Modeling and Solving the Time-Dependent in-Building Delivery Problem in Last-Mile Logistics

This article introduces, models, and solves the time-dependent in-building delivery problem in last-mile logistics. It determines efficient travel sequences for a worker (e.g., delivery person, deliveryman, mailman, agent) who delivers goods or provides services directly to customers located within a building using its elevation system. We study, in detail, all the steps involved in a travel sequence inside a building: horizontal trips, unloading products to the customers, waiting for elevators, and vertical trips within elevators. The sequences and their total times vary depending on the building type, the elevation system, the moment of the day, and the arrival time because of the daily building traffic intensity variations. A mixed-integer linear programming model and a genetic algorithm-based metaheuristic are proposed to solve a set of instances in two office buildings. The results show that it is very important to determine the best time to visit a building because of its time dependency. The variation in delivery time between off-peak hours versus peak hours is between 15% and 30% for the set of solved instances. Moreover, the order of customer visits differs drastically depending on the arrival time to the building.