Solving Large Scale Vehicle Routing Problems With Unsplittable Demands Via Limited Information

This paper addresses the capacitated vehicle routing problem with unsplittable stochastic demand (UCVRP), in the limited information regime. We integrate ideas from region partitioning and online bin packing to propose a provably near-optimal and scalable algorithm. Our algorithm performs double partitioning: it first assigns routes to each vehicle a priori and then solves the recourse problem via a highly-efficient online bin-packing algorithm. One salient feature of our algorithm is that each driver only needs to know the information of a small number of customers, even when the total number of customers is extremely large. We characterize the performance of the algorithm and its convergence rate to the optimal offline solution with respect to the amount of customer information through asymptotic analysis. Moreover, we analyze the impact of adding additional overlapping routes and show in heavy traffic scenarios, additional overlapping does not improve the rate of convergence to the optimal solution except by constants. Finally, the effectiveness of the algorithm is further verified through numerical simulations.

In a unified and carefully developed presentation, this book systematically examines recent developments in VRP. The book focuses on a portfolio of significant technical advances that have evolved over the past few years for modeling and solving vehicle routing problems and VRP variations. Reflecting the most recent scholarship, this book is written by one of the top research scholars in Vehicle Routing and is one of the most important books in VRP to be published in recent times.

We present solution methodologies for vehicle routing problems (VRPs) with stochastic demand, with a specific focus on the vehicle routing problem with stochastic demand (VRPSD) and the vehicle routing problem with stochastic demand and duration limits (VRPSDL). The VRPSD and the VRPSDL are fundamental problems underlying many operational challenges in the fields of logistics and supply chain management. We model the VRPSD and the VRPSDL as large-scale Markov decision processes. We develop cyclic-order neighborhoods, a general methodology for solving a broad class of VRPs, and use this technique to obtain static, fixed route policies for the VRPSD. We develop pre-decision, post-decision, and hybrid rollout policies for approximate dynamic programming (ADP). These policies lay a methodological foundation for solving large-scale sequential decision problems and provide a framework for developing dynamic routing policies. Our dynamic rollout policies for the VRPSDL significantly improve upon a method frequently implemented in practice. We also identify circumstances in which our rollout policies appear to offer little or no benefit compared to this benchmark. These observations can guide managerial decision making regarding when the use of our procedures is justifiable. We also demonstrate that our methodology lends itself to real-time implementation, thereby providing a mechanism to make high-quality, dynamic routing decisions for large-scale operations. Finally, we consider a more traditional ADP approach to the VRPSDL by developing a parameterized linear function to approximate the value functions corresponding to our problem formulation. We estimate parameters via a simulation-based algorithm and show that initializing parameter values via our rollout policies leads to significant improvements. However, we conclude that additional research is required to develop a parametric ADP methodology comparable or superior to our rollout policies.

Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Operations researchers have made significant developments in the algorithms for their solution, and Vehicle Routing: Problems, Methods, and Applications, Second Edition reflects these advances. The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area; it emphasizes methodology related to specific classes of vehicle routing problems and, since vehicle routing is used as a benchmark for all new solution techniques, contains a complete overview of current solutions to combinatorial optimization problems. It also includes several chapters on important and emerging applications, such as disaster relief and green vehicle routing.

In the logistics industry, many resources are spent on handling the challenges in complex transportation planning problems. The growth of e-commerce demand scalable and hybrid delivery solutions that are in-time, cost-efficient, and clean. Increased workloads demand sophisticated scheduling and routing timelines. Therefore, governments and major logistics companies are launching different programs to promote sustainable distribution processes that leverage multiple transportation modes. In this way, the transportation network costs will be decreased and the carbon efficiency will be improved. Such increasing need for detailed and multimodal plans to larger transportation problems makes the current decision support tools indispensable. The low-quality solutions and the lack of big-data capability have concerned the practitioners for a long time. The problem of routing and scheduling with different types of carriers and modes have drawn limited attentions in previous research. There is no comprehensive research that discusses implementable models and algorithms with most real-world constraints on such transportation mode decision problem. The problem implies the design of long-haul transport, efficient last-mile deliveries to fulfill the demands within in strict time windows. Because it may take several days to cover a long-haul route, it is mandatory to consider breaks or layovers during the trip. Due to the capacity limit, some non-profitable deliveries are subcontracted to third-party carriers. This strategy allows the company to fill their vehicle fleets to the maximum. To further optimize the cost and carbon efficiencies of the vehicle fleets, different types of vehicles are to be evaluated. While the traditional diesel trailers can efficiently handle large amount of cargo, the travel costs and the greenhouse gas emissions cannot be negligible. While the technologies of electric vehicles are becoming mature, the driving-range issue and the high purchase cost still worry the industry. These challenges inhibit the success of a multimodal transportation network. In this dissertation, we investigate the three related optimization problems via meta-heuristics and mathematical programming – 1) a vehicle routing problem with common carriers and time regulation (VRPCCTR), in which the working hour limit is specified and third-party common carriers’ services are considered for unprofitable deliveries; 2) an extended version of the first problem where heterogeneous-sized vehicle fleets are involved (called HVRPCCTR); 3) the electric vehicles are introduced to the problem so that the mode decision becomes determining optimal routes between mixed vehicle types and sizes (called MVRPC) observing the time windows, recharging needs, service of hours regulations, and other constraints. In short, we study a new variant of the vehicle routing problem with three shipping modes – heterogeneous internal combustion vehicles, electric vehicles, and common carriers. Our main contributions are three-fold: We propose a novel meta-heuristic algorithm called Red-Black Ant Colony System for the problems, where the black ants are searching for regular routes using different sizes of vehicles whereas the red ants re-optimize within the common carrier deliveries to build efficient dedicated fleet routes. A developed tool can solve the mode decision problem for 150,000 deliveries. And its implementation has conducted over $5 million of dollars of savings for DHL and its customers annually. For each of the three problems, we give mixed integer linear programming (MILP) models and introduce strong valid inequalities. We prove the strengths of each set of valid inequalities by analyzing the linear relaxation bounds of the models. The endeavors of reducing the symmetry in the MILP models can be seen as the complexities grow from VRPCCTR through HVRPCCTR to MVRPC. We extend our work to incorporate green transportation plans. The recharges for electric vehicles and layover needs are efficiently modeled as renewable resources. This dissertation presents the first exact method based on a branch-and-cut- and-pricing algorithm for variants of MVRPC. The algorithm is tested on real data set from small sizes to medium sizes. Its performance and sensitivity are analyzed. The results show that the our algorithm can solve the problems up to 120 customers to exact optimality. Our results provide analytical insights and implementable large-scale algorithms for multimodal transportation networks of the next-generation logistic operations. The algorithms can also be utilized to study other types of scaling networks such as social networks, electrical grid, 3D printing models, etc. Other industries, such as manufacturing, digital communication, shared economy, etc., can also benefit from our results.