Coordinating a three-level supply chain with combined contracts under stochastic demand

The problem of how to coordinate a two-level supply chain with contracts is discussed in most literature, but supply chain often consists of more than two separate firms in fact. This paper aims to study the coordination issue of a three-level supply chain selling short life cycle products in a single period model. We construct the so-called combined contracts mechanism, a buy-back contract between the retailer and the distributor and a profit-sharing contract between the manufacture and the distributor, to coordinate the channel under stochastic demand. We show that the three-level supply chain can be fully coordinated by designing appropriate contract parameters and the total profit of the channel can be allocated with some specified ratios among the firms. Finally, the validity of the contract mechanism is illustrated by a numerical example.