We consider a variant of the vehicle routing problem (VRP) where each customer has a unit demand and the goal is to minimize the total cost of routing a fleet of capacitated vehicles from one or multiple depots to visit all customers. We propose two parallel algorithms to efficiently solve the column-generation-based linear-programming relaxation for this VRP. Specifically, we focus on algorithms for the “pricing problem,” which corresponds to the resource-constrained elementary shortest path problem. The first algorithm extends the pulse algorithm for which we derive a new bounding scheme on the maximum load of any route. The second algorithm is based on random coloring from parameterized complexity which can be also combined with other techniques in the literature for improving VRPs, including cutting planes and column enumeration. We conduct numerical studies using VRP benchmarks (with 50–957 nodes) and instances of a medical home care delivery problem using census data in Wayne County, Michigan. Using parallel computing, both pulse and random coloring can significantly improve column generation for solving the linear programming relaxations and we can obtain heuristic integer solutions with small optimality gaps. Combining random coloring with column enumeration, we can obtain improved integer solutions having less than 2% optimality gaps for most VRP benchmark instances and less than 1% optimality gaps for the medical home care delivery instances, both under a 30-minute computational time limit. The use of cutting planes (e.g., robust cuts) can further reduce optimality gaps on some hard instances, without much increase in the run time. Summary of Contribution: The vehicle routing problem (VRP) is a fundamental combinatorial problem, and its variants have been studied extensively in the literature of operations research and computer science. In this paper, we consider general-purpose algorithms for solving VRPs, including the column-generation approach for the linear programming relaxations of the integer programs of VRPs and the column-enumeration approach for seeking improved integer solutions. We revise the pulse algorithm and also propose a random-coloring algorithm that can be used for solving the elementary shortest path problem that formulates the pricing problem in the column-generation approach. We show that the parallel implementation of both algorithms can significantly improve the performance of column generation and the random coloring algorithm can improve the solution time and quality of the VRP integer solutions produced by the column-enumeration approach. We focus on algorithmic design for VRPs and conduct extensive computational tests to demonstrate the performance of various approaches.
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This content will become publicly available on September 1, 2024
A-VRPD: Automating Drone-Based Last-Mile Delivery Using Self-Driving Cars
Drone-based last-mile delivery is an emerging technology that uses drones loaded onto a truck to deliver parcels to customers. In this paper, we introduce a fully automated system for drone-based last-mile delivery through incorporation of autonomous vehicles (AVs). A novel problem called the autonomous vehicle routing problem with drones (A-VRPD) is defined. A-VRPD is to select AVs from a pool of available AVs based on crowd sourcing, assign selected AVs to customer groups, and schedule routes for selected AVs to optimize the total operational cost. We formulate A-VRPD as a Mixed Integer Linear Program (MILP) and propose an optimization framework to solve the problem. A greedy algorithm is also developed to significantly improve the running time for large-scale delivery scenarios. Extensive simulations were conducted taking into account real-world operational costs for different types of AVs, traveled distances calculated considering the real-time traffic conditions using Google Map API, and varying load capacities of AVs. We evaluated the performance in comparison with two different state-of-the-art solutions: an algorithm designed to address the traditional vehicle routing problem with drones (VRP-D), which involves human-operated trucks working in tandem with drones to deliver parcels, and an algorithm for the two echelon vehicle routing problem (2E-VRP), wherein parcels are first transported to satellite locations and subsequently delivered from those satellites to the customers. The results indicate a substantial increase in profits for both the delivery company and vehicle owners compared with the state-of-the-art algorithms.
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- Award ID(s):
- 2209829
- NSF-PAR ID:
- 10483486
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Intelligent Transportation Systems
- Volume:
- 24
- Issue:
- 9
- ISSN:
- 1524-9050
- Page Range / eLocation ID:
- 9599 to 9612
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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