Collaborative Advertising in a Two-Echelon Supply Chain with Production Capacity and Advertising Budget Constraints with a Bi-Level Programming Approach

Advertising is one of the most effective means of increasing sales of supply chain members. In order to increase sales and meet demand, chain members must coordinate their efforts. Since advertising and production decisions in the supply chain are interactive between members, it is necessary to create a form of integration or participation in decision-making. Two retailers and a manufacturer are part of the supply chain considered in this study. On the one hand, the manufacturer uses global advertisements to strengthen the business brand, and on the other hand, retailers use local advertisements to increase sales. The manufacturer participates in financing local advertising costs with retailers. Additionally, it is assumed that there are production capacity constraints for the manufacturer, as well as advertising budgets for each member of the supply chain. A manufacturer's limited capacity creates a competition between retailers to meet demand and an advertising budget restriction creates competition among them to attract the most participation in advertising expenses. The governing structure of the optimization model is a bi-level programming type where the manufacturer is at the first level and the competing retailers are at the second level. From the game theory perspective, a type of generalized Stackelberg-Nash game prevails between the players. A solution method based on variational inequalities is proposed to find the equilibrium of this game, and numerical analyses are provided to evaluate the model and solution method. Finally, managerial implications based on the results of numerical experiments have been proposed.