The family capacitated vehicle routing problem

Abstract

In this article, we address the family capacitated vehicle routing problem (F-CVRP), an NP-hard problem that generalizes both the FTSP and the capacitated vehicle routing problem. The F-CVRP has practical application in warehouse management in warehouses with scattered storage. We present several mixed integer linear programming formulations for this problem and establish a theoretical and empirical comparison. We also propose valid inequalities adapted from known routing problems from the literature. Some formulations are solved using a branch-and-cut algorithm, which is tested with a newly generated data set. The computational experiment allows us to identify the instances’ most challenging characteristics and the exact methods’ limitations. Finally, we develop an iterated local search (ILS) algorithm to efficiently obtain feasible solutions for the instances that could not be solved to proven optimality. The ILS algorithm is very efficient and can improve the upper bounds obtained by the exact methods within the set time limit.