Airports and airlines are examining and committing to the electrification of Ground Support Equipment (GSE). To be able to estimate the required quantity of eGSE, the charging requirements of eGSE, the change of airport electricity requirements, and the scheduling possibilities of eGSE charging for the existing turnaround procedures, a model was developed to simulate and optimize the GSE operations at airports. This was done by means of a Task Scheduling Problem (TSP), that is optimized using Mixed-Integer Linear Programming (MILP). A case study was performed on KLM's GSE fleet at Amsterdam Airport Schiphol. Based on this, it was concluded that there is no difference in the capacity that can be achieved for GSE types that can last an entire day on a single battery charge. However, another group of GSE types experiences battery depletion before the day concludes, requiring measures to maintain the capacity. The results indicate the model's suitability for strategic decision-making. Next to that, the model is effective on an operational level. The use of the model has the potential to make the use of resources in the operation more efficient.