Vehicle routing with split deliveries
Discrete Applied Mathematics
The vehicle routing problem
Solving a Practical Pickup and Delivery Problem
Transportation Science
Complexity and Reducibility of the Skip Delivery Problem
Transportation Science
Robust Branch-and-Cut-and-Price for the Capacitated Vehicle Routing Problem
Mathematical Programming: Series A and B
A Branch-and-Cut Algorithm for the Multiple Depot Vehicle Scheduling Problem
Operations Research
Dual-Optimal Inequalities for Stabilized Column Generation
Operations Research
Worst-Case Analysis for Split Delivery Vehicle Routing Problems
Transportation Science
Bi-dynamic constraint aggregation and subproblem reduction
Computers and Operations Research
Long-Haul Vehicle Routing and Scheduling with Working Hour Rules
Transportation Science
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We present an optimization algorithm developed for a provider of software-planning tools for distribution logistics companies. The algorithm computes a daily plan for a heterogeneous fleet of vehicles that depart from different depots and must visit a set of customers for delivery operations. In this rich vehicle-routing problem (VRP), we consider multiple capacities; time windows associated with depots and customers; incompatibility constraints between goods, depots, vehicles, and customers; maximum route length and duration; upper limits on the number of consecutive driving hours and compulsory drivers' rest periods; the possibility of skipping some customers and using express courier services instead of the given fleet to fulfill some orders; the option of splitting up the orders; and the possibility of open routes that do not terminate at depots. Moreover, the cost of each vehicle route is computed through a system of fees depending on the locations visited by the vehicle, the distance traveled, the vehicle load, and the number of stops along the route. We developed a column generation algorithm where the pricing problem is a particular resource-constrained elementary shortest-path problem, solved through a bounded bidirectional dynamic programming algorithm. We describe how to encode the cost function and the complicating constraints by an appropriate use of resources, and we present computational results on real instances obtained from the software company.