Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Theoretical results about Johnsons problem with stochastic processing times are few. In general, just finding the expected makespan of a given sequence is already difficult, even for discrete processing time distributions. Furthermore, to obtain optimal service level  need to compute the entire distribution of the makespan. Therefore the use of heu- ristics and simulation is justified.  show that pursuing the minimal expected makespan by two heuristics is empiri- cally effective for obtaining excellent overall distributions. The first is to use Johnsons rule on the means. The second is based on pair-switching and converges to some known stochastically optimal solutions when they apply.  show that the first heuristic is asymptotically optimal under mild conditions.  also investigate the effect of sequencing on the makespan variance. � 2005 Elsevier B.V. All rights reserved.
['Victor Portougal', 'Dan Trietsch']
I am writing a research paper on a idea Johnson's problem with stochastic processing times and optimal service level
[{"from": "human", "value": "I am writing a research paper on a idea Johnson's problem with stochastic processing times and optimal service level"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Theoretical results about Johnsons problem with stochastic processing times are few. In general, just finding the expected makespan of a given sequence is already difficult, even for discrete processing time distributions. Furthermore, to obtain optimal service level  need to compute the entire distribution of the makespan. Therefore the use of heu- ristics and simulation is justified.  show that pursuing the minimal expected makespan by two heuristics is empiri- cally effective for obtaining excellent overall distributions. The first is to use Johnsons rule on the means. The second is based on pair-switching and converges to some known stochastically optimal solutions when they apply.  show that the first heuristic is asymptotically optimal under mild conditions.  also investigate the effect of sequencing on the makespan variance. \ufffd 2005 Elsevier B.V. All rights reserved."}]