An exact algorithm for the multi-trip container drayage problem with truck platooning

Abstract

Container Drayage Problem (CDP) refers to the optimization problem of routing and scheduling a set of container trucks around a container terminal. Conventionally, a driver is stuck to one container truck and allowed to perform multiple trips (multi-trip) to the terminal within their working time. The recent development of automation technologies enables semi-autonomous trucks to follow the leading human-driven truck as a platoon on the road; therefore, truck platooning can save human labor and reduce the fuel cost of following trucks through aerodynamic drag reduction. In this paper, we study a multi-trip container drayage problem with truck platooning (MT-CDP-TP), where multi-trip, truck platooning, and fuel cost reduction are simultaneously considered in a CDP. Despite the operational benefits brought by the MT-CDP-TP, the problem is challenging to solve due to its NP-hardness when formulated as a multi-trip pickup and delivery problem with load-dependent cost. We propose a Branch-and-Price-and-Cut (BPC) algorithm, with a route-based set partitioning model and tight linear relaxations, to yield the exact solutions. Valid inequalities are generated based on a graph structure, where each node represents a feasible route, and each arc stands for the conflict between two routes. Moreover, we design a tailored pulse propagation algorithm with novel pruning procedures based on the dual information from the master problem and valid inequalities to solve the pricing problem efficiently. Extensive numerical experiments are conducted for performance validation, and the computational results show that the proposed exact algorithm can solve instances with up to 100 task nodes (i.e., 50 customers) and facilitate reducing the labor cost and fuel consumption by a wide margin in container drayage operations.