Vehicle routing with varying levels of demand information

The vehicle routing problem is the problem of serving a set of customers with a fleet of vehicles such that the travel costs of those vehicles are minimized, while making sure each vehicle starts and ends at a central depot. In this thesis, we focus on exact methodology for the vehicle routing problem with three different levels of demand information: deterministic, stochastic and sensor-driven.First, we look at set partitioning and set covering problems that are solved by a branch-price-and-cut algorithm. We introduce a new category of cuts, called “resource-robust”, which do not complicate the pricing problem if specific resources are included. We create new cuts for the capacitated vehicle routing problem, with deterministic demands, that are resource-robust when the ng-route relaxation is used, which leads to speedups for certain instances.Second, we focus on the vehicle routing problem with stochastic demands. We develop a state-of-the-art integer L-shaped method to solve the problem to optimality. The algorithm uses all techniques from the literature, improves on some of these and uses new valid inequalities. Using this algorithm, we also investigate three commonly-made assumptions in the literature from a theoretical and computational perspective.Third, we investigate a single-period waste collection problem with sensors. We can adjust our routing decisions based on the sensor readings. We derive theoretical properties and develop an algorithm to approximate the cost savings achieved given a certain sensor placement. Then, we investigate the effectiveness of several sensor placement rules and how they fare under sensor uncertainty.<br/

Vehicle routing with varying levels of demand information

The vehicle routing problem is the problem of serving a set of customers with a fleet of vehicles such that the travel costs of those vehicles are minimized, while making sure each vehicle starts and ends at a central depot. In this thesis, we focus on exact methodology for the vehicle routing problem with three different levels of demand information: deterministic, stochastic and sensor-driven.First, we look at set partitioning and set covering problems that are solved by a branch-price-and-cut algorithm. We introduce a new category of cuts, called “resource-robust”, which do not complicate the pricing problem if specific resources are included. We create new cuts for the capacitated vehicle routing problem, with deterministic demands, that are resource-robust when the ng-route relaxation is used, which leads to speedups for certain instances.Second, we focus on the vehicle routing problem with stochastic demands. We develop a state-of-the-art integer L-shaped method to solve the problem to optimality. The algorithm uses all techniques from the literature, improves on some of these and uses new valid inequalities. Using this algorithm, we also investigate three commonly-made assumptions in the literature from a theoretical and computational perspective.Third, we investigate a single-period waste collection problem with sensors. We can adjust our routing decisions based on the sensor readings. We derive theoretical properties and develop an algorithm to approximate the cost savings achieved given a certain sensor placement. Then, we investigate the effectiveness of several sensor placement rules and how they fare under sensor uncertainty.<br/

A Column Generation Approach to the Capacitated Vehicle Routing Problem with Stochastic Demands

In this article we introduce a new exact solution approach to the Capacitated Vehicle Routing Problem with Stochastic Demands (CVRPSD). In particular, we consider the case where all customer demands are distributed independently and where each customer’s demand follows a Poisson distribution. The CVRPSD can be formulated as a Set Partitioning Problem. We show that, under the above assumptions on demands, the associated column generation subproblem can be solved using a dynamic programming scheme which is similar to that used in the case of deterministic demands. To evaluate the potential of our approach we have embedded this column generation scheme in a branch-and-price algorithm. Computational experiments on a large set of test instances show promising resultsRouting; Stochastic programming; Logistics; Branch and Bound; Dynamic programming

The Pyramidal Capacitated Vehicle Routing Problem

This paper introduces the Pyramidal Capacitated Vehicle Routing Problem (PCVRP) as a restricted version of the Capacitated Vehicle Routing Problem (CVRP). In the PCVRP each route is required to be pyramidal in a sense generalized from the Pyramidal Traveling Salesman Problem (PTSP). A pyramidal route is de ned as a route on which the vehicle rst visits customers in increasing order of customer index, and on the remaining part of the route visits customers in decreasing order of customer index. Provided that customers are indexed in nondecreasing order of distance from the depot, the shape of a pyramidal route is such that its traversal can be divided in two parts, where on the rst part of the route, customers are visited in nondecreasing distance from the depot, and on the remaining part of the route, customers are visited in nonincreasing distance from the depot. Such a route shape is indeed found in many optimal solutions to CVRP instances. An optimal solution to the PCVRP may therefore be useful in itself as a heuristic solution to the CVRP. Further, an attempt can be made to nd an even better CVRP solution by solving a TSP, possibly leading to a non-pyramidal route, for each of the routes in the PCVRP solution. This paper develops an exact branch-and-cut-and-price (BCP) algorithm for the PCVRP. At the pricing stage, elementary routes can be computed in pseudo-polynomial time in the PCVRP, unlike in the CVRP. We have therefore implemented pricing algorithms that generate only elementary routes. Computational results suggest that PCVRP solutions are highly useful for obtaining near-optimal solutions to the CVRP. Moreover, pricing of pyramidal routes may due to its eciency prove to be very useful in column generation for the CVRP.vehicle routing; pyramidal traveling salesman; branch-and-cut-and-price

The stochastic vehicle routing problem : a literature review, part II : solution methods

Building on the work of Gendreau et al. (Oper Res 44(3):469–477, 1996), and complementing the first part of this survey, we review the solution methods used for the past 20 years in the scientific literature on stochastic vehicle routing problems (SVRP). We describe the methods and indicate how they are used when dealing with stochastic vehicle routing problems. Keywords: vehicle routing (VRP), stochastic programmingm, SVRPpublishedVersio

On the heterogeneous vehicle routing problem under demand uncertainty

In this paper we study the heterogeneous vehicle routing problem under demand uncertainty, on which there has been little research to our knowledge. The focus of the paper is to provide a strong formulation that also easily allows tractable robust and chance-constrained counterparts. To this end, we propose a basic Miller-Tucker-Zemlin (MTZ) formulation with the main advantage that uncertainty is restricted to the right-hand side of the constraints. This leads to compact and tractable counterparts of demand uncertainty. On the other hand, since the MTZ formulation is well known to provide a rather weak linear programming relaxation, we propose to strengthen the initial formulation with valid inequalities and lifting techniques and, furthermore, to dynamically add cutting planes that successively reduce the polyhedral region using a branch-and-cut algorithm. We complete our study with extensive computational analysis with different performance measures on different classes of instances taken from the literature. In addition, using simulation, we conduct a scenario-based risk level analysis for both cases where either unmet demand is allowed or not