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_56 considered a variant of the SS-VRPTW-C, , the Courier Delivery Problem with Uncertainty. Potential customers have deterministic soft time windows but are present probabilistically, with uncertain service times. Vehicles are uncapacitated and share a common hard deadline for returning to the depot. The objective is to construct an a priori solution, to be used every day as a basis for adapting to daily customer requests. Unlike the SS-VRPTW-CR, the set of customers is revealed at the beginning of the operations.
@cite_56
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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. In the pickup and delivery problem with time windows (PDPTW), vehicles have to transport loads from origins to destinations respecting capacity and time constraints. In this paper, we present a two-phase method to solve the PDPTW. In the first phase, we apply a novel construction heuristics to generate an initial solution. In the second phase, a tabu search method is proposed to improve the solution. Another contribution of this paper is a strategy to generate good problem instances and benchmarking solutions for PDPTW, based on Solomon's benchmark test cases for VRPTW. Experimental results show that our approach yields very good solutions when compared with the benchmarking solutions. Vehicle Routing Problems have been extensively analyzed to reduce transportation costs. More particularly, the Vehicle Routing Problem with Time Windows (VRPTW) imposes the period of time of customer availability as a constraint, a common characteristic in real world situations. Using minimization of the total distance as the main objective to be fulfilled, this work implements an efficient algorithm which associates non-monotonic Simulated Annealing to Hill-Climbing and Random Restart. The algorithm is compared to the best results published in the literature for the 56 Solomon instances and it is shown how statistical methods can be used to boost the performance of the method. Vehicle routing problem with time windows (VRPTW) is a generalisation of the classical vehicle routing problem, where a group of customers with given capacity demand are required to be serviced, and the servicing of the customer demands has to be started within a restricted available time window at the customer locations. This class of routing problems can be used to solve many practical problems such as container truck routing, delivery service scheduling and many logistics system problems. In this paper, we present a route construction heuristic with an adaptive parallel scheme. The result from extensive computation experiments shows the proposed parallel route construction heuristic is efficient and effective for routes construction, which is particularly useful for generation of the initial solutions for many metaheuristic approaches with improved solution quality and convergence of the solution process.