Vehicle Routing Problem in Competitive Environment: Two-Person Nonzero Sum Game Approach

Vehicle routing problem is one of the most important issues in transportation. Among VRP problems, the competitive VRP is more important because there is a tough competition between distributors and retailers. In this study we introduced new method for VRP in competitive environment. In these methods Two-Person Nonzero Sum games are defined to choose equilibrium solution. Therefore, revenue given in each route is different. In this paper, two distributors has been considered in a city with a set of customers and the best route with maximum revenue has been determined. First we introduced the Hawk-Dove procedure for the VRP problem and then by using Nash bargaining model the equilibrium strategy of the game is calculated. The result of this method is different based on the kind of the strategy that each distributor chooses. In the Hawk-Dove game, if both of distributors choose the Dove procedure, they will get equal but less revenue. In the Nash Bargaining Game, the equilibrium strategy will obtained when distance of revenues of both distributors form its breakdown payoff is maximum.