Handling Customer Preferences in Last-Mile Location-Routing: A Bilevel Optimization Approach

Abstract

This paper introduces the Location-Routing Problem with Delivery Preferences, a last-mile delivery problem with service flexibility that integrates collection-point activation and routing decisions while accounting for customer choice. The company determines which collection points to activate, which customers to offer home delivery, and the corresponding delivery route. Customers subsequently decide whether to accept the proposed home-delivery service or collect their parcels from an activated collection point according to ranked preferences over delivery time intervals and collection points. This hierarchical interaction is modeled through a bilevel optimization framework, which can be formulated as a mixed-integer bilevel program that incorporates compensation mechanisms for service inconvenience. Two equivalent single-level reformulations that exploit the structure of the customers' problems are developed. In addition, a two-phase heuristic is proposed to generate feasible solutions that can be used as warm starts for the formulations. The computational experiments run to compare the performance of the formulations, show that the warm-start strategy becomes particularly effective as the instance size increases. The comparison with a benchmark model that ignores customer preferences indicates that explicitly accounting for customer choice alters the resulting location-routing configuration while improving customer preference satisfaction at a small increase in the company's overall cost. These findings highlight the importance of jointly considering operational efficiency, service flexibility, and customer autonomy in last-mile delivery planning.