Randomized Lagrangian heuristic based on Nash equilibrium for large scale single machine scheduling problem

Lagrangian relaxation method for jobshop scheduling problems has been studied in the framework of combinatorial auction. In this paper a noncooperative game model is built for the Lagrangian relaxation method, and we prove that the equivalent continuous relaxation computed from the Lagrangian dual problem provides a mixed strategy Nash equilibrium for this game model. Based on this interpretation a randomized heuristic is exploited to get feasible schedules. Numerical experiments are carried out on a large scale single machine problem.