The Split Delivery Vehicle Routing Problem with Time Windows and Customer Inconvenience Constraints

In classical routing problems, each customer is visited exactly once. By contrast, when allowing split deliveries, customers may be served through multiple visits. This potentially results in substantial savings in travel costs. Even if split deliveries are beneficial to the transport company, several visits may be undesirable on the customer side: at each visit the customer has to interrupt his primary activities and handle the goods receipt. The contribution of the present paper consists in a thorough analysis of the possibilities and limitations of split delivery distribution strategies. To this end, we investigate two different types of measures for limiting customer inconvenience (a maximum number of visits and the temporal synchronization of deliveries) and evaluate the impact of these measures on carrier efficiency by means of different objective functions (comprising variable routing costs, costs related to route durations, fixed fleet costs). We consider the vehicle routing problem with time windows in which split deliveries are allowed (SDVRPTW) and define the corresponding generalization that takes into account customer inconvenience constraints (SDVRPTW-IC). We design an extended branch-and-cut algorithm to solve the SDVRPTW-IC and report on experimental results showing the impact of customer inconvenience constraints. We finally draw useful insights for logistics managers on the basis of the experimental analysis carried out

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 aweighted 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 synchronized carefully in the planning. The contribution of the paper is twofold: First, we present an exact branch-And-price-And-cut algorithm for this class of routing problems with synchronization constraints. To our knowledge, this algorithm is the first such approach that considers explicitly the temporal interdependencies between active and passive vehicles. The algorithm is based on a nontrivial network representation that models the logical relationships between the different transport tasks necessary to fulfill a request as well as the synchronization of the movements of active and passive vehicles. Second, we contribute to the development of branch-And-price methods in general, in that we solve, for the first time, an ng-path relaxation of a pricing problem with linear vertex costs by means of a bidirectional labeling algorithm. Computational experiments show that the proposed algorithm delivers improved bounds and solutions for a number of APVRP benchmark instances. It is able to solve instances with up to 76 tasks, four active, and eight passive vehicles to optimality within two hours of CPU time