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

Hanyu Gu, Yugeng Xi, Jiping Tao

Abstract: 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.