The cyclic inventory routing problem with environmental considerations: Model, solution procedure, and insights

This paper introduces and studies the Cyclic Inventory Routing Problem with Environmental (CIRP-E) considerations which plans the distribution from a single depot to multiple customers with the objective of minimizing the average cost of transportation, inventory, fuel, and carbon emissions subject to constraints related to demand satisfaction, vehicle and storage capacities, and driving hours limitations. CIRP-E integrates strategic fleet sizing, tactical route design, lot sizing and speed selection, together with operational vehicle scheduling. We derive analytical results for vehicle speed and cycle times, and study how they affect fleet sizing and vehicle scheduling. These results and insights are then exploited to develop heuristics which are embedded in a powerful two-phase metaheuristic solution approach for CIRP-E. The first phase designs vehicle routes and decides on vehicle speed and cycle times to minimize the total cost rate. The second phase takes the designed routes as input and decides on fleet sizing and scheduling of deliveries, while adjusting vehicle speeds and cycle times. Computational experiments show that the proposed solution approach adequately trades-off the various cost components and outperforms different adaptations of a state-of-the-art solution method for the classical cyclic inventory routing problem.