Last mile delivery routing problem with some-day option

E-commerce retailers are challenged to maintain cost-efficiency and customer satisfaction while pursuing sustainability, especially in the last mile. In response, retailers are offering a range of delivery speeds, including same-day and instant options. Faster deliveries, while trending, often increase costs and emissions due to limited planning time and reduced consolidation opportunities in the last mile. In contrast, this paper proposes the inclusion of a slower delivery option, termed some-day. Slowing down the delivery process allows for greater shipment consolidation, achieving cost savings and environmental goals simultaneously. We introduce the dynamic and stochastic some-day delivery problem, which accounts for a latest delivery day, customer time windows, and capacity limitations within a multi-period planning framework. Our solution approach is based on addressing auxiliary prize-collecting vehicle routing problems with time windows (PCVRPTW) on a daily basis, where the prize reflects the benefit of promptly serving the customer. We develop a hybrid adaptive large neighborhood search with granular insertion operators, outperforming existing metaheuristics for PCVRPTWs. Our numerical study shows significant cost savings with only small increases in delivery times compared to an earliest policy.