Scheduling trucks in cross-docking systems: Robust meta-heuristics B. Vahdani a , M. Zandieh b, * a Department of Industrial and Mechanical Engineering, Qazvin Islamic Azad University, Qazvin, Iran b Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, GC, Tehran, Iran article info Article history: Received 7 February 2009 Received in revised form 21 June 2009 Accepted 22 June 2009 Available online 25 June 2009 Keywords: Logistics Scheduling Cross-docking Meta-heuristics Response surface methodology (RSM) Multi objective decision making (MODM) abstract Cross-docking is a logistics technique that minimizes the storage and order picking functions of a ware- house while still allowing it to serve its receiving and shipping functions. The idea is to transfer ship- ments directly from incoming to outgoing trailers without storage in between. In this paper we apply five meta-heuristic algorithms: genetic algorithm (GA), tabu search (TS), simulated annealing (SA), elec- tromagnetism-like algorithm (EMA) and variable neighbourhood search (VNS) to schedule the trucks in cross-dock systems such that minimize total operation time when a temporary storage buffer to hold items temporarily is located at the shipping dock. A design procedure is developed to specify and adjust significant parameters for GA, TS, SA, EMA and VNS. The proposed procedure is based on the response surface methodology (RSM). Two different types of objective functions are considered to develop multi- ple objective decision making model. For the purpose of comparing meta-heuristics, makespan and CPU time are considered as two response variables representing effectiveness and efficiency of the algorithms. Based on obtained results, VNS is recommended for scheduling trucks in cross-docking systems. Also, since for real size problems, it is not possible to reach optimum solution, a lower bound is presented to evaluate the resultant solutions. Ó 2009 Published by Elsevier Ltd. 1. Introduction Cross-docking is a warehouse management concept in which items delivered to a warehouse by delivery trucks are immediately sorted out and reorganized based on customer demands and are routed and loaded into shipping trucks for delivery to customers without actually being held in inventory in the warehouse. Because accuracy in material management is required in such operations, a cross-docking operation is heavily dependent on accurate flow of information. Generally, cross-docking facilities include four major functions of warehousing: receiving; storage; order picking; and shipping, the middle two are typically the most costly. Storage is expensive because of inventory holding costs, and order picking because it is labour intensive. It is estimated that cross-docking can save up to 70% of the cost of warehousing. Moreover, cross-docking is a logis- tics technique that minimizes the storage and order picking func- tions of a warehouse while still allowing it to serve its receiving and shipping functions. The idea is to transfer shipments directly from incoming to outgoing trailers without storage in between. Shipments typically spend less than 24 h in a cross-dock, some- times less than an hour. Also cross-docks are essentially trans- shipment facilities to which trucks arrive with goods that must be sorted, consolidated with other products, and loaded onto out- bound trucks. In a cross-docking model, the customer is known be- fore the product gets to the warehouse and there is no need to move it to storage. Clearly cross-docking places constraints on the design of the warehouse internally and with respect to its footprint. The cross-docking system in this research does not consider the operations inside the warehouse or distribution center such as scanning and sorting operations etc. Therefore, the arrival se- quence of the products at the shipping dock is the same as their unloading sequence at the receiving dock. Moreover, it is assumed that there is a temporary storage in front of the shipping dock. If a product arriving at the shipping dock is not intended for loading into the outbound truck currently at the dock, the product is stored in the temporary storage until the appropriate outbound truck comes into the shipping dock. The truck docking pattern employed requires that both inbound and outbound trucks must stay in docks until they finish their task once they come into docks. In general, there are a little works in the literature of scheduling transportation facilities in cross-dock systems. Lau, Sim, and Teo (2003) suggested a tabu search algorithm to minimize transporta- tion costs for vehicle routing in cross-docking system with speci- fied time windows and a finite number of vehicles. Young Hae Lee, Jung, and Lee (2006) proposed a model integrating cross-dock- ing with the pickup and delivery process in the supply chain. Also, a mathematical model was developed to determine an optimal 0360-8352/$ - see front matter Ó 2009 Published by Elsevier Ltd. doi:10.1016/j.cie.2009.06.006 * Corresponding author. Tel./fax: +98 21 29902352. E-mail address: M_zandieh@sbu.ac.ir (M. Zandieh). Computers & Industrial Engineering 58 (2010) 12–24 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie