Abstract
Last-mile delivery — the final leg of a package’s journey from warehouse to doorstep — accounts for a disproportionate share of logistics costs and environmental impact. Emerging technologies are reshaping this landscape: autonomous delivery robots can handle short-range deliveries at low cost, crowdsourced delivery networks offer flexible capacity, and traditional trucks provide reliable backbone coverage. The optimization challenge is to combine these heterogeneous resources — each with different range, capacity, speed, cost, and energy constraints — into an integrated system that minimizes cost while meeting service requirements.
This project develops mixed-integer linear programming (MILP) models for multi-modal delivery planning using combinations of trucks, robots, and crowdsourced delivery. A particular focus is the practical constraints that make these problems hard: battery limitations for robots (including the logistics of battery swapping), transshipment points where packages transfer between vehicle types, and the multi-objective nature of the problem (minimizing cost, time, and environmental impact simultaneously).
We developed a mathematical model for an efficient two-tiered truck-robot delivery system, presented at the IEEE Conference on Service Operations and Logistics and Informatics (SOLI, 2024). A follow-up study compared different MILP formulations for handling transshipments and battery swapping, presented at the IISE Annual Conference (2025). While the primary application domain is commercial logistics, the modeling framework has potential applications in healthcare delivery — medication distribution, sample transport, and equipment logistics — where similar multi-modal coordination challenges arise.