A Bi-criterion Steiner Traveling Salesperson Problem with Time Windows for Last-Mile Electric Vehicle Logistics

TL;DR

This paper introduces a bi-criterion routing problem for electric delivery vehicles that balances energy consumption and safety, proposing exact and heuristic methods validated on real-world Amazon delivery data.

Contribution

It formulates a novel Bi-criterion Steiner TSP with Time Windows considering energy and safety, and develops an efficient heuristic for large instances.

Findings

Heuristic solutions are near-optimal within reasonable time.

The approach effectively balances energy use and safety.

Validated on real Amazon delivery routes.

Abstract

This paper addresses the problem of energy-efficient and safe routing of last-mile electric freight vehicles. With the rising environmental footprint of the transportation sector and the growing popularity of E-Commerce, freight companies are likely to benefit from optimal time-window-feasible tours that minimize energy usage while reducing traffic conflicts at intersections and thereby improving safety. We formulate this problem as a Bi-criterion Steiner Traveling Salesperson Problem with Time Windows (BSTSPTW) with energy consumed and the number of left turns at intersections as the two objectives while also considering regenerative braking capabilities. We first discuss an exact mixed-integer programming model with scalarization to enumerate points on the efficiency frontier for small instances. For larger networks, we develop an efficient local search-based heuristic, which uses several operators to intensify and diversify the search process. We demonstrate the utility of the proposed methods using benchmark data and real-world instances from Amazon delivery routes in Austin, US. Comparisons with state-of-the-art solvers shows that our heuristics can generate near-optimal solutions within reasonable time budgets, effectively balancing energy efficiency and safety under practical delivery constraints.