Feasibility assessment in attended home delivery with basket uncertainty

In grocery home delivery, most retailers allow customers to select a delivery time slot for receiving their orders. Since delivery capacity (vehicles and drivers) is typically fixed in the short term, retailers must use it efficiently. To do this, they may dynamically restrict which time slots are available to new customers based on orders already accepted. This demand management is complicated by a key uncertainty: customers often reserve their delivery slot before finalizing their shopping basket. As a result, retailers do not know how large each order will be when allocating delivery capacity, making it difficult to determine how much vehicle capacity to reserve for each customer during the booking process. We study how basket size uncertainty affects time slot management for attended home delivery. To address this challenge, we propose fast decision-making strategies that use basket size scenarios to assess whether accepting a new order will likely result in a feasible delivery schedule. These strategies, based on heuristics and machine learning, are evaluated on their impact on overall system performance. Our experiments demonstrate the strengths and limitations of each approach. Insertion heuristics accept fewer customer orders and require increasing computation time as the number of customers grows, limiting scalability. In contrast, machine learning-based scenario approaches and simple threshold methods scale more effectively and accommodate more customers, though they must balance feasibility constraints against order acceptance rates. Overall, our study provides practical, scalable strategies for online grocery retailers to manage time slot availability when basket sizes are uncertain at booking. These insights can be adapted to different operational contexts and business priorities.