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Online grocers typically let customers choose a delivery time slot to receive their goods. To ensure reliable service, the retailer may want to close time slots as capacity fills up. The number of customers that can be served per slot largely depends on the specific order sizes and delivery locations. Conceptually, checking whether it is possible to serve a certain customer in a certain time slot given a set of already accepted customer orders involves solving a vehicle routing problem with time windows. This is challenging in practice as there is little time available and not all relevant information is known in advance. We explore the use of machine learning to support time slot decisions in this context. Our results on realistic instances using a commercial route solver suggest that machine learning can be a promising way to assess the feasibility of customer insertions. On large-scale routing problems it performs better than insertion heuristics. History: This paper has been accepted for the Transportation Science Special Issue on Machine Learning Methods and Applications in Large-Scale Route Planning Problems. Funding: This research was funded by the Netherlands Organization for Scientific Research under the City Logistics Living Laboratory project [Grant 439.18.424]. [ABSTRACT FROM AUTHOR]