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

Recourse policies in the vehicle routing problem with stochastic demands

Dans le domaine de la logistique, de nombreux problèmes pratiques peuvent être formulés comme le problème de tournées de véhicules (PTV). Dans son image la plus large, le PTV vise à concevoir un ensemble d’itinéraires de collecte ou de livraison des marchandises à travers un ensemble de clients avec des coûts minimaux. Dans le PTV déterministe, tous les paramètres du problème sont supposés connus au préalable. Dans de nombreuses variantes de la vie réelle du PTV, cependant, ils impliquent diverses sources d’aléatoire. Le PTV traite du caractère aléatoire inhérent aux demandes, présence des clients, temps de parcours ou temps de service. Les PTV, dans lesquels un ou plusieurs paramètres sont stochastiques, sont appelés des problèmes stochastiques de tournées de véhicules (PSTV). Dans cette dissertation, nous étudions spécifiquement le problème de tournées de véhicules avec les demandes stochastiques (PTVDS). Dans cette variante de PSTV, les demandes des clients ne sont connues qu’en arrivant à l’emplacement du client et sont définies par des distributions de probabilité. Dans ce contexte, le véhicule qui exécute une route planifiée peut ne pas répondre à un client, lorsque la demande observée dépasse la capacité résiduelle du véhicule. Ces événements sont appelés les échecs de l’itinéraire; dans ce cas, l’itinéraire planifié devient non-réalisable. Il existe deux approches face aux échecs de l’itinéraire. Au client où l’échec s’est produit, on peut récupérer la realisabilite en exécutant un aller-retour vers le dépôt, pour remplir la capacité du véhicule et compléter le service. En prévision des échecs d’itinéraire, on peut exécuter des retours préventifs lorsque la capacité résiduelle est inférieure à une valeur seuil. Toutes les décisions supplémentaires, qui sont sous la forme de retours au dépôt dans le contexte PTVDS, sont appelées des actions de recours. Pour modéliser le PTVDS, une politique de recours, régissant l’exécution des actions de recours, doit être conçue. L’objectif de cette dissertation est d’élaborer des politiques de recours rentables, dans lesquelles les conventions opérationnelles fixes peuvent régir l’exécution des actions de recours. Nous fournissons un cadre général pour classer les conventions opérationnelles fixes pour être utilisées dans le cadre PTVDS. Dans cette classification, les conventions opérationnelles fixes peuvent être regroupées dans (i) les politiques basées sur le volume, (ii) les politiques basées sur le risque et (iii) les politiques basées sur le distance. Les politiques hybrides, dans lesquelles plusieurs règles fixes sont incorporées, peuvent être envisagées. Dans la première partie de cette thèse, nous proposons une politique fixe basée sur les règles, par laquelle l’exécution des retours préventifs est régie par les seuils prédéfinis. Nous proposons notamment trois politiques basées sur le volume qui tiennent compte de la capacité du véhicule, de la demande attendue du prochain client et de la demande attendue des clients non visités. La méthode “Integer L-Shaped" est réaménagée pour résoudre le PTVDS selon la politique basée sur les règles. Dans la deuxième partie, nous proposons une politique de recours hybride, qui combine le risque d’échec et de distance à parcourir en une seule règle de recours, régissant l’exécution des recours. Nous proposons d’abord une mesure de risque pour contrôler le risque d’échec au prochain client. Lorsque le risque d’échec n’est ni trop élevé ni trop bas, nous utilisons une mesure de distance, ce qui compare le coût de retour préventif avec les coûts d’échecs futurs. Dans la dernière partie de cette thèse, nous développons une méthodologie de solution exacte pour résoudre le VRPSD dans le cadre d’une politique de restockage optimale. La politique de restockage optimale résulte d’un ensemble de seuils spécifiques au client, de sorte que le coût de recours prévu soit réduit au minimum.In the field of logistics, many practical problems can be formulated as the vehicle routing problem (VRP). In its broadest picture, the VRP aims at designing a set of vehicle routes to pickup or delivery goods through a set of customers with the minimum costs. In the deterministic VRP, all problem parameters are assumed known beforehand. The VRPs in real-life applications, however, involve various sources of uncertainty. Uncertainty is appeared in several parameters of the VRPs like demands, customer, service or traveling times. The VRPs in which one or more parameters appear to be uncertain are called stochastic VRPs (SVRPs). In this dissertation, we examine vehicle routing problem with stochastic demands (VRPSD). In this variant of SVRPs, the customer demands are only known upon arriving at the customer location and are defined through probability distributions. In this setting, the vehicle executing a planned route may fail to service a customer, whenever the observed demand exceeds the residual capacity of the vehicle. Such occurrences are called route failures; in this case the planned route becomes infeasible. There are two approaches when facing route failures. At the customer where the failure occurred, one can recover routing feasibility by executing back-and-forth trips to the depot to replenish the vehicle capacity and complete the service. In anticipation of route failures, one can perform preventive returns whenever the residual capacity falls below a threshold value. All the extra decisions, which are in the form of return trips to the depot in the VRPSD context, preserving routing feasibility are called recourse actions. To model the VRPSD, a recourse policy, governing the execution of such recourse actions, must be designed. The goal of this dissertation is to develop cost-effective recourse policies, in which the fixed operational conventions can govern the execution of recourse actions. In the first part of this dissertation, we propose a fixed rule-based policy, by which the execution of preventive returns is governed through the preset thresholds. We particularly introduce three volume based policies which consider the vehicle capacity, expected demand of the next customer and the expected demand of the remaining unvisited customers. Then, the integer L-shaped algorithm is redeveloped to solve the VRPSD under the rule-based policy. The contribution with regard to this study has been submitted to the Journal of Transportation Science. In the second part, we propose a hybrid recourse policy, which combines the risk of failure and distances-to-travel into a single recourse rule, governing the execution of recourse actions. We employ a risk measure to control the risk of failure at the next customer. When the risk of failure is neither too high nor too low, we apply a distance measure, which compares the preventive return cost with future failures cost. The contribution with regard to this study has been submitted to the EURO Journal on Transportation and Logistics. In the last part of this dissertation, we develop an exact solution methodology to solve the VRPSD under an optimal restocking policy. The optimal restocking policy derives a set of customer-specific thresholds such that the expected recourse cost is minimized. The contribution with regard to this study will be submitted to the European Journal of Operational Research

A Multistage Stochastic Programming Approach to the Dynamic and Stochastic VRPTW - Extended version

We consider a dynamic vehicle routing problem with time windows and stochastic customers (DS-VRPTW), such that customers may request for services as vehicles have already started their tours. To solve this problem, the goal is to provide a decision rule for choosing, at each time step, the next action to perform in light of known requests and probabilistic knowledge on requests likelihood. We introduce a new decision rule, called Global Stochastic Assessment (GSA) rule for the DS-VRPTW, and we compare it with existing decision rules, such as MSA. In particular, we show that GSA fully integrates nonanticipativity constraints so that it leads to better decisions in our stochastic context. We describe a new heuristic approach for efficiently approximating our GSA rule. We introduce a new waiting strategy. Experiments on dynamic and stochastic benchmarks, which include instances of different degrees of dynamism, show that not only our approach is competitive with state-of-the-art methods, but also enables to compute meaningful offline solutions to fully dynamic problems where absolutely no a priori customer request is provided.Comment: Extended version of the same-name study submitted for publication in conference CPAIOR201

Planning and Scheduling Transportation Vehicle Fleet in a Congested Traffic Environment

Transportation is a main component of supply chain competitiveness since it plays a major role in the inbound, inter-facility, and outbound logistics. In this context, assigning and scheduling vehicle routing is a crucial management problem. Despite numerous publications dealing with efficient scheduling methods for vehicle routing, very few addressed the inherent stochastic nature of travel times in this problem. In this paper, a vehicle routing problem with time windows and stochastic travel times due to potential traffic congestion is considered. The approach developed introduces mainly the traffic congestion component based on queueing theory. This is an innovative modeling scheme to capture the stochastic behavior of travel times. A case study is used both to illustrate the appropriateness of the approach as well as to show that time-independent solutions are often unrealistic within a congested traffic environment which is often the case on the european road networkstransportation; vehicle fleet; planning; scheduling; congested traffic

Economic effects of mobile technologies on operations of sales agents

In the presented paper we introduce an approach to assess particular economic effects which may arise with bringing mobile technologies into the field of sales and distribution. The research problem posed here comprises quite a special case where sales operations of a company are carried by its sales representatives, which may count as a resource allocation problem. We apply stochastic programming methodology to model the agent's multistage decision making in a distribution system with uncertain customer demands, and exemplify a potential improvement in the company's overall performance when mobile facilities are utilized for making decisions. We provide finally an efficient computational algorithm that delivers optimal decision making with and without mobile technologies, and computers the expected overall performance in both cases, for any configuration of a distribution system. Some computational results are presented. --

Genetic programming hyper-heuristic with vehicle collaboration for uncertain capacitated arc routing problem

Due to its direct relevance to post-disaster operations, meter reading and civil refuse collection, the Uncertain Capacitated Arc Routing Problem (UCARP) is an important optimisation problem. Stochastic models are critical to study as they more accurately represent the real world than their deterministic counterparts. Although there have been extensive studies in solving routing problems under uncertainty, very few have considered UCARP, and none consider collaboration between vehicles to handle the negative effects of uncertainty. This article proposes a novel Solution Construction Procedure (SCP) that generates solutions to UCARP within a collaborative, multi-vehicle framework. It consists of two types of collaborative activities: one when a vehicle unexpectedly expends capacity (route failure), and the other during the refill process. Then, we propose a Genetic Programming Hyper-Heuristic (GPHH) algorithm to evolve the routing policy used within the collaborative framework. The experimental studies show that the new heuristic with vehicle collaboration and GP-evolved routing policy significantly outperforms the compared state-of-the-art algorithms on commonly studied test problems. This is shown to be especially true on instances with larger numbers of tasks and vehicles. This clearly shows the advantage of vehicle collaboration in handling the uncertain environment, and the effectiveness of the newly proposed algorithm

A space biased-sampling approach for the vehicle routing problem with stochastic demands

International audienceThe vehicle routing problem with stochastic demands consists of designing transportation routes of minimal expected cost to satisfy a set of customers with random demands of known probability distribution. We propose a metaheuristic that uses randomized heuristics for the traveling salesman problem, a tour partitioning procedure, and a set-partitioning formulation to sample the solution space and find solutions for the problem. Computational experiments show that our approach is competitive with state-of-the-art algorithms for the problem in terms of both accuracy and efficiency