Sustainable logistics: Optimizing multi-day routes with flexible endpoints

Abstract

Strategic route planning is critical for incorporating efficiency into transport, particularly in minimizing empty mileage, which is directly linked to reducing fossil fuel consumption. This study addresses a multi-day open-close vehicle routing problem with time windows (MDOC-VRPTW), motivated by bulk material transport operations. The problem incorporates real-world-inspired constraints, including legislative regulations (e.g., working hours), vehicle, trailer and material properties (e.g., compatibility), driver requirements (scheduled doctors and vacations) and customer-specific requirements (e.g., time windows for loading and/or unloading). A key challenge arises from vehicle-specific endpoint conditions: some vehicles follow closed routes with fixed endpoints, while others operate on open routes requiring optimization to determine optimal endpoints with regard to the first transport request of the following day. These flexible endpoints significantly influence multi-day planning by shaping vehicle starting positions for subsequent days. However, this aspect is rarely addressed explicitly in existing multi-day routing approaches. Integrating flexible endpoint determination into the optimization process requires a novel approach, ensuring daily efficiency and strategic positioning for future operations. Further complexity arises from incomplete transport request portfolio data where only current-day requests are fully known, while subsequent days rely on partial information. Moreover, not all available requests can always be served and must therefore be selected by the optimization process. To address this, an iterative two-day approach was proposed and implemented using Google's open-source OR-Tools to model the MDOC-VRPTW. The proposed method was validated using real-world data from a Czech logistics company operating a large bulk-material fleet. A case study covering more than 3500 transport requests and over 120 vehicles demonstrated that the proposed method achieves a 5.6% reduction in empty transits. This translates to annual savings of approximately 365,000 km and 312 tons of CO2 emissions for a fleet of comparable size, highlighting its potential for improving operational efficiency and environmental sustainability. Furthermore, the approach significantly improved resource utilization (with 62% of the fleet operating at over 95% capacity) and demonstrated significant reliability by fulfilling 97.4% of high-priority requests.