Variable Neighborhood Search for Order Batching in a Warehouse 1 Maria Albareda-Sambola Department of Statistics and Operations Research, Technical University of Catalonia, Spain Antonio Alonso-Ayuso (corresponding author) Department of Statistics and Operations Research, University Rey Juan Carlos, Spain e-mail: antonio.alonso@urjc.es Elisenda Molina Department of Statistics, University Carlos III de Madrid, Spain Clara Sim´ on de Blas Department of Statistics and Operations Research, University Rey Juan Carlos, Spain Abstract In this paper we address the problem of batching orders in a warehouse, with the objective of minimizing the total travel time. Order batching is an NP-hard optimization problem that is very difficult to solve exactly in practice. Thus, most implemented solutions are based on elementary heuristic methods that perform a relatively limited exploration of the solution space. As an alternative, we propose a heuristic based on variable neighborhood search, where the emphasis is placed on performing an intensive exploration of the most promising regions of the solution space. Simulations are conducted to study the performance of the method with different warehouse configurations, and an exhaustive comparative analysis, which considers all the best known heuristics, is carried out. The results obtained show that the proposed heuristic is competitive and that it provides a suitable method which can be used in practice. Additionally, since the performance of the algorithms depends heavily on factors such as storage policy, routing strategies, or the structure of the orders, we have developed an ANOVA study in order to consider the effect of all the above factors on the different methods tested. Keywords: Warehousing, Order Batching, Metaheuristics, VNS. 1 Introduction In recent years, excess global capacity in most sectors of industry has created an intense com- petition. As Ghiani et al. [9] and Shamlaty [27] point out, the growth of e-commerce and the availability of a wide range of alternatives for most products has given rise to a very demanding type of customer, who expects to be served much faster than in the past. So, logistic activities 1 Partially supported by the grants MTM2006-14961-C05-01/05 from MCyT, Spain, and CCG06-UC3M/ESP- 0767 from CAM-UC3M, Madrid. 1