Quantifying the impact of delivery day flexibility on last-mile delivery costs

Last-mile delivery operations are often required to uphold rigid delivery dates, such as the day after an order is placed. However, given the inherent temporal stochasticity in customer order placement, this practice can overwhelm the available vehicle fleet with long routes and the need for driver overtime. This work explores the potential benefits of customer flexibility, wherein the delivery day can be chosen by the distributor from among pre-agreed delivery day windows spanning two or more consecutive days, allowing the delivery day to be co-optimized along the associated vehicle routes and leading to distribution cost savings. To that end, we develop a rolling horizon simulation framework that integrates a novel forecasting scheme for sampling order realizations with a branch-and-cut algorithm for solving the multi-period vehicle routing instances arising on each day. Computational studies using real-life industrial data are conducted to compare various decision policies and quantify the long-term cost savings that are possible when allowing such flexibility. In certain cases, we reveal the potential of significant cost savings-up to 12%-compared to the current "next-day " delivery policy. Our study also investigates the extent of discount incentives that may be offered to customers for accepting flexible delivery days.