Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study,  leverage on our previous work on the single machine total ighted tardiness (TWT) and total ighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lor bound. Moreover, it offers a near-optimal partition of the jobs to the machines.  then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem.  demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs.
['Halil Şen', 'Kerem Bülbül']
I am writing a research paper on a idea A Strong Preemptive Relaxation for Weighted Tardiness and Earliness/Tardiness Problems on Unrelated Parallel Machines
[{"from": "human", "value": "I am writing a research paper on a idea A Strong Preemptive Relaxation for Weighted Tardiness and Earliness/Tardiness Problems on Unrelated Parallel Machines"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Research on due date-oriented objectives in the parallel machine environment is at best scarce compared to objectives such as minimizing the makespan or the completion time-related performance measures. Moreover, almost all existing work in this area is focused on the identical parallel machine environment. In this study,  leverage on our previous work on the single machine total ighted tardiness (TWT) and total ighted earliness/tardiness (TWET) problems and develop a new preemptive relaxation for both problems on a bank of unrelated parallel machines. The key contribution of this paper is devising a computationally effective Benders decomposition algorithm to solve the preemptive relaxation formulated as a mixed-integer linear program. The optimal solution of the preemptive relaxation provides a tight lor bound. Moreover, it offers a near-optimal partition of the jobs to the machines.  then exploit recent advances in solving the nonpreemptive single-machine TWT and TWET problems for constructing nonpreemptive solutions of high quality to the original problem.  demonstrate the effectiveness of our approach with instances of up to five machines and 200 jobs."}]