A dynamic approach for the vehicle routing problem with stochastic demands

The Vehicle Routing Problem with Stochastic Demands (VRPSD) is a variation of the classical Capacitated Vehicle Routing Problem (CVRP). In contrast to the deterministic CVRP, in the VRPSD the demand of each customer is modeled as a random variable and its realization is only known upon vehicle arrival to the customer site. Under this uncertain scenario, a possible outcome is that the demand of a customer ends up exceeding the remaining capacity of the vehicle, leading to a route failure. In this study we will focus on the single vehicle VRPSD in which the fleet is limited to one vehicle with finite capacity, that can execute various routes sequentially. The present work is based on an adaptation of an optimization framework developed initially for the vehicle routing problem with dynamic customers (i.e., customers appear while the vehicles are executing their routes)

Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

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

Exploring Heuristics for the Vehicle Routing Problem with Split Deliveries and Time Windows

This dissertation investigates the Vehicle Routing Problem with Split Deliveries and Time Windows. This problem assumes a depot of homogeneous vehicles and set of customers with deterministic demands requiring delivery. Split deliveries allow multiple visits to a customer and time windows restrict the time during which a delivery can be made. Several construction and local search heuristics are tested to determine their relative usefulness in generating solutions for this problem. This research shows a particular subset of the local search operators is particularly influential on solution quality and run time. Conversely, the construction heuristics tested do not significantly impact either. Several problem features are also investigated to determine their impact. Of the features explored, the ratio of customer demand to vehicle ratio revealed a significant impact on solution quality and influence on the effectiveness of the heuristics tested. Finally, this research introduces an ant colony metaheuristic coupled with a local search heuristic embedded within a dynamic program seeking to solve a Military Inventory Routing Problem with multiple-customer routes, stochastic supply, and deterministic demand. Also proposed is a suite of test problems for the Military Inventory Routing Problem

THE VEHICLE ROUTING PROBLEM WITH STOCHASTIC DEMANDS IN AN URBAN AREA – A CASE STUDY

The vehicle routing problem with stochastic demands (VRPSD) is a combinatorial optimization problem. The VRPSD looks for vehicle routes to connect all customers with a depot, so that the total distance is minimized, each customer visited once by one vehicle, every route starts and ends at a depot, and the travelled distance and capacity of each vehicle are less than or equal to the given maximum value. Contrary to the classical VRP, in the VRPSD the demand in a node is known only after a vehicle arrives at the very node. This means that the vehicle routes are designed in uncertain conditions. This paper presents a heuristic and meta-heuristic approach for solving the VRPSD and discusses the real problem of municipal waste collection in the City of Niš

A Tabu Search, Augment-Merge Heuristic to Solve the Stochastic Location Arc Routing Problem

The location arc routing problem (LARP) is a network optimization problem combining strategic facility location decisions and tactical or operational vehicle routing decisions for customer demand located on arcs of a network. The LARP seeks to locate facilities, or depots, and create vehicle delivery routes to minimize costs. The total cost is comprised of three components: fixed facility locations costs, fixed route creation (or vehicle acquisition) costs, and variable arc traversal costs. The applications of the LARP are varied and often include public services such as mail delivery, garbage collection, and street sweeping. In all of these applications, the magnitude of customer demand may be unknown at the outset of the problem and realized uncertainty can greatly affect the final solution. To the author’s knowledge, there is currently no discussion of formulating or solving a LARP with uncertainty. This paper presents an iterative tabu search, augment-merge heuristic to solve the LARP with stochastic customer demand. Each realization of customer demand for a particular network, represented by an individual scenario, was generated using the deterministic mval instances (with 24-50 nodes and 44-138 arcs) created by Hashemi Doulabi and Seifi (2013) and a truncated normal probability distribution. The tabu search phase handles the depot location decisions and chooses a set of depots to be used across all scenarios. The augment-merge phase creates a set of vehicle routes for each scenario. One-third of the initial experiments resulted in stochastic solution costs less than their deterministic counterparts indicating the promising value of considering customer demand uncertainty using the proposed stochastic LARP algorithm

Job Selection in a Network of Autonomous UAVs for Delivery of Goods

This article analyzes two classes of job selection policies that control how a network of autonomous aerial vehicles delivers goods from depots to customers. Customer requests (jobs) occur according to a spatio-temporal stochastic process not known by the system. If job selection uses a policy in which the first job (FJ) is served first, the system may collapse to instability by removing just one vehicle. Policies that serve the nearest job (NJ) first show such threshold behavior only in some settings and can be implemented in a distributed manner. The timing of job selection has significant impact on delivery time and stability for NJ while it has no impact for FJ. Based on these findings we introduce a methodological approach for decision-making support to set up and operate such a system, taking into account the trade-off between monetary cost and service quality. In particular, we compute a lower bound for the infrastructure expenditure required to achieve a certain expected delivery time. The approach includes three time horizons: long-term decisions on the number of depots to deploy in the service area, mid-term decisions on the number of vehicles to use, and short-term decisions on the policy to operate the vehicles

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