A Tabu search heuristic for the vehicle routing problem with two‐dimensional loading constraints

Abstract This article addresses the well‐known Capacitated Vehicle Routing Problem (CVRP), in the special case where the demand of a customer consists of a certain number of two‐dimensional weighted items. The problem calls for the minimization of the cost of transportation needed for the delivery of the goods demanded by the customers, and carried out by a fleet of vehicles based at a central depot. In order to accommodate all items on the vehicles, a feasibility check of the two‐dimensional packing (2L) must be executed on each vehicle. The overall problem, denoted as 2L‐CVRP, is NP‐hard and particularly difficult to solve in practice. We propose a Tabu Search algorithm, in which the loading component of the problem is solved through heuristics, lower bounds, and a truncated branch‐and‐bound procedure. The effectiveness of the algorithm is demonstrated through extensive computational experiments. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008