A note on "Revenue-sharing vs. wholesale-price contracts in assembly systems with random demand"

Gerchak and Wang [Gerchak, Y., Wang, Y., 2004. Revenue-sharing vs. wholesale-price contracts in assembly systems with random demand. Production and Operations Management 13(1), 23-33] develop a buy-back contract to coordinate a decentralized push assembly system. However, there exists deficiency in their coordination contract, because, as shown in this note, the highest expected profit a supplier in the push system can get is negative in some cases. Thus, we develop a modified buy-back contract to coordinate the push system. We also show that the modified buy-back contract has sufficient flexibility to allocate the expected profit of the system and achieves Pareto improvements.