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Double-deep multi-tier shuttle warehousing systems (DMSWS) have been increasingly applied for store-and-retrieval stock-keeping unit tasks, with the advantage of a reduced number of aisles and improved space utilization. Scheduling different devices for retrieval tasks to increase system efficiency is an important concern. In this paper, a Pareto optimization model of task operations based on the cycle time and carbon emissions is presented. The impact of the rearrangement operation is considered in this model. The cycle time model is converted into a flow-shop scheduling model with parallel machines by analyzing the retrieval operation process. Moreover, the carbon emissions of the shuttle in the waiting process, the carbon emissions of the lift during the free process, and the carbon emissions of the retrieval operation are considered in the carbon emissions model, which can help us to evaluate the carbon emissions of the equipment more comprehensively during the entire retrieval task process. The elitist non-dominated sorting genetic algorithm II (NSGA-II) is adopted to solve the non-linear multi-objective optimization function. Finally, a real case is adopted to illustrate the findings of this study. The results show that this method can reduce carbon emissions and improve system efficiency. In addition, it also help managers to reduce operational costs and improve the utilization of shuttles.

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