2,329 research outputs found

    On the heterogeneous vehicle routing problem under demand uncertainty

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    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 diïŹ€erent 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

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

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    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

    Recourse policies in the vehicle routing problem with stochastic demands

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    Dans le domaine de la logistique, de nombreux problĂšmes pratiques peuvent ĂȘtre formulĂ©s comme le problĂšme de tournĂ©es de vĂ©hicules (PTV). Dans son image la plus large, le PTV vise Ă  concevoir un ensemble d’itinĂ©raires de collecte ou de livraison des marchandises Ă  travers un ensemble de clients avec des coĂ»ts minimaux. Dans le PTV dĂ©terministe, tous les paramĂštres du problĂšme sont supposĂ©s connus au prĂ©alable. Dans de nombreuses variantes de la vie rĂ©elle du PTV, cependant, ils impliquent diverses sources d’alĂ©atoire. Le PTV traite du caractĂšre alĂ©atoire inhĂ©rent aux demandes, prĂ©sence des clients, temps de parcours ou temps de service. Les PTV, dans lesquels un ou plusieurs paramĂštres sont stochastiques, sont appelĂ©s des problĂšmes stochastiques de tournĂ©es de vĂ©hicules (PSTV). Dans cette dissertation, nous Ă©tudions spĂ©cifiquement le problĂšme de tournĂ©es de vĂ©hicules avec les demandes stochastiques (PTVDS). Dans cette variante de PSTV, les demandes des clients ne sont connues qu’en arrivant Ă  l’emplacement du client et sont dĂ©finies par des distributions de probabilitĂ©. Dans ce contexte, le vĂ©hicule qui exĂ©cute une route planifiĂ©e peut ne pas rĂ©pondre Ă  un client, lorsque la demande observĂ©e dĂ©passe la capacitĂ© rĂ©siduelle du vĂ©hicule. Ces Ă©vĂ©nements sont appelĂ©s les Ă©checs de l’itinĂ©raire; dans ce cas, l’itinĂ©raire planifiĂ© devient non-rĂ©alisable. Il existe deux approches face aux Ă©checs de l’itinĂ©raire. Au client oĂč l’échec s’est produit, on peut rĂ©cupĂ©rer la realisabilite en exĂ©cutant un aller-retour vers le dĂ©pĂŽt, pour remplir la capacitĂ© du vĂ©hicule et complĂ©ter le service. En prĂ©vision des Ă©checs d’itinĂ©raire, on peut exĂ©cuter des retours prĂ©ventifs lorsque la capacitĂ© rĂ©siduelle est infĂ©rieure Ă  une valeur seuil. Toutes les dĂ©cisions supplĂ©mentaires, qui sont sous la forme de retours au dĂ©pĂŽt dans le contexte PTVDS, sont appelĂ©es des actions de recours. Pour modĂ©liser le PTVDS, une politique de recours, rĂ©gissant l’exĂ©cution des actions de recours, doit ĂȘtre conçue. L’objectif de cette dissertation est d’élaborer des politiques de recours rentables, dans lesquelles les conventions opĂ©rationnelles fixes peuvent rĂ©gir l’exĂ©cution des actions de recours. Nous fournissons un cadre gĂ©nĂ©ral pour classer les conventions opĂ©rationnelles fixes pour ĂȘtre utilisĂ©es dans le cadre PTVDS. Dans cette classification, les conventions opĂ©rationnelles fixes peuvent ĂȘtre regroupĂ©es dans (i) les politiques basĂ©es sur le volume, (ii) les politiques basĂ©es sur le risque et (iii) les politiques basĂ©es sur le distance. Les politiques hybrides, dans lesquelles plusieurs rĂšgles fixes sont incorporĂ©es, peuvent ĂȘtre envisagĂ©es. Dans la premiĂšre partie de cette thĂšse, nous proposons une politique fixe basĂ©e sur les rĂšgles, par laquelle l’exĂ©cution des retours prĂ©ventifs est rĂ©gie par les seuils prĂ©dĂ©finis. Nous proposons notamment trois politiques basĂ©es sur le volume qui tiennent compte de la capacitĂ© du vĂ©hicule, de la demande attendue du prochain client et de la demande attendue des clients non visitĂ©s. La mĂ©thode “Integer L-Shaped" est rĂ©amĂ©nagĂ©e pour rĂ©soudre le PTVDS selon la politique basĂ©e sur les rĂšgles. Dans la deuxiĂšme partie, nous proposons une politique de recours hybride, qui combine le risque d’échec et de distance Ă  parcourir en une seule rĂšgle de recours, rĂ©gissant l’exĂ©cution des recours. Nous proposons d’abord une mesure de risque pour contrĂŽler le risque d’échec au prochain client. Lorsque le risque d’échec n’est ni trop Ă©levĂ© ni trop bas, nous utilisons une mesure de distance, ce qui compare le coĂ»t de retour prĂ©ventif avec les coĂ»ts d’échecs futurs. Dans la derniĂšre partie de cette thĂšse, nous dĂ©veloppons une mĂ©thodologie de solution exacte pour rĂ©soudre le VRPSD dans le cadre d’une politique de restockage optimale. La politique de restockage optimale rĂ©sulte d’un ensemble de seuils spĂ©cifiques au client, de sorte que le coĂ»t de recours prĂ©vu soit rĂ©duit 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

    Large scale stochastic inventory routing problems with split delivery and service level constraints

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    A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC

    The stochastic vehicle routing problem : a literature review, part I : models

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    Building on the work of Gendreau et al. (Eur J Oper Res 88(1):3–12; 1996), we review the past 20 years of scientific literature on stochastic vehicle routing problems. The numerous variants of the problem that have been studied in the literature are described and categorized. Keywords: vehicle routing (VRP), stochastic programming, SVRPpublishedVersio

    Robust vehicle routing in disaster relief and ride-sharing: models and algorithms

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    In this dissertation, the variants of vehicle routing problems (VRPs) are specifically considered in two applications: disaster relief routing and ride-sharing. In disaster relief operations, VRPs are important, especially in the immediate response phase, as vehicles are an essential part of the supply chain for delivering critical supplies. This dissertation addresses the capacitated vehicle routing problem (CVRP) and the split delivery vehicle routing problem (SDVRP) with uncertain travel times and demands when planning vehicle routes for delivering critical supplies to the affected population in need after a disaster. A robust optimization approach is used for the CVRP and the SDVRP considering the five objective functions: minimization of the total number of vehicles deployed (minV), the total travel time/travel cost (minT), the summation of arrival times (minS), the summation of demand-weighted arrival times (minD), and the latest arrival time (minL), out of which we claim that minS, minD, and minL are critical for deliveries to be fast and fair for relief efforts, while minV and minT are common cost-based objective functions in the traditional VRP. In ride-sharing problem, the participants\u27 information is provided in a short notice, for which driver-rider matching and associated routes need to be decided quickly. The uncertain travel time is considered explicitly when matching and route decisions are made, and a robust optimization approach is proposed to handle it properly. To achieve computational tractability, a new two-stage heuristic method that combines the extended insertion algorithm and tabu search (TS) is proposed to solve the models for large-scale problems. In addition, a new hybrid algorithm named scoring tabu search with variable neighborhood (STSVN) is proposed to solve the models and compared with TS. The solutions of the CVRP and the SDVRP are compared for different examples using five different metrics in which the results show that the latter is not only capable of accommodating the demand greater than the vehicle capacity but also is quite effective to mitigate demand and travel time uncertainty, thereby outperforms CVRP in the disaster relief routing perspective. The results of ride-sharing problem show the influence of parameters and uncertain travel time on the solutions. The performance of TS and STSVN are compared in terms of solving the models for disaster relief routing and ride-sharing problems and the results show that STSVN outperforms TS in searching the near-optimal/optimal solutions within the same CPU time
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