Demand Steering in a Last-Mile Delivery Problem with Home and Pickup Point Delivery Options

To increase the efficiency of last-mile delivery, online retailers can adopt pickup points in their operations. The retailer may then incentivize customers to steer them from home to pickup point delivery to reduce costs. However, it is usually uncertain whether the customer accepts this incentive to switch to pickup delivery. This setup gives rise to a new last-mile delivery problem with integrated incentive and routing decisions under uncertainty. We model this problem as a two-stage stochastic program with decision dependent uncertainty. In the first stage, a retailer decides which customers to incentivize. However, customers' reaction to the incentive is stochastic: they may accept the offer and switch to pickup point delivery, or they may decline the offer and stick with home delivery. In the second stage, after customers' final delivery choices are revealed, a vehicle route is planned to serve customers via the delivery option of their choice. We develop an exact branch-and-bound algorithm and propose several heuristics to improve the algorithm's scalability. Our algorithm solves instances with up to 50 customers, realizing on average 4%-8% lower last-mile delivery costs compared with the commonly applied approaches in the industry that do not use incentives or offer incentives to all customers. We also develop a benchmark policy that gives very fast solutions with a 2% average optimality gap for small instances and up to 2% average cost increase compared with the heuristic solutions.