THE VEHICLE ROUTING PROBLEM WITH DEMAND RANGES

The classic Capacitated Vehicle Routing Problem (CVRP) has been studied in the Operations Research field for over 5 decades. This thesis formulates the vehicle routing problem with a variation that has not been studied in detail. It is called the Vehicle Routing Problem with Demand Ranges (VRPDR). With increasing competition, corporations are looking to minimize costs. This problem aims to reduce the cost of distributing goods by allowing flexibility in the delivered or dropped off quantity. This benefits the customer as well, by reducing storage and other inventory costs. We solve the VRPDR problem where the customer gives the distributor a demand range. The distributor is rewarded for delivering more. A metaheuristic, record-to-record travel with demand range (RTRDR), is developed which is capable of solving large problem instances. The metaheuristic is a modification of a successful CVRP metaheuristic used in the past. In this thesis, we report results on problems ranging in size from 560 to 1200 customers. The developed metaheuristic uses the Clarke-Wright procedure to get initial solutions and then applies record-to-record travel in conjunction with two-opt moves, one point moves, and two point moves. Since the problem has not been studied yet from a computational point of view, we have developed a comparison algorithm, which takes advantage of the demand range flexibility of this problem only after the algorithm has optimized for distance alone. We use the results from this algorithm as a benchmark to compare with our proposed metaheuristic RTRDR

Approximation Algorithms for Capacitated k-Travelling Repairmen Problems

We study variants of the capacitated vehicle routing problem. In the multiple depot capacitated k-travelling repairmen problem (MD-CkTRP), we have a collection of clients to be served by one vehicle in a fleet of k identical vehicles based at given depots. Each client has a given demand that must be satisfied, and each vehicle can carry a total of at most Q demand before it must resupply at its original depot. We wish to route the vehicles in a way that obeys the constraints while minimizing the average time (latency) required to serve a client. This generalizes the Multi-depot k-Travelling Repairman Problem (MD-kTRP) [Chekuri and Kumar, IEEE-FOCS, 2003; Post and Swamy, ACM-SIAM SODA, 2015] to the capacitated vehicle setting, and while it has been previously studied [Lysgaard and Wohlk, EJOR, 2014; Rivera et al, Comput Optim Appl, 2015], no approximation algorithm with a proven ratio is known. We give a 42.49-approximation to this general problem, and refine this constant to 25.49 when clients have unit demands. As far as we are aware, these are the first constant-factor approximations for capacitated vehicle routing problems with a latency objective. We achieve these results by developing a framework allowing us to solve a wider range of latency problems, and crafting various orienteering-style oracles for use in this framework. We also show a simple LP rounding algorithm has a better approximation ratio for the maximum coverage problem with groups (MCG), first studied by Chekuri and Kumar [APPROX, 2004], and use it as a subroutine in our framework. Our approximation ratio for MD-CkTRP when restricted to uncapacitated setting matches the best known bound for it [Post and Swamy, ACM-SIAM SODA, 2015]. With our framework, any improvements to our oracles or our MCG approximation will result in improved approximations to the corresponding k-TRP problem

A simheuristic for routing electric vehicles with limited driving ranges and stochastic travel times

Green transportation is becoming relevant in the context of smart cities, where the use of electric vehicles represents a promising strategy to support sustainability policies. However the use of electric vehicles shows some drawbacks as well, such as their limited driving-range capacity. This paper analyses a realistic vehicle routing problem in which both driving-range constraints and stochastic travel times are considered. Thus, the main goal is to minimize the expected time-based cost required to complete the freight distribution plan. In order to design reliable Routing plans, a simheuristic algorithm is proposed. It combines Monte Carlo simulation with a multi-start metaheuristic, which also employs biased-randomization techniques. By including simulation, simheuristics extend the capabilities of metaheuristics to deal with stochastic problems. A series of computational experiments are performed to test our solving approach as well as to analyse the effect of uncertainty on the routing plans.Peer Reviewe

Towards a Testbed for Dynamic Vehicle Routing Algorithms

Since modern transport services are becoming more flexible, demand-responsive, and energy/cost efficient, there is a growing demand for large-scale microscopic simulation platforms in order to test sophisticated routing algorithms. Such platforms have to simulate in detail, not only the dynamically changing demand and supply of the relevant service, but also traffic flow and other relevant transport services. This paper presents the DVRP extension to the open-source MATSim simulator. The extension is designed to be highly general and customizable to simulate a wide range of dynamic rich vehicle routing problems. The extension allows plugging in of various algorithms that are responsible for continuous re-optimisation of routes in response to changes in the system. The DVRP extension has been used in many research and commercial projects dealing with simulation of electric and autonomous taxis, demand-responsive transport, personal rapid transport, free-floating car sharing and parking search

A Hybrid Model to Extend Vehicular Intercommunication V2V through D2D Architecture

In the recent years, many solutions for Vehicle to Vehicle (V2V) communication were proposed to overcome failure problems (also known as dead ends). This paper proposes a novel framework for V2V failure recovery using Device-to-Device (D2D) communications. Based on the unified Intelligent Transportation Systems (ITS) architecture, LTE-based D2D mechanisms can improve V2V dead ends failure recovery delays. This new paradigm of hybrid V2V-D2D communications overcomes the limitations of traditional V2V routing techniques. According to NS2 simulation results, the proposed hybrid model decreases the end to end delay (E2E) of messages delivery. A complete comparison of different D2D use cases (best & worst scenarios) is presented to show the enhancements brought by our solution compared to traditional V2V techniques.Comment: 6 page

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