Literature review
Return policy is also called buy back contract and is widely used for short life cycle products. When the product sales cycle declines, the manufacturer would provide the retailer a return mechanism for unsold goods. The policy mitigates the retailers' overstock to achieve risk pooling.
Wang et al. (2004) analyzed performance of supplier and retailer under consignment contract with revenue sharing. Giannoccaro and Pontrandolfo (2004) developed a supply chain contract model based on revenue sharing mechanism in three-stage supply chain. Chauhan and Proth (2005) proposed an approach to maximize provider and retailer profits by using revenue sharing mechanism. Hou et al. (2009) developed a coordination model between one supplier and one retailer under revenue sharing and bargaining.
In this case, bi-level programming is used. Bi-level programming regards the model as upper-level (leader) and lower-level (follower) decision makers affecting each other. The leader makes plan, and the follower reacts to the plan. The decisions are made based on their respective objective function. Colson et al. (2007) applied the bi-level method on revenue management and emergency management. Chang (2007) solved a bi-level programming model with Stackelberg equilibrium relation and Nash equilibrium between government (leader) and transport companies (follower) by Genetic algorithm. Yang et al. (2007) considered a bi-level model with response, production and transport time. The leader proposed an optimal response time; the follower then reacts on the production and the transportation time to maximize the supply chain profit.