Tackling Dynamic Vehicle Routing Problem with Time Windows by means of Ant Colony System

The Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) is an extension of the well-known Vehicle Routing Problem (VRP), which takes into account the dynamic nature of the problem. This aspect requires the vehicle routes to be updated in an ongoing manner as new customer requests arrive in the system and must be incorporated into an evolving schedule during the working day. Besides the vehicle capacity constraint involved in the classical VRP, DVRPTW considers in addition time windows, which are able to better capture real-world situations. Despite this, so far, few studies have focused on tackling this problem of greater practical importance. To this end, this study devises for the resolution of DVRPTW, an ant colony optimization based algorithm, which resorts to a joint solution construction mechanism, able to construct in parallel the vehicle routes. This method is coupled with a local search procedure, aimed to further improve the solutions built by ants, and with an insertion heuristics, which tries to reduce the number of vehicles used to service the available customers. The experiments indicate that the proposed algorithm is competitive and effective, and on DVRPTW instances with a higher dynamicity level, it is able to yield better results compared to existing ant-based approaches.Comment: 10 pages, 2 figure

Optimal Routing of Energy-aware Vehicles in Networks with Inhomogeneous Charging Nodes

We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed time for vehicles to reach their destinations considering both traveling and recharging times at nodes when the vehicles do not have adequate energy for the entire journey. We study two versions of the problem. In the single vehicle routing problem, we formulate a mixed-integer nonlinear programming (MINLP) problem and show that it can be reduced to a lower dimensionality problem by exploiting properties of an optimal solution. We also obtain a Linear Programming (LP) formulation allowing us to decompose it into two simpler problems yielding near-optimal solutions. For a multi-vehicle problem, where traffic congestion effects are included, we use a similar approach by grouping vehicles into "subflows". We also provide an alternative flow optimization formulation leading to a computationally simpler problem solution with minimal loss in accuracy. Numerical results are included to illustrate these approaches.Comment: To appear in proceeding of 22nd Mediterranean Conference on Control and Automation, MED'1

Dynamic Collection Scheduling Using Remote Asset Monitoring: Case Study in the UK Charity Sector

Remote sensing technology is now coming onto the market in the waste collection sector. This technology allows waste and recycling receptacles to report their fill levels at regular intervals. This reporting enables collection schedules to be optimized dynamically to meet true servicing needs in a better way and so reduce transport costs and ensure that visits to clients are made in a timely fashion. This paper describes a real-life logistics problem faced by a leading UK charity that services its textile and book donation banks and its high street stores by using a common fleet of vehicles with various carrying capacities. Use of a common fleet gives rise to a vehicle routing problem in which visits to stores are on fixed days of the week with time window constraints and visits to banks (fitted with remote fill-monitoring technology) are made in a timely fashion so that the banks do not become full before collection. A tabu search algorithm was developed to provide vehicle routes for the next day of operation on the basis of the maximization of profit. A longer look-ahead period was not considered because donation rates to banks are highly variable. The algorithm included parameters that specified the minimum fill level (e.g., 50%) required to allow a visit to a bank and a penalty function used to encourage visits to banks that are becoming full. The results showed that the algorithm significantly reduced visits to banks and increased profit by up to 2.4%, with the best performance obtained when the donation rates were more variable

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