# Hybrid Algorithms for Inbound and Outbound Truck Scheduling in Cross-Docking Systems
## 1 Introduction  
Due to the dramatic evolution of technology, a modern warehouse is widely designed to be an intelligent distribution center (DC). The difference between a traditional warehouse and an intelligent DC is that an intelligent DC can receive, sort, process, and ship packages or products in real-time to achieve the on-time delivery of orders. For handling these massive orders, the inputs and outputs of the DC must be precisely evaluated with an intelligent mechanism. Moreover, capacity and inventory problems also have a huge influence on the performance of a DC. Therefore, a cross-docking system is designed to provide great facility efficiency by reducing the inventory and product process time. According to the 2011 report of Saddle Creek Corporation, a world-famous American third-party logistics company, there are 68.5% enterprises employing cross-docking systems in their logistic facilities, which improve their service level by 19.4%, reduce their transportation cost by 14.3%, and provide 13.1% benefits for product integration. The contribution is that cross-docking systems address the product delivery within only 24 h based on a better schedule to reduce the product storage cost. Otherwise, the purpose of a cross-docking system is to integrate the products from different sources with different sizes but the same destination in order to make the transportation activities be within the economic scale and reduce the operational cost. Due to the fact that the facility can handle a huge number of products in a short time, it can also eliminate the wasted space of trucks for every transportation mission. In a cross-docking system, the products will be sorted in the operational area and will then be moved directly from the receiving dock to the shipping dock without any storage activities besides storing products temporarily. However, in a DC with a cross-docking system, the number of inbound and outbound docks is fixed. In other words, there are only few limited parking spaces for the trucks to load and unloadproducts. For this reason, the arrival time, operation time, and departure time of trucks must be scheduled well to enhance system efficiency. Generally, cross-docking planning issues can be classified into three time periods: short-term, medium-term, and long-term. [PERSON] et al. [1] propose the classification of short-term planning with five kinds of problems, including scheduling problems, transshipment problems, dock door assignment problems, vehicle routing problems, and product allocation problems.  
This study discusses the problem of truck scheduling in short-term planning. The main consideration is that, in the cross-dock system, the truck enters the inbound dock for unloading, and the goods are rearranged and sent to the outbound dock for loading. How to make the trucks enter the dock to unload and load the goods in the shortest time is the question of this research. At the same time, the assumptions of the problem are set to consider the operation mode of a single terminal and multiple trucks, but the details of the upstream and downstream manufacturers of the goods are not considered. The location, internal operation design, and vehicle routing of goods outside the cross-dock area are all outside the scope of this study.  
This study is further organized as follows. In Section 2, a summary of a literature review related to cross-docking systems is presented. The problem descriptions and the design concepts of the proposed approaches are introduced in Section 3. In Section 4, some computational experiments are designed and conducted to test the performance of the proposed approaches. Finally, the conclusions and future works of this study are in Section 5.