treatment (T3) maximizes yield, it suffers from diminishing marginal returns (MR/MC = 0.72) and high sensitivity to energy price fluctuations. Conversely, the 16°C treatment (T2) emerged as the sole energy-efficient and econom-ically resilient configuration. We conclude that 16°C is the global optimal point for balancing biological potential and resource efficiency, providing a scientific basis for precision thermal management in cold-region greenhouses.