Managing production and procurement through option contracts in supply chains with random yield

We study the management problems of production and procurement in a decentralized supply chain consisting of one supplier (providing key component) and one manufacturer. The supplier's production yield is random, and the manufacturer's demand is stochastic. The manufacturer may purchase option contracts from the supplier before the demand is realized (called an option order), or order after the demand is realized (called an instant order), which is subject to random pricing and uncertain availability. We show that the supplier's profit function is piece-wise concave and explore structural properties for the manufacturer. Finally, we provide sensitivity analysis on different parameters.