Abstract: We study the Vehicle Routing Problem with Probabilistic Customers (VRP-PC), a two-stage optimization model, which is a fundamental building block within the broad family of stochastic routing problems. This problem is mainly motivated by logistics distribution networks in which customers receive frequent delivery services, and by the last mile problem faced by companies such as UPS and FedEx. In a first stage before customer service requests realize, a dispatcher determines a set of vehicle routes serving all potential customer locations. In a second stage occurring after observing all customer requests, vehicles execute planned routes skipping all locations of customers not requiring service. The objective is to minimize the expected vehicle travel cost assuming known customer realization probabilities. We propose a column generation framework to solve the VRP-PC to a given optimality tolerance. Specifically, we present two novel algorithms, one that under -approximates a solution's expected cost, and another that uses its exact expected cost. Each algorithm is equipped with a route pricing mechanism that iteratively improves the approximation precision of a route's reduced cost; this produces fast route insertions at the start of the algorithm and reaches termination conditions at the end of the execution. Compared to branch-and-cut algorithms for arc-based formulations, our framework can more readily incorporate sequence-dependent constraints, which are typically required in routing problems. We provide a priori and a posteriori performance guarantees for these algorithms, and demonstrate their effectiveness via a computational study on instances with realization probabilities ranging from 0.5 to 0.9.

Abstract: This study introduces the Territory Design for the Multi-Period Vehicle Routing Problem with Time Windows (TD-MPVRPTW) problem, motivated by a real-world application at a food company's distribution center. This problem deals with the design of contiguous and compact territories for delivery of orders from a depot to a set of customers, with time windows, over a multi-period planning horizon. Customers and their demands vary over time. The problem is modeled as a mixed-integer linear program (MILP) and solved by a proposed heuristic. The heuristic solutions are compared with the proposed MILP solutions on a set of small artificial instances and the food company's solutions on a set of real-world instances. Computational results show that the proposed algorithm can yield high-quality solutions within moderate running times. A methodology is proposed in which the territories computed by the proposed heuristic on the past demand of one month are used for the operational routing during the following month, in which the demand is known only one day in advance. An evaluation shows that the territories obtained with our methodology would have led to levels of service significantly better than the ones that were experienced by the company, using a significantly lower number of vehicles to execute the deliveries.

Abstract: Multi-Attribute Vehicle Routing Problems (MAVRP) are variants of Vehicle Routing Problems (VRP) in which, besides the original constraint on vehicle capacity present in Capacitated Vehicle Routing Problem (CVRP), other attributes that model diverse real-life system characteristics are present. Among the most common attributes studied in the literature are vehicle capacity and route duration constraints. The influence of these restrictions on the overall structure of the problem and the performance of local search algorithms used to solve it has yet to be well known. This paper aims to explain the impact of constraints present in different variants of VRP through the alterations of the structure of the underlying search space that they cause. We focus on Local Optima Network Analysis (LONA) for multiple Traveling Salesman Problem (m-TSP) and VRP with vehicle capacity (CVRP), route duration (DVRP), and both (DCVRP) constraints. We present results that indicate that measures obtained for a sample of local optima provide valuable information on the behavior of the landscape under modifications in the problem's constraints. Additionally, we use the LONA measures to explain the difficulty of VRP instances for solving by local search algorithms.