Coordinating a Three-Level Fresh Agricultural Product Supply Chain considering Option Contract under Spot Price Uncertainty

We consider a three-level fresh agricultural product supply chain consisting of a producer, a supplier, and a retailer, where the producer plants the initial 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 and spot price. This paper discusses coordination mechanism of wholesale price contracts or option contracts between the supplier and the retailer and wholesale price contracts between the supplier and the producer. Based on this, we not only explore the conditions for supply chain full coordination and Pareto improvement but also analyze the effect of the retailer's spot market volatility by comparing two scenarios of the retailer with or without a random spot market. Results show that the wholesale price contract cannot coordinate the supply chain regardless of whether the retailer has a random spot market or not. The supply chain can be simultaneously fully coordinated and achieve Pareto improvement by setting reasonable option contract parameters, but the conditions for coordination are rigorous. When the expected value of reduction from the retailer's spot market in unit shortage loss cost is greater, the total profit of supply chain will increase. Numerical analysis shows that the option exercise price must be set higher when the retailer has a spot market to achieve Pareto improvement. The loss rate in distribution process and other volatility risks will also affect the coordination of the agricultural supply chain.