Abstract: Under the condition that emergencies cause random fluctuations in market demand and market price, the option and quantity discount contract are integrated into a new option discount contract, and a call option discount contract model is used to coordinate the supply chain. It is known that the supply chain has an optimal decision through Hessian Matrix, and the example analysis is given. The results show that both the call option discount contract and the quantity discount contract can effectively improve the revenue of the supply chain when the market demand is increased due to emergencies, and the increase of the call option discount contract is greater. When the market demand is reduced due to an emergency, neither of the two contracts can reverse the situation that the revenue of the whole supply chain decreases significantly, and the discount contract of call option declines even more. In order to obtain the excess profit, the decision maker must obtain the market information sufficiently and forecast market demand accurately to make the new contract mechanism more effectively. Under the new premise, the call option discount contract model can effectively coordinate the supply chain and improve the performance of the whole supply chain system. This contract realizes risk sharing and benefit win-win and improves the flexibility of supply chain to some extent.

Key words: price randomization, option contract, quantity discount contract, Hessian Matrix, supply chain coordination