Unlike its deterministic counterpart, static and stochastic vehicle routing problems (SS-VRP) aim at modeling and solving real-life operational problems by considering uncertainty on data. We consider the SS-VRPTW-CR introduced in Saint- (2017). Like the SS-VRP introduced by Bertsimas (1992), we search for optimal first stage routes for a fleet of vehicles to handle a set of stochastic customer demands, i.e., demands are uncertain and we only know their probabilities. In addition to capacity constraints, customer demands are also constrained by time windows. Unlike all SS-VRP variants, the SS-VRPTW-CR does not make any assumption on the time at which a stochastic demand is revealed, i.e., the reveal time is stochastic as well. To handle this new problem, we introduce waiting locations: Each vehicle is assigned a sequence of waiting locations from which it may serve some associated demands, and the objective is to minimize the expected number of demands that cannot be satisfied in time. In this paper, we propose two new recourse strategies for the SS-VRPTW-CR, together with their closed-form expressions for efficiently computing their expectations: The first one allows us to take vehicle capacities into account; The second one allows us to optimize routes by avoiding some useless trips. We propose two algorithms for searching for routes with optimal expected costs: The first one is an extended branch-and-cut algorithm, based on a stochastic integer formulation, and the second one is a local search based heuristic method. We also introduce a new public benchmark for the SS-VRPTW-CR, based on real-world data coming from the city of Lyon. We evaluate our two algorithms on this benchmark and empirically demonstrate the expected superiority of the SS-VRPTW-CR anticipative actions over a basic "wait-and-serve" policy.
   The purpose of this paper is to develop structural classification of Stochastic Vehicle Routing Problem (SVRP) by different domains and attributes. This research used a systematic review and meta-analysis on SVRP literatures. This includes browsing relevant researches and publications, screening related articles, identifying domains, attributes and categorising the articles based on the identified domains and attributes. The findings of the study show clear differences on the number of studies under each domain and attribute. Most studied attributes are stochastic customer demand, capacitated vehicle, synthesis data and objective function with cost minimization. Whereas the least studied are maximisation objective function, stochastic service time, and an applied model using stochastic with recurs. The research helps to summarise and map a comprehensive survey on SVRP literatures so that various contributions in the field are organised in a manner that provide a clear view for the readers and identify future research directions. This paper is the first of its kind in the field of SVRP that develop a classification scheme for articles published since 1993 to enhances the development of this newly emerging discipline.  Abstract The purpose of this review article is to provide a summary of the scientific literature on stochastic vehicle routing problems. The main problems are described within a broad classification scheme and the most important contributions are summarized in table form. This article introduces a new exact algorithm for the capacitated vehicle routing problem with stochastic demands (CVRPSD). The CVRPSD can be formulated as a set partitioning problem and it is shown that the associated column generation subproblem can be solved using a dynamic programming scheme. Computational experiments show promising results. We consider stochastic vehicle routing problems on a network with random travel and service times. A fleet of one or more vehicles is available to be routed through the network to service each node. Two versions of the model are developed based on alternative objective functions. We provide bounds on optimal objective function values and conditions under which reductions to simpler models can be made. Our solution method embeds a branch-and-cut scheme within a Monte Carlo sampling-based procedure. This paper studies a version of stochastic vehicle routing problems, in which travel and service times are stochastic, and a time window constraint is associated with each customer. This problem is originally formulated as a chance constrained programming model and a stochastic programming model with recourse in terms of different optimization criteria. To efficiently solve these two models, a heuristic based on tabu search, which takes into account the stochastic nature of this problem, is then proposed. Finally, some testing instances with different properties are established to investigate the algorithmic performance, and the computational results are then reported. The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps. We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0 of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time. Abstract This paper proposes a state-of-the-art branch-cut-and-price algorithm for the vehicle routing problem with stochastic demands (VRPSD). We adapt the model of Christiansen and Lysgaard [6] and formulate the VRPSD as a set partitioning model with additional constraints. Feasible routes are generated using a dynamic programming algorithm executed over a state-space graph. Our method combines 2-cycle elimination with ng -routes. In addition, our pricing problem is significantly accelerated by the introduction of a new aggregate dominance rule. To speed up the generation of negative reduced cost columns, we use a tabu search heuristic and a bidirectional labeling algorithm. We also add capacity and subset-row inequalities dynamically in order to strengthen the linear relaxation of the master problem. As extensive computational tests illustrate, our algorithm is very competitive with the one of [6] . We solve 20 additional instances from the 40-instance set considered by these authors and we considerably improve the computing times for instances already closed. We also solve 17 new instances from the literature. This paper considers vehicle routing problems (VRPs) with stochastic service and travel times, in which vehicles incur a penalty proportional to the duration of their route in excess of a preset constant. Three mathematical programming models are presented: a chance constrained model, a three-index simple recourse model and a two-index recourse model. A general branch and cut algorithm for the three models is described. Computational results indicate that moderate size problems can be solved to optimality. Vehicle routing problems, among the most studied in combinatorial optimization, arise in many practical contexts (freight distribution and collection, transportation, garbage collection, newspaper delivery, etc.). Operations researchers have made significant developments in the algorithms for their solution, and Vehicle Routing: Problems, Methods, and Applications, Second Edition reflects these advances. The text of the new edition is either completely new or significantly revised and provides extensive and complete state-of-the-art coverage of vehicle routing by those who have done most of the innovative research in the area; it emphasizes methodology related to specific classes of vehicle routing problems and, since vehicle routing is used as a benchmark for all new solution techniques, contains a complete overview of current solutions to combinatorial optimization problems. It also includes several chapters on important and emerging applications, such as disaster relief and green vehicle routing. Audience: This book is intended for both researchers and graduate level students in operations research and applied mathematics. Practitioners will find this book particularly useful. Readers need a basic knowledge of the main methods for the solution of combinatorial optimization problems. An increasing number of companies focus on customer satisfaction to increase the lifetime value of each customer. In vehicle routing, customer satisfaction is often a result of consistent service. Customers appreciate service at regular times of the day provided by the same driver each time. Additionally, drivers become more familiar with their tasks if they visit the same customers and service regions repeatedly. In this article, we survey literature that addresses service consistency in vehicle routing. We present early solution approaches, starting from the 1970s, that focus on reducing the operational complexity resulting from planning and executing new routes each day. One side benefit of these approaches is service consistency; therefore, many recent solution approaches devised for improving customer satisfaction are based on previous achievements. We classify the literature according to three consistency features: arrival time consistency, person-oriented consistency, and delivery consistency. For each feature, we survey different modeling concepts and measurements, demonstrate solution approaches, and examine the increase in cost of improving service consistency. We close the article by presenting challenging ideas for future research. © 2014 The Authors Networks Published by Wiley Periodicals, Inc. NETWORKS, Vol. 643, 192-213 2014 A number of technological advances have led to a renewed interest in dynamic vehicle routing problems. This survey classifies routing problems from the perspective of information quality and evolution. After presenting a general description of dynamic routing, we introduce the notion of degree of dynamism, and present a comprehensive review of applications and solution methods for dynamic vehicle routing problems.  In recent years new insights and algorithms have been obtained for the classical, deterministic vehicle routing problem as well as for natural stochastic and dynamic variations of it. These new developments are based on theoretical analysis, combine probabilistic and combinatorial modeling, and lead to new algorithms that produce near-optimal solutions, and a deeper understanding of uncertainty issues in vehicle routing. In this paper, we survey these new developments with an emphasis on the insights gained and on the algorithms proposed.