E-commerce marketplaces often offer fast and scheduled delivery services for free to attract customers, imposing strict time constraints on delivery, but do all people really want such services? This study aims to quantitatively analyze heterogeneous customers' preferences for home delivery timing. We propose two willingness-to-pay measures, namely, the value of delivery time savings (VODT) and the value of time slot shortening (VOTS). We capture their distributions in a data-oriented manner by estimating an extended mixed logit model with a semi-nonparametric approach. The estimated VODT ranged from -47.9 to 219.4 JPY/day, with a median of 25.6 JPY/day. This result shows a large taste variation and that most customers were not willing to pay even 10% of the delivery fee (set between 300–600 JPY) to save the waiting time by one day. Moreover, VOTS was found to be low, distributed with a median of 5.0 JPY/hour. The fact that some customers do not necessarily highly value the reduction in delivery lead-time or time slot size sheds light on demand management to reduce delivery burden while maintaining customer satisfaction. In addition, the valuation varied according to the category and price of the purchased good as well as the e-shopping frequency of customers, which suggests a possibility of differentiated pricing or real-time design of service attributes as a retailing strategy.