Airports and airlines are examining and committing to the electrification of Ground Support Equipment (GSE). In line with this trend, in this paper, we develop a model to simulate and optimize the GSE operations at airports. The aim is to estimate the required quantity of eGSE, the charging requirements of eGSE, the change in airport electricity requirements, and the scheduling possibilities of eGSE charging for the existing turnaround procedures. This is done by means of a Task Scheduling Problem (TSP), that is optimized using Mixed-Integer Linear Programming (MILP). A case study is performed on KLM's GSE fleet at Amsterdam Airport Schiphol. Based on this, it is concluded that daily operations can be sustained without increasing fleet size for GSE types capable of lasting a full day on a single charge, assuming vehicles can recharge overnight. This is the case at many airports due to nighttime curfews. The operational procedures used by the handler play a key role in achieving this outcome. The results confirm that the model is suitable for strategic decision-making and it is effective at the operational level. The model has the potential to lead to a more efficient use of resources in the operation.