Lot sizing and dynamic pricing with different yield qualities

The literature under random component yield has focused on coordination of supply chain at the determined price, where decision maker chooses its optimal production quantities. We considered a centralized system when the price is not determined under both random yield and demand. Type A with perfect quality and type B with imperfect quality are produced due to the random yield. We prove the unique concavity of expected profit in centralized system at determined price. Then dynamic pricing is considered and algorithm is put forward for dynamic pricing. Errors can be sufficiently small as long as some parameters can be set suitably. Apart from lot sizing and dynamic pricing, we also provide qualitative insights based on numerical illustration of centralized and decentralized solutions.