Workload Equity in Vehicle Routing Problems: A Survey and Analysis

Over the past two decades, equity aspects have been considered in a growing number of models and methods for vehicle routing problems (VRPs). Equity concerns most often relate to fairly allocating workloads and to balancing the utilization of resources, and many practical applications have been reported in the literature. However, there has been only limited discussion about how workload equity should be modeled in VRPs, and various measures for optimizing such objectives have been proposed and implemented without a critical evaluation of their respective merits and consequences. This article addresses this gap with an analysis of classical and alternative equity functions for biobjective VRP models. In our survey, we review and categorize the existing literature on equitable VRPs. In the analysis, we identify a set of axiomatic properties that an ideal equity measure should satisfy, collect six common measures, and point out important connections between their properties and those of the resulting Pareto-optimal solutions. To gauge the extent of these implications, we also conduct a numerical study on small biobjective VRP instances solvable to optimality. Our study reveals two undesirable consequences when optimizing equity with nonmonotonic functions: Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent, i.e. composed of tours whose workloads are all equal to or longer than those of other Pareto-optimal solutions. We show that the extent of these phenomena should not be underestimated. The results of our biobjective analysis are valid also for weighted sum, constraint-based, or single-objective models. Based on this analysis, we conclude that monotonic equity functions are more appropriate for certain types of VRP models, and suggest promising avenues for further research.Comment: Accepted Manuscrip

Combining meta-heuristics to effectively solve the vehicle routing problems with time windows

The vehicle routing problems with time windows are challenging delivery problems in which instances involving 100 customers or more can be difficult to solve. There were many interesting heuristics proposed to handle these problems effectively. In this paper, we examined two well-known meta-heuristics and carefully combined the short-term and long-term memory-like mechanisms of both methods to achieve better results. Our prototype was shown to compare favorably against the original search methods and other related search hybrids on the Solomon's test cases. More importantly, our proposal of integration opens up many exciting directions for further investigation.postprin

A Two-Stage Approach for Routing Multiple Unmanned Aerial Vehicles with Stochastic Fuel Consumption

The past decade has seen a substantial increase in the use of small unmanned aerial vehicles (UAVs) in both civil and military applications. This article addresses an important aspect of refueling in the context of routing multiple small UAVs to complete a surveillance or data collection mission. Specifically, this article formulates a multiple-UAV routing problem with the refueling constraint of minimizing the overall fuel consumption for all of the vehicles as a two-stage stochastic optimization problem with uncertainty associated with the fuel consumption of each vehicle. The two-stage model allows for the application of sample average approximation (SAA). Although the SAA solution asymptotically converges to the optimal solution for the two-stage model, the SAA run time can be prohibitive for medium- and large-scale test instances. Hence, we develop a tabu-search-based heuristic that exploits the model structure while considering the uncertainty in fuel consumption. Extensive computational experiments corroborate the benefits of the two-stage model compared to a deterministic model and the effectiveness of the heuristic for obtaining high-quality solutions.Comment: 18 page

A flexible metaheuristic framework for solving rich vehicle routing problems

Route planning is one of the most studied research topics in the operations research area. While the standard vehicle routing problem (VRP) is the classical problem formulation, additional requirements arising from practical scenarios such as time windows or vehicle compartments are covered in a wide range of so-called rich VRPs. Many solution algorithms for various VRP variants have been developed over time as well, especially within the class of so-called metaheuristics. In practice, routing software must be tailored to the business rules and planning problems of a specific company to provide valuable decision support. This also concerns the embedded solution methods of such decision support systems. Yet, publications dealing with flexibility and customization of VRP heuristics are rare. To fill this gap this thesis describes the design of a flexible framework to facilitate and accelerate the development of custom metaheuristics for the solution of a broad range of rich VRPs. The first part of the thesis provides background information to the reader on the field of vehicle routing problems and on metaheuristic solution methods - the most common and widely-used solution methods to solve VRPs. Specifically, emphasis is put on methods based on local search (for intensification of the search) and large neighborhood search (for diversification of the search), which are combined to hybrid methods and which are the foundation of the proposed framework. Then, the main part elaborates on the concepts and the design of the metaheuristic VRP framework. The framework fulfills requirements of flexibility, simplicity, accuracy, and speed, enforcing the structuring and standardization of the development process and enabling the reuse of code. Essentially, it provides a library of well-known and accepted heuristics for the standard VRP together with a set of mechanisms to adapt these heuristics to specific VRPs. Heuristics and adaptation mechanisms such as templates for user-definable checking functions are explained on a pseudocode level first, and the most relevant classes of a reference implementation using the Microsoft .NET framework are presented afterwards. Finally, the third part of the thesis demonstrates the use of the framework for developing problem-specific solution methods by exemplifying specific customizations for five rich VRPs with diverse characteristics, namely the VRP with time windows, the VRP with compartments, the split delivery VRP, the periodic VRP, and the truck and trailer routing problem. These adaptations refer to data structures and neighborhood search methods and can serve as a source of inspiration to the reader when designing algorithms for new, so far unstudied VRPs. Computational results are presented to show the effectiveness and efficiency of the proposed framework and methods, which are competitive with current state-of-the-art solvers of the literature. Special attention is given to the overall robustness of heuristics, which is an important aspect for practical application

A review of the Tabu Search Literature on Traveling Salesman Problems

The Traveling Salesman Problem (TSP) is one of the most widely studied problems inrncombinatorial optimization. It has long been known to be NP-hard and hence research onrndeveloping algorithms for the TSP has focused on approximate methods in addition to exactrnmethods. Tabu search is one of the most widely applied metaheuristic for solving the TSP. Inrnthis paper, we review the tabu search literature on the TSP, point out trends in it, and bringrnout some interesting research gaps in this literature.

A hybrid algorithm for the vehicle routing problem with three-dimensional loading constraints and mixed backhauls

In this paper, a variant of the vehicle routing problem with mixed backhauls (VRPMB) is presented, i.e. goods have to be delivered from a central depot to linehaul customers, and, at the same time, goods have to be picked up from backhaul customers and brought to the depot. Both types of customers can be visited in mixed sequences. The goods to be delivered or picked up are three-dimensional (cuboid) items. Hence, in addition to a routing plan, a feasible packing plan for each tour has to be provided considering a number of loading constraints. The resulting problem is the vehicle routing problem with three-dimensional loading constraints and mixed backhauls (3L-VRPMB)