Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Lagrangian relaxation technique has been used for solving a wide variety of scheduling problems to obtain near optimal solutions. The approach has been successfully applied to jobshop scheduling problems by relaxing the capacity constraints on machines by using Lagrange multipliers. The relaxed problem can be decomposed into independent job-level subproblems which can be solved by dynamic programming. By extending the technique, in this paper,  propose a successive Lagrangian relaxation method for solving flowshop scheduling problems with total ighted tardiness. In the proposed method, the quality of lor bound is improved by successively solving the Lagrangian dual problem embedding cuts into the Lagrangian relaxation problem. The state space reduction for dynamic programming is also incorporated. The effectiveness of the proposed method is demonstrated from numerical experiments.
['Tatsushi Nishi', 'Yuichiro Hiranaka', 'Masahiro Inuiguchi']
I am writing a research paper on a idea A Successive Lagrangian Relaxation Method for Solving Flowshop Scheduling Problems with Total Weighted Tardiness
[{"from": "human", "value": "I am writing a research paper on a idea A Successive Lagrangian Relaxation Method for Solving Flowshop Scheduling Problems with Total Weighted Tardiness"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Lagrangian relaxation technique has been used for solving a wide variety of scheduling problems to obtain near optimal solutions. The approach has been successfully applied to jobshop scheduling problems by relaxing the capacity constraints on machines by using Lagrange multipliers. The relaxed problem can be decomposed into independent job-level subproblems which can be solved by dynamic programming. By extending the technique, in this paper,  propose a successive Lagrangian relaxation method for solving flowshop scheduling problems with total ighted tardiness. In the proposed method, the quality of lor bound is improved by successively solving the Lagrangian dual problem embedding cuts into the Lagrangian relaxation problem. The state space reduction for dynamic programming is also incorporated. The effectiveness of the proposed method is demonstrated from numerical experiments."}]