Coordinating a three-level contract farming supply chain with option contracts considering risk-averse farmer and retailer

We considered a three-level contract farming supply chain comprising a risk-averse farmer, a risk-neutral supplier, and a risk-averse retailer. The farmer plants and grows fresh agricultural products with yield uncertainty, the supplier is the leader of the supply chain and the designer of the contracts, and the retailer sells processed products with random demand. Under CVaR criterion, this paper discusses three option contracts between the supplier and the retailer, as well as wholesale price contracts or replenishment cost-sharing contracts between the supplier and the farmer. Results show that when the farmer is risk-neutral, option contracts with or without replenishment cost-sharing contracts can maximize the total profit and increase the profits of all members simultaneously. When the farmer and the retailer are risk-averse, only option contracts with replenishment cost-sharing contracts can ensure supply chain full coordination and Pareto improvement by adjusting the option parameters and making the farmer's sharing ratio equal to his risk aversion coefficient. Moreover, through numerical analysis, we discovered that the interval of the Pareto improvement decreases with the retailer's risk aversion coefficient and the quantity loss rate, and increases with the farmer's risk aversion coefficient. The supplier will not be able to increase his own profits when the loss rate is excessively large. Therefore, the leader should consider the risk aversion degree of all parties and the quantity loss rate of fresh agricultural products before choosing contracts.