Fleet sizing with price-sensitive customers in Attended Home Delivery

Retailers offering Attended Home Delivery (AHD) struggle with thin profit margins due to high delivery costs and constrained routing flexibility. AHD requires retailers and customers to agree on specific time windows, limiting operational efficiency and increasing fleet requirements, particularly when customer preferences tend to cluster around peak times. While retailers have some ability to influence customer choices through pricing and availability strategies, failing to account for fleet costs and delivery constraints can lead to inefficient operations and reduced profitability. This study introduces an integrated approach to fleet sizing and time-window pricing for price-sensitive customers. We propose a Mixed Integer Programming (MIP) model that maximizes profit by balancing revenue and delivery costs, leveraging a nonparametric rank-based choice model to capture customer behavior while explicitly considering routing constraints and fleet ownership expenses over multiple periods. Using computational experiments on small-sized instances inspired by real-world data, we evaluate the impact of explicitly modeling routing costs, compare different pricing strategies, examine the effects of multi-period fleet planning, and assess sensitivity to varying customer and cost conditions. Results show that explicitly modeling routing constraints reduces profit loss by 29% compared to traditional cost approximations but increases computational complexity. To address this, we develop a Fix & Optimize (F&O) matheuristic approximate solution method that enables the application of our model to larger instances. Our findings emphasize the need for retailers to integrate demand management and fleet planning to optimize operational profitability.