The quality of the delivery service is a crucial asset for an e-grocer to create and maintain a loyal customer-base. With the rapid market growth of e-grocers over the last decade, there is an urgent need for e-grocer specific routing systems. Although stochastic and dynamic routing models are studied for a wide range of applications, e-grocer specific models are missing in the literature. This paper investigates the concept of flexible deliveries, which introduces differentiated time window sizes. This creates the possibility for real-time re-optimization of the sequence of customers in a trip in order to improve the on-time delivery performance. The potential of flexible deliveries is investigated by means of computational experiments in which historic trip instances from the Dutch e-grocer Picnic are used. It is shown that, when re-optimization is activated, on-time delivery performance is improved and this benefit is significant when flexible deliveries represent at least 10% of the deliveries. When 10% of the deliveries are flexible, the number of late deliveries can be reduced by up to 18% and the number of extreme late deliveries (≥15 min late) up to 27%. This improved on-time delivery performance comes at the cost of a maximum of 2% increase in the average time spent per delivery.