A cost function approximation method for dynamic vehicle routing with docking and LIFO constraints

TL;DR

The paper tackles a dynamic pickup-and-delivery problem with docking constraints and LIFO unloading, proposing a cost function approximation framework to improve adaptability to real-time requests. By perturbing the objective with penalties for waiting and idle vehicles and solving per-epoch instances with a LIFO-aware Variable Neighborhood Search, the method encourages flexible and efficient routes. Key contributions include the CFA formulation, three LIFO-oriented neighborhood operators, and a structured initial-route construction that prioritizes urgent orders; evaluation on the ICAPS 2021 DPDP dataset shows substantial performance gains over state-of-the-art methods, especially on large-scale instances. The work demonstrates that explicit waiting penalties and route diversification can dramatically improve responsiveness to dynamic demand in docking-constrained environments, with practical impact for real-world logistics operations.

Abstract

In this paper, we study a dynamic pickup and delivery problem with docking constraints. There is a homogeneous fleet of vehicles to serve pickup-and-delivery requests at given locations. The vehicles can be loaded up to their capacity, while unloading has to follow the last-in-first-out (LIFO) rule. The locations have a limited number of docking ports for loading and unloading, which may force the vehicles to wait. The problem is dynamic since the transportation requests arrive real-time, over the day. Accordingly, the routes of the vehicles are to be determined dynamically. The goal is to satisfy all the requests such that a combination of tardiness penalties and traveling costs is minimized. We propose a cost function approximation based solution method. In each decision epoch, we solve the respective optimization problem with a perturbed objective function to ensure the solutions remain adaptable to accommodate new requests. We penalize waiting times and idle vehicles. We propose a variable neighborhood search based method for solving the optimization problems, and we apply two existing local search operators, and we also introduce a new one. We evaluate our method using a widely adopted benchmark dataset, and the results demonstrate that our approach significantly surpasses the current state-of-the-art methods.

Figures (10)

• Figure 1: An example for loading and unloading during a vehicle route. Orders are depicted as boxes, factories are depicted as pentagons. Unloading the orders from a vehicle has to follow the LIFO rule, see the order of orders above the factories, and also the position of the orders on the vehicle.
• Figure 2: An example for serving vehicles at a factory. The two docking ports, P1 and P2, of the factory are occupied by vehicles 1 and 2, respectively, thus the service of vehicles 3 and 4 cannot start at this moment, and the vehicles must wait until a docking port becomes free.
• Figure 3: Sequential decision process.
• Figure 4: An example for a route plan of a vehicle at different states and actions. Left pane shows the route at an intermediate state of the decision process. Center pane shows the updated route according to an action. Right pane shows the route at the next state of the decision process.
• Figure 5: Example for a route. The first and the last node is indicated with black and white rectangles, respectively. Each internal node represents a pickup or delivery, depicted with black or white circles, respectively. Above each pickup/delivery node the order, and below it the factory is indicated.