# Scheduling Algorithms for a Hybrid Flow Shop under Uncertainty
## 4 Computation of Schedules
In addition, we have shown that, depending on the application, quantile analysis for scrap is an adequate method to reduce unfulfilled orders. Above a certain value of the quantile, their effect on preventing incompletely fulfilled demand positions is adversely affected by extreme overproduction and increased makespans. Thus, it is of high importance to analyze the quantiles and makespans depending on the application case. Our approach can be developed further by using more efficient forecasting techniques to predict model parameters, by developing an upper bound for scrap rates, by additional heuristics and metaheuristics to generate schedules for the optimization model, and by combining the simulation model with additional techniques to optimize schedules. With the mentioned extensions, more efficient schedules are possible with regard to limiting overproduction, and achieving optimum production is possible. However, it is not expected that we will obtain significantly closer results to the simulation with modifications to the optimization methods because the simulation results are already very near to the results of the deterministic optimization. Conceptualization, C.S. ; methodology, C.S. ; software, C.S. ; validation, C.S. ; formal analysis, C.S. ; investigation, C.S. ; resources, P.B. ; data curation, C.S. ; writing--original draft preparation, C.S. and P.B. ; writing--review and editing, C.S. and P.B. ; visualization, C.S. ; supervision, P.B. ; project administration, C.S. ; funding acquisition, P.B. All authors have read and agreed to the published version of the manuscript. This research was funded by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant number 276879186/GRK2193, within the Research Training Group GRK 2193 \"Adaption Intelligence of Factories in a Dynamic and Complex Environment\". Special thanks goes to the company that generously provided us with the data for the use case and, in particular, to the production planer for their excellent cooperation. We want to express our great gratitude to our (former) student assistants- [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON]--for their engagement and support with the project. In addition, we wish to thank the other members of the GRK 2193 for their productive collaboration. The authors declare no conflicts of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. ## Abbreviations

The following abbreviations are used in this manuscript: \begin{tabular}{l l} SPT & Shortest Processing Time \\ ECT & Earliest Completion Time \\ \end{tabular} 

## References

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