Heuristic solutions for transshipment problems in a multiple door cross docking warehouse Gülgün Alpan ⇑ , Anne-Laure Ladier, Rim Larbi, Bernard Penz Laboratoire G-SCOP, Grenoble INP-UJF-CNRS, 46 ave. Félix Viallet, Grenoble, France article info Article history: Available online 19 September 2010 Keywords: Cross docking Multiple docks Scheduling Heuristics Transshipment abstract Cross docking is a practice in logistics with the main operations of unloading products from an incoming truck, regrouping them with respect to their destinations and loading them directly into an outbound truck with minimum storage in between these operations. In this article, we study the transshipment scheduling problem in a multiple inbound and outbound dock configuration. The operations manager has several decisions to make: he can decide to transship products directly from inbound to an outbound truck, if an outbound truck is available; he can temporarily store certain products and have them loaded later on; or he can replace an outbound truck to facilitate direct loading. The objective is to find the best schedule of transshipment operations to minimize the sum of inventory holding and truck replacement costs. In this article, we present several heuristics to attain this objective. Numerical experiments are presented and the results are compared with the optimal solution to evaluate the performance of the heuristics. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction Cross docking is a lean warehousing strategy with numerous advantages such as no or very few inventory levels, low transpor- tation costs due to product consolidation, increase in product flow speeds and so on. Materials arriving to a cross docking warehouse from different destinations are unloaded from the inbound trailers, sorted according to their destinations, repacked with other products if necessary and reloaded into the outbound trailers. All operations take place within <24 h in general. Within the context of supply chain management, several research directions are observed related to the cross docking strat- egy. We can group them based on the type of decisions considered. Some of the earlier studies are considered as strategical decision making while others enter in the category of operational decision making. For instance decisions on cross dock network design (see Chen, Guo, Lim, & Rodrigues, 2006; Donaldson, Jonhson, Ratliff, & Zhang, 1998; Ratliff, Vate, & Zhang, 1998) or the layout of cross docking platforms (see Bartholdi & Gue, 2002, 2004; Gue, 1999) are examples of strategical decisions to be taken related to cross docking. Whereas, the assignment of inbound and outbound trucks on the docks (see Tsui & Chang, 1990, 1992; Bartholdi & Gue, 2001) or the scheduling of transshipment operations inside the cross docking platforms (see Baptiste, Penz, & Larbi, 2007; Baptiste & Maknoon, 2007; Larbi, Alpan, Baptiste, & Penz, 2007; Sadykov, 2009; Yu & Egbelu, 2008) are the examples of operational deci- sions. The study presented here is a part of the operational decision making and is particularly related to the scheduling of operations in a cross docking warehouse. The studies on the operational level are quite recent and most of the existing work is limited to the scheduling of operations for a restricted class of warehouses, such as the single input and output platforms (Baptiste et al., 2007; Baptiste & Maknoon, 2007; Larbi et al., 2007; Sadykov, 2009; Yu & Egbelu, 2008). Even though these studies give interesting insights on the solution structure for such problems, no practical application is possible since the cross dock under study is a hypothetical one with a mono input and output platform. Some recent studies remove this restrictive assumption. In Song and Chen (2007), the transshipment scheduling problem is extended to a warehouse with a single inbound dock while the outbound side is allowed to be multi dock. In a further study the authors removed the restriction on the inbound side (Chen & Song, 2009). In this general case, finding optimal solution is proved to be NP hard and near optimal solutions are presented. In both cases, the authors seek to optimize the makespan. Another study on the multi dock environment is presented in Alpan, Bauchau, Larbi, and Penz (2008). Unlike (Chen & Song, 2009), where the objective is to minimize some time related performance measures, in Alpan et al. (2008) a dynamic program based model is presented to find the schedule of transshipment 0360-8352/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2010.09.010 ⇑ Corresponding author. Tel.: +33 476574333. E-mail addresses: gulgun.alpan@grenoble-inp.fr (G. Alpan), anne-laure.ladier@ gi-etu.grenoble-inp.fr (A.-L. Ladier), rim.larbi@grenoble-inp.fr (R. Larbi), Bernard. Penz@grenoble-inp.fr (B. Penz). Computers & Industrial Engineering 61 (2011) 402–408 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie