Robust optimization framework for the electric vehicle location-routing problem with split deliveries and incompatible loading

Electric freight vehicles (EFV) are key innovations in efforts to reduce pollutant emissions. The extended location-routing problem with incompatible loading constraints and split delivery by order (ELRPILC-SDO) was evaluated for EFVs in the present study. Routing scenarios that allow divisible shipments and classical location-routing problems were targeted. First, an integer programming model was formulated to maximize the operational efficiency of the EFV by minimizing operating costs. Subsequently, a robust optimization layer that partitions delivery cost uncertainty into multiple ranges and controls deviations was added. Afterward, heuristics that combine iterative greedy algorithms with a mechanism for dynamically evaluating extensive solution spaces were developed. The performance of these methodologies was validated through comprehensive numerical experiments. Finally, the impact of delivery costs and splitting delivery orders on the overall service strategy was analyzed; the algorithm’s ability to solve the ELRPILC-SDO in a real-world distribution network in Zhongyuan District, Zhengzhou, China, was validated; and the influence of EFVs on the economy and emission reductions in a practical logistics distribution network was discussed. The experimental results indicate that (1) the developed methodologies require 0.046% of the runtime of a standard exact algorithm while they improve the solution quality by 1.40%, and (2) allowing order splitting reduces the total costs by up to 6.14% and the routing costs by up to 9.71%. These findings highlight that the demand split-by-order strategy offers flexible delivery options. Using EFVs as transportation vehicles helps reduce pollutant emissions, particularly as the battery range increases.