Routing for an on-demand logistics service

In this paper, we examine an optimization problem for a shipping company that provides an on-demand delivery service in which its customers visit a specified location called a delivery center (e.g., a convenience store or Amazon locker) to pick up their items themselves, rather than delivering the products purchased online to the customers directly. In this problem, we select delivery centers that are accessible for all customers and determine the optimal delivery route that minimizes the costs proportional to the distance traveled by the delivery vehicle, the delivery time, and costs. This is an extension of the traveling salesman problem with a time window constraint, which simultaneously determines the locations of the delivery centers for customer pickup and the delivery route. To solve this problem and to improve managerial practice, we propose a mathematical programming model and an efficient two-phase solution algorithm based on an ant colony heuristic that is better suited to reality. By addressing on-demand delivery optimization problems, shipping companies can guarantee customer satisfaction while reducing shipping costs.