Single machine scheduling problem with cost constraints based on customer driven and its noncooperative game

Abstract

This paper considers the single machine scheduling problem with cost constraints based on customer driven using noncooperative game theory. The single machine scheduling problem with cost constraints based on customer driven is introduced, and customers bidding strategy is analyzed using noncooperative game method. Then noncooperative game model of single machine scheduling with cost constraints is defined using noncooperative game theory, in which the customer is mapped to the player, customer quotation corresponds to player strategy, and a payoff function of players is defined on condition of two main customer objectives. The satisfactory result of scheduling problem can be achieved by seeking Nash equilibrium solution, and the steps of seeking Nash equilibrium solution for the proposed scheduling game model are given. A single scheduling case is analyzed and solved, and the result verifies the validity of the proposed game model and the solving method.