Nested branch-and-price-and-cut for vehicle routing problems with multiple resource interdependencies
Abstract This paper considers vehicle routing problems (VRPs) with multiple resource interdependencies and addresses the development and computational evaluation of an exact branch-and-price-and-cut algorithm for their solution. An interdependency between two resources means that the two resource consumptions influence one another in such a way that a tradeoff exists between them. This impacts the feasibility and/or the cost of a solution. The subproblem in branch-and-price-and-cut procedures for VRPs is very often a variant of the shortest-path problem with resource constraints (SPPRC). For the exact solution of many SPPRC variants, dynamic-programming based labeling algorithms are predomi…
Bidirectional labeling in column-generation algorithms for pickup-and-delivery problems
Abstract For the exact solution of many types of vehicle-routing problems, column-generation based algorithms have become predominant. The column-generation subproblems are then variants of the shortest-path problem with resource constraints which can be solved well with dynamic-programming labeling algorithms. For vehicle-routing problems with a pickup-and-delivery structure, the strongest known dominance between two labels requires the delivery triangle inequality (DTI) for reduced costs to hold. When the direction of labeling is altered from forward labeling to backward labeling, the DTI requirement becomes the pickup triangle inequality (PTI). DTI and PTI cannot be guaranteed at the sam…
The last-mile vehicle routing problem with delivery options
AbstractThe ongoing rise in e-commerce comes along with an increasing number of first-time delivery failures due to the absence of the customer at the delivery location. Failed deliveries result in rework which in turn has a large impact on the carriers’ delivery cost. In the classical vehicle routing problem (VRP) with time windows, each customer request has only one location and one time window describing where and when shipments need to be delivered. In contrast, we introduce and analyze the vehicle routing problem with delivery options (VRPDO), in which some requests can be shipped to alternative locations with possibly different time windows. Furthermore, customers may prefer some deli…
Branch-and-Price-and-Cut for the Active-Passive Vehicle-Routing Problem
This paper presents a branch-and-price-and-cut algorithm for the exact solution of the active-passive vehicle-routing problem (APVRP). The APVRP covers a range of logistics applications where pickup-and-delivery requests necessitate a joint operation of active vehicles (e.g., trucks) and passive vehicles (e.g., loading devices such as containers or swap bodies). The objective is to minimize a weighted sum of the total distance traveled, the total completion time of the routes, and the number of unserved requests. To this end, the problem supports a flexible coupling and decoupling of active and passive vehicles at customer locations. Accordingly, the operations of the vehicles have to be s…
Hybridizing large neighborhood search and exact methods for generalized vehicle routing problems with time windows
International audience; Delivery options are at the heart of the generalized vehicle routing problem with time windows (GVRPTW) allowing that customer requests are shipped to alternative delivery locations which can also have different time windows. Recently, the vehicle routing problem with delivery options was introduced into the scientific literature. It extends the GVRPTW by capacities of shared locations and by specifying service-level constraints defined by the customers' preferences for delivery options. The vehicle routing problem with delivery options also generalizes the vehicle routing problem with home roaming delivery locations and the vehicle routing problem with multiple time…
Asymmetry matters: Dynamic half-way points in bidirectional labeling for solving shortest path problems with resource constraints faster
Abstract With their paper “Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints” [Discrete Optimization 3, 2006, pp. 255–273] Righini and Salani introduced bounded bidirectional dynamic programming (DP) as an acceleration technique for solving variants of the shortest path problem with resource constraints (SPPRC). SPPRCs must be solved iteratively when vehicle routing and scheduling problems are tackled via Lagrangian relaxation or column-generation techniques. Righini and Salani and several subsequent works have shown that bounded bidirectional DP algorithms are often superior to their monodirectional counterparts, s…
Combined column-and-row-generation for the optimal communication spanning tree problem
Abstract This paper considers the exact solution of the optimal communication spanning tree problem (OCSTP), which can be described as follows: Given an undirected graph with transportation costs on every edge and communication requirements for all pairs of vertices, the OCSTP seeks for a spanning tree that minimizes the sum of the communication costs between all pairs of vertices, where the communication cost of a pair of vertices is defined as their communication requirement multiplied by the transportation cost of the unique tree path that connects the two vertices. Two types of compact formulations for OCSTP were presented in the literature. The first one is a four-index model based on …
A branch-price-and-cut algorithm for the capacitated multiple vehicle traveling purchaser problem with unitary demand
Abstract The multiple vehicle traveling purchaser problem (MVTPP) consists of simultaneously selecting suppliers and routing a fleet of homogeneous vehicles to purchase different products at the selected suppliers so that all product demands are fulfilled and traveling and purchasing costs are minimized. We consider variants of the MVTPP in which the capacity of the vehicles can become binding and the demand for each product is one unit. Corresponding solution algorithms from the literature are either branch-and-cut or branch-and-price algorithms, where in the latter case the route-generation subproblem is solved on an expanded graph by applying standard dynamic-programming techniques. Our …
Bidirectional labeling for solving vehicle routing and truck driver scheduling problems
Abstract This paper studies the vehicle routing and truck driver scheduling problem where routes and schedules must comply with hours of service regulations for truck drivers. It presents a backward labeling method for generating feasible schedules and shows how the labels generated with the backward method can be combined with labels generated by a forward labeling method. The bidirectional labeling is embedded into a branch-and-price-and-cut approach and evaluated for hours of service regulations in the United States and the European Union. Computational experiments show that the resulting bidirectional branch-and-price-and-cut approach is significantly faster than unidirectional counterp…