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.
@cite_45 introduced the Dial-a-Ride Problem (DARP) with stochastic customer delays. The DARP is a generalization of the VRPTW that distinguishes between pickup and delivery locations and involves customer ride time constraints. Each customer is present at its pickup location with a stochastic delay. A customer is then skipped if it is absent when the vehicle visits the corresponding location, involving the cost of fulfilling the request by an alternative service (, a taxi). In a sense, stochastic delays imply that each request is revealed at some uncertain time during the planning horizon. That study is thus related to our problem, although in the SS-VRPTW-CR only a subset of the requests are actually revealed. Similarly, @cite_51 studied a probabilistic DARP where a priori routes are modified by removing absent customers at the beginning of the day, and proposed local search based heuristics.
@cite_45 @cite_51
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This paper considers a single-vehicle Dial-a-Ride Problem in which customers may experience stochastic delays at their pickup locations. If a customer is absent when the vehicle serves the pickup location, the request is fulfilled by an alternative service (e.g., a taxi) whose cost is added to the total cost of the tour. In this case, the vehicle skips the corresponding delivery location, which yields a reduction in the total tour cost. The aim of the problem is to determine an a priori Hamiltonian tour minimizing the expected cost of the solution. This problem is solved by means of an integer L-shaped algorithm. Computational experiments show that the algorithm yields optimal solutions on several instances within reasonable CPU times. It is also shown that the actual cost of an optimal solution obtained with this algorithm can be significantly smaller than that of an optimal solution obtained with a deterministic formulation. We consider the courier delivery problem (CDP), a variant of the vehicle routing problem with time windows (VRPTW) in which customers appear probabilistically and their service times are uncertain. We use scenario-based stochastic programming with recourse to model the uncertainty in customers and robust optimization for the uncertainty in service times. Our proposed model generates a master plan and daily schedules by maximizing the coverage of customers and the similarity of routes in each scenario, while minimizing the total time spent by the couriers and the total earliness and lateness penalty. To solve large-scale problem instances, we develop an insertion-based solution heuristic, called master and daily scheduler (MADS), and a tabu search improvement procedure. The computational results show that our heuristic improves the similarity of routes and the lateness penalty at the expense of increased total time spent when compared to a solution of independently scheduling each day. Our experimental results also show improvements over current industry practice on two real-world data sets. The problem of transporting patients or elderly people has been widely studied in literature and is usually modeled as a dial-a-ride problem (DARP). In this paper we analyze the corresponding problem arising in the daily operation of the Austrian Red Cross. This nongovernmental organization is the largest organization performing patient transportation in Austria. The aim is to design vehicle routes to serve partially dynamic transportation requests using a fixed vehicle fleet. Each request requires transportation from a patient's home location to a hospital (outbound request) or back home from the hospital (inbound request). Some of these requests are known in advance. Some requests are dynamic in the sense that they appear during the day without any prior information. Finally, some inbound requests are stochastic. More precisely, with a certain probability each outbound request causes a corresponding inbound request on the same day. Some stochastic information about these return transports is available from historical data. The purpose of this study is to investigate, whether using this information in designing the routes has a significant positive effect on the solution quality. The problem is modeled as a dynamic stochastic dial-a-ride problem with expected return transports. We propose four different modifications of metaheuristic solution approaches for this problem. In detail, we test dynamic versions of variable neighborhood search (VNS) and stochastic VNS (S-VNS) as well as modified versions of the multiple plan approach (MPA) and the multiple scenario approach (MSA). Tests are performed using 12 sets of test instances based on a real road network. Various demand scenarios are generated based on the available real data. Results show that using the stochastic information on return transports leads to average improvements of around 15 . Moreover, improvements of up to 41 can be achieved for some test instances. The Dial-a-Ride Problem (DARP) consists of designing vehicle routes and schedules for n users who specify pick-up and drop-off requests between origins and destinations. The aim is to plan a set of m minimum cost vehicle routes capable of accommodating as many users as possible, under a set of constraints. The most common example arises in door-to-door transportation for elderly or disabled people. The purpose of this article is to review the scientific literature on the DARP. The main features of the problem are described and classified and some modeling issues are discussed. A summary of the most important algorithms is provided.