Agricultural product harvest equilibrium with transportation bottleneck and random disasters

Abstract

The decentralized planting practices of farmers often result in non-cooperative harvesting and transportation of agricultural products. The high concentration of harvesting demand can cause transportation and processing bottlenecks, resulting in queuing congestion in planting, which in turn affects farmers’ decisions on harvest timing. Thus, the fully competed decision-making process leads to a game equilibrium. To solve this harvest equilibrium problem, a nonlinear equation model with transportation bottleneck capacity constraints is developed. Assumptions to be made are that the value of the pre-harvest product is a non-negative continuously differentiable strictly concave function about the harvest time, and that post-harvest losses are a linear increasing function of queuing time. Subsequently, the model is further extended to incorporate the effects of random natural disasters. Additionally, this paper derives optimal harvest schedules for comparison. A numerical example is used to analyze how the related parameters and the probability of disasters influence farmers’ harvest decisions and the unit benefits of agricultural produce. The analysis results show that a larger total volume of agricultural products prompts earlier harvesting and reduces unit benefits in both equilibrium and optimal harvesting scenarios. Expanding bottleneck capacity allows farmers to harvest closer to the optimal time and increases unit benefits, although the marginal increase diminishes at the margin as bottleneck capacity increases. Increasing the queuing penalty within a range leads to an earlier harvest and reduces the unit benefits in equilibrium and optimality until a critical value is reached, beyond which it has no effect. A higher probability of natural disasters will incentivize farmers to harvest earlier, which in turn will reduce unit benefits.