Production, Manufacturing and Logistics Using a TSP heuristic for routing order pickers in warehouses Christophe Theys a, * , Olli Bräysy b , Wout Dullaert a,c , Birger Raa d a Institute of Transport and Maritime Management Antwerp (ITMMA), University of Antwerp, Keizerstraat 64, 2000 Antwerp, Belgium b Agora Innoroad Laboratory, University of Jyväskylä, Agora Center, P.O. Box 35, FI-40014, Finland c Antwerp Maritime Academy, Noordkasteel Oost 6, 2030 Antwerp, Belgium d Department of Management Information and Operations Management, Ghent University, Tweekerkenstraat 2, 9000 Gent, Belgium article info Article history: Received 20 August 2007 Accepted 24 January 2009 Available online 4 February 2009 Keywords: Routing Order picking Warehousing Logistics abstract In this paper, we deal with the sequencing and routing problem of order pickers in conventional multi- parallel-aisle warehouse systems. For this NP-hard Steiner travelling salesman problem (TSP), exact algo- rithms only exist for warehouses with at most three cross aisles, while for other warehouse types liter- ature provides a selection of dedicated construction heuristics. We evaluate to what extent reformulating and solving the problem as a classical TSP leads to performance improvements compared to existing ded- icated heuristics. We report average savings in route distance of up to 47% when using the LKH (Lin–Ker- nighan–Helsgaun) TSP heuristic. Additionally, we examine if combining problem-specific solution concepts from dedicated heuristics with high-quality local search features could be useful. Lastly, we ver- ify whether the sophistication of ‘state-of-the-art’ local search heuristics is necessary for routing order pickers in warehouses, or whether a subset of features suffices to generate high-quality solutions. Ó 2009 Elsevier B.V. All rights reserved. 1. Introduction In most modern warehouses, order picking is one of the main activities to be performed. The process typically involves the col- lection of stock keeping units which are demanded by customers, from a number of locations in the warehouse. Order picking ac- counts for no less than 55% (Bartholdi and Hackman, 2006) to 65% (Coyle et al., 1996) of the total operational warehouse costs. Furthermore, research has shown that order picking represents up to 60% of a warehouse’s total job package (Drury, 1988) of which more than 55% is related to travelling (Bartholdi and Hack- man, 2006). As such, warehouse design (including decisions on where the stock keeping units (SKUs) are to be located within the warehouse) and efficient policies for picking (allocation of items to pickers) and routing (determination of the route of a sin- gle picker) within warehouses hold a large potential for cost sav- ings. Previous work has shown that picking and storage strategies are closely interrelated, implying that decisions on the storage policy have a major influence on order picking perfor- mance (see e.g. Petersen, 1999; Petersen and Aase, 2004). Although we will discuss the impact of two relatively straightforward stor- age policies on order picking performance, this paper mainly fo- cuses on the actual order picking process. For an extensive overview of storage policies, we refer to De Koster et al. (2007). For a given storage and picking policy, this is when all SKUs have been assigned to storage locations and all items to be picked are already allocated to one or more pickers, one still needs to cal- culate the order picker’s route through the warehouse. So far, pro- cedures for this particular routing problem have been analyzed for four types of warehouse systems (see Gu et al., 2007). The most common type of order picking warehouse system, the conventional multi-parallel-aisle system (multiple-block warehouse), is the sub- ject of this research. Other variants are the automated storage and retrieval systems (AS/RS), both the man-on-board AS/RS and the unit-load AS/RS, and the carousel systems. The heuristics devel- oped for the operational process of routing order pickers in mul- ti-block warehouses are fairly simple construction heuristics which construct a feasible solution, without attempting any improvement by means of local search or metaheuristic search. Based on the impressive results obtained by (meta)heuristic search for reducing distance in the classical travelling salesman problem (TSP) and other traditional routing problems such as the vehicle routing problem (VRP) and the vehicle routing problem with time windows (VRPTW), further research on routing order pickers seems appropriate (for extensive literature reviews on metaheuris- tic search for the VRP(TW), see e.g. Bräysy and Gendreau, 2005a,b; Golden et al., 2008). In this respect, Makris and Giakoumakis (2003) propose to use a TSP-based k-interchange method for the problem of routing order pickers in single-block warehouses. Their procedure is compared to the well-known S-shape heuristic (see Section 2) and outper- formed the latter in seven out of eleven examined cases. Renaud 0377-2217/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2009.01.036 * Corresponding author. Tel.: +32 3 275 51 55; fax: +32 3 275 51 50. E-mail addresses: Christophe.Theys@ua.ac.be (C. Theys), Olli.Braysy@jyu.fi (O. Bräysy), Wout.Dullaert@ua.ac.be (W. Dullaert), Birger.Raa@ugent.be (B. Raa). European Journal of Operational Research 200 (2010) 755–763 Contents lists available at ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor