Optimizing Cooperative Advertizing, Profit Sharing, and Inventory Policies in a VMI Supply Chain: A Nash Bargaining Model and Hybrid Algorithm

Members in a vendor managed inventory (VMI) supply chain make joint decisions on inventory policy and cooperative advertizing by capitalizing on their interactions. However, very few investigations have been reported to develop methods to facilitate such joint decision making due to the modeling difficulty and computation complexity. This study is, thus, to address the joint VMI, cooperative advertizing, and profit-sharing decision making in a coordinative way. It considers a two-level VMI supply chain including a manufacturer and m retailers, and deals with many decisions, e.g., chain members' advertizing investments profit sharing. A nonlinear mixed integer Nash bargaining model is developed to model the complex joint decision making of (m +1) players. In view of the difficulties in model solving, this study further develops a solution methodology, including an integrated model and hybrid algorithm for obtaining optimal solutions. Thanks to the integrated model, the hybrid algorithm, which is developed based on analytical methods, a genetic algorithm, and a Lagrange multiplier method, obtains optimal solutions to the Nash bargaining model while greatly reducing computation complexity. Numerical examples demonstrate the validity of the Nash bargaining model and the effectiveness of the solution methodology. Finally, a number of managerial implications are drawn based on sensitivity analysis.