An option contract for coordinating a supply chain with price-dependent stochastic demand

Almost all the literature about option contracts in a supply chain assumed the retail price is fixed or exogenously given and the market demand is just stochastic. However, in many cases, the retailer has a right to adjust the retail price in some extent and the market demand is price-dependent and stochastic. So in this paper we solve the coordination problem in this supply chain setting. In our paper we develop a capacity option contract by which the manufacturer provides the option price and the exercise price. We derive the appropriate option and exercise prices by the manufacturer to incentive the retailer to make optimal pricing decision and option order quantity for coordinating the channel. The option contract not only coordinates the supply chain also can divide arbitrarily the profit between the manufacturer and the retailer.