Combined production, option procurement and pricing strategies under random yield

We consider a manufacturer facility where the assembly of a product needs a critical component. The production of the component faces random yield. To prevent the shortage, the manufacturer can also purchase the component from another supplier with an option contract. According to the contract, a certain quantity of components can be reserved with a reservation price per unit, and an execution price per unit of actual needed quantity will be charged by the supplier when the random yield is realized. With deterministic but price-dependent demand of the product, we analyze the optimal component production quantity in the manufacturer facility, the optimal reserving decisions from the supplier and the optimal product pricing strategies. The results show that it is profitable for the manufacturer to reserve from the supplier only when the product price is greater than a certain threshold. The manufacturer will consider whether to choose the lower price strategy only if the threshold is high enough. Otherwise, the manufacturer surely chooses the higher price strategy.