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

A Vehicle Routing Problem with Multiple Service Agreements

We consider a logistics service provider which arranges transportation services to customers with different service agreements. The most prominent feature of this service agreement is the time period in which these customers send their orders and want to retrieve delivery information. After customers place their orders, they require information about the driver and an early indication of the arrival times. At the moment, this information needs to be provided. The order information of other customers with a different service agreement that needs to be serviced in the same period might still be unknown. Ultimately all customers have to be planned, constrained by the information provided to the customers in the earlier stage. In this paper, we investigate how the logistic service provider plans its routes and communicates the driver and arrival time information in the phase where not all customers are known (stage 1). Once all customer orders are known (stage 2), the final routes can be determined, which adhere to the already communicated driver and arrival time information from stage 1, minimizing total routing cost. For this problem, an exact algorithm is presented. This problem is solved using a novel tractable branch-and-bound method and re-optimization in stage 2. Detailed results are presented, showing the improvements of using re-optimization. We show that integrating the planning of the customers with the different service agreements leads to significant cost savings compared to treating the customers separately (as is currently done by most logistics service providers).</p

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

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

The Relationship between Vehicle Routing & Scheduling and Green Logistics - A Literature Survey

The basic Vehicle Routing and Scheduling Problem (VRSP) is described followed by an outline of solution approaches. Different variations of the basic VRSP are examined that involve the consideration of additional constraints or other changes in the structure of the appropriate model. An introduction is provided to Green Logistics issues that are relevant to vehicle routing and scheduling including discussion of the environmental objectives that should be considered. Particular consideration is given to VRSP models that relate to environmental issues including the timedependent VRSP, the transportation of hazardous materials and dynamic VRSP models. Finally some conclusions are drawn about further research needs in this area and the relation to road pricing

A survey on metaheuristics for stochastic combinatorial optimization

Metaheuristics are general algorithmic frameworks, often nature-inspired, designed to solve complex optimization problems, and they are a growing research area since a few decades. In recent years, metaheuristics are emerging as successful alternatives to more classical approaches also for solving optimization problems that include in their mathematical formulation uncertain, stochastic, and dynamic information. In this paper metaheuristics such as Ant Colony Optimization, Evolutionary Computation, Simulated Annealing, Tabu Search and others are introduced, and their applications to the class of Stochastic Combinatorial Optimization Problems (SCOPs) is thoroughly reviewed. Issues common to all metaheuristics, open problems, and possible directions of research are proposed and discussed. In this survey, the reader familiar to metaheuristics finds also pointers to classical algorithmic approaches to optimization under uncertainty, and useful informations to start working on this problem domain, while the reader new to metaheuristics should find a good tutorial in those metaheuristics that are currently being applied to optimization under uncertainty, and motivations for interest in this fiel