Comparison of heuristic approaches for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problemis a well-known problem that consists of determining least-cost schedulesfor vehicles assigned to several depots such that each task is accomplishedexactly once by a vehicle. In this paper, we propose to compare theperformance of five different heuristic approaches for this problem,namely, a heuristic \\mip solver, a Lagrangian heuristic, a columngeneration heuristic, a large neighborhood search heuristic using columngeneration for neighborhood evaluation, and a tabu search heuristic. Thefirst three methods are adaptations of existing methods, while the last twoare novel approaches for this problem. Computational results on randomlygenerated instances show that the column generation heuristic performs thebest when enough computational time is available and stability is required,while the large neighborhood search method is the best alternative whenlooking for a compromise between computational time and solution quality.tabu search;column generation;vehicle scheduling;heuristics;Lagrangian heuristic;large neighborhood search;multiple depot

Path Planning for Cooperative Routing of Air-Ground Vehicles

We consider a cooperative vehicle routing problem for surveillance and reconnaissance missions with communication constraints between the vehicles. We propose a framework which involves a ground vehicle and an aerial vehicle; the vehicles travel cooperatively satisfying the communication limits, and visit a set of targets. We present a mixed integer linear programming (MILP) formulation and develop a branch-and-cut algorithm to solve the path planning problem for the ground and air vehicles. The effectiveness of the proposed approach is corroborated through extensive computational experiments on several randomly generated instances

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

Identifying Best Practices for Snowplow Route Optimization

Well-designed winter maintenance routes result in snow and ice control service that is both more effective, because roads are cleared more rapidly, and more cost efficient, because deadheading, route overlap and other inefficiencies are reduced or eliminated. There are an increasing number of computerized tools to facilitate the routing process, but these tools are not yet widely used by winter maintenance practitioners. The purpose of this report is to provide practitioners with an overview of computerized route optimization processes and concrete recommendations about how to ensure that route improvement efforts produce actionable results. Recommendations are synthesized from nine recent and ongoing snowplow routing projects using a variety of computerized routing tools. Project descriptions, based on interviews with project personnel, focus on project goals, optimization software features used, and lessons learned. Multiple route optimization projects report route length reductions on the order of 5% to 10%, with reductions as high as 50% reported in one case. These snowplow route optimization projects show that route optimization is a powerful tool for improving routing efficiency but that it does not replace the need for expert judgment in the route design process. Successful route optimization projects rely on close cooperation between experienced winter maintenance professionals and the individuals conducting the route optimization as well as a highly accurate, snowplow-routing specific representation of the road network. Successful projects also include time to review and revise new routes to identify potential problem spots prior to implementation

Mapping constrained optimization problems to quantum annealing with application to fault diagnosis

Current quantum annealing (QA) hardware suffers from practical limitations such as finite temperature, sparse connectivity, small qubit numbers, and control error. We propose new algorithms for mapping boolean constraint satisfaction problems (CSPs) onto QA hardware mitigating these limitations. In particular we develop a new embedding algorithm for mapping a CSP onto a hardware Ising model with a fixed sparse set of interactions, and propose two new decomposition algorithms for solving problems too large to map directly into hardware. The mapping technique is locally-structured, as hardware compatible Ising models are generated for each problem constraint, and variables appearing in different constraints are chained together using ferromagnetic couplings. In contrast, global embedding techniques generate a hardware independent Ising model for all the constraints, and then use a minor-embedding algorithm to generate a hardware compatible Ising model. We give an example of a class of CSPs for which the scaling performance of D-Wave's QA hardware using the local mapping technique is significantly better than global embedding. We validate the approach by applying D-Wave's hardware to circuit-based fault-diagnosis. For circuits that embed directly, we find that the hardware is typically able to find all solutions from a min-fault diagnosis set of size N using 1000N samples, using an annealing rate that is 25 times faster than a leading SAT-based sampling method. Further, we apply decomposition algorithms to find min-cardinality faults for circuits that are up to 5 times larger than can be solved directly on current hardware.Comment: 22 pages, 4 figure

Motor Carrier Service Network Design

This chapter introduces service network design (SND) operations research models and solution methodologies specifically focused on problems that arise in the planning of operations in the trucking, or motor freight, industry. Consolidation carriers such as less-than-truckload and package trucking companies face flow planning problems to decide how to route freight between transfer terminals, and load planning problems to decide how to consolidate shipments into trailerloads and containerloads for dispatch. Integer programming models are introduced for these network design decision problems as well as exact and heuristic solution methods

A novel modeling approach for express package carrier planning

Express package carrier networks have large numbers of heavily-interconnected and tightly-constrained resources, making the planning process difficult. A decision made in one area of the network can impact virtually any other area as well. Mathematical programming therefore seems like a logical approach to solving such problems, taking into account all of these interactions. The tight time windows and nonlinear cost functions of these systems, however, often make traditional approaches such as multicommodity flow formulations intractable. This is due to both the large number of constraints and the weakness of the linear programming (LP) relaxations arising in these formulations. To overcome these obstacles, we propose a model in which variables represent combinations of loads and their corresponding routings, rather than assigning individual loads to individual arcs in the network. In doing so, we incorporate much of the problem complexity implicitly within the variable definition, rather than explicitly within the constraints. This approach enables us to linearize the cost structure, strengthen the LP relaxation of the formulation, and drastically reduce the number of constraints. In addition, it greatly facilitates the inclusion of other stages of the (typically decomposed) planning process. We show how the use of templates, in place of traditional delayed column generation, allows us to identify promising candidate variables, ensuring high-quality solutions in reasonable run times while also enabling the inclusion of additional operational considerations that would be difficult if not impossible to capture in a traditional approach. Computational results are presented using data from a major international package carrier. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/60965/1/20310_ftp.pd

Routing design for less-than-truckload motor carriers using ant colony techniques

One of the most important challenges for Less-Than-Truck-Load carriers consists of determining how to consolidate flows of small shipments to minimize costs while maintaining a certain level of service. For any origin-destination pair, there are several strategies to consolidate flows, but the most usual ones are: peddling/collecting routes and shipping through one or more break-bulk terminals. Therefore, the target is determining a route for each origin-destination pair that minimizes the total transportation and handling cost guaranteeing a certain level of service. Exact resolution is not viable for real size problems due to the excessive computational time required. This research studies different aspects of the problem and provides a metaheuristic algorithm (based on Ant Colonies Optimization techniques) capable of solving real problems in a reasonable computational time. The viability of the approach has been proved by means of the application of the algorithm to a real Spanish case, obtaining encouraging results