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Multiple-product & Various Truck Capacities Cross-docking Problem Introduction
Customer demands are getting more complicated and even harder to be satisfied nowadays. It is highly needed for the company to have such flexibility, agility and reliability in terms of answering the demand requests from their customers. But their limitations in improving customer satisfaction might be a big problem for them and the operation of single company can have a bad impact on those of the other companies in the supply chain, meaning that if one company fails to fulfill the demands required, it will affect the related companies and obviously will put them in jeopardy in terms of customers trust and the cost they would have to spend. Therefore, improving supply chain management is really attractive for those companies looking to efficiently improve their customer satisfaction. Apte and Viswanathan (2000) stated that distribution process is responsible for 30% of an item price and this is the reason why there are a lot of companies trying their very best to develop new distribution strategies in order to manage their product flow in efficient manner. Cross docking is definitely one of those strategies people believe to be an efficient strategy to minimize inventory and to reduce cycle times. Apte and Viswanathan (2000) also defined cross docking as the continuous process to the final destination through the cross-dock storing products and materials in the distribution center. When cross-docking is implemented in the supply chain, products in multiple locations are collected in the cross-dock before eventually transporting them to their final destination. After consolidation according to product destination in the cross-dock is performed, products are then moved from the cross-dock to their respective destinations. There are a lot of studies discussing about cross docking nowadays and commonly they are divided into two general categories. The first category is about dock-door assignment and problems and the second one elaborates more about distribution planning problem of a cross docking network (Musa et. al, 2010). Some of the studies related to cross-docking can be seen below: Year| Author(s)| Problem Statement|

1992| Tsui & Chang| Developing general model of the dock-doors assignment employing Branch-and-Bound (B&B) algorithm| 1999| Donaldson et. al| Schedule-driven transportation planning in the cross-docking network| 1999| Ratliff, Vate & Zhang| Performing a study related to the automobile delivery network to generate a distribution plan by determining the ideal number andlocation of cross-docks together| 2001| Bartholdi, Gue, & Kang| Staging of products in a cross-dock to avoid floor congestion and increase throughput.| 2006| Chen et. al| Performing a study related to distribution planning for the cross-docking network taking into consideration delivery and pick-up time windows, warehouse capacities and inventory-handling costs. Simulated annealing and Tabu search heuristics were employed as solution methods because of the complexity of their problem| 2010| Musa et. al| Employing ant-colony algorithm in order to solve the transportation problem of cross docking network. These researchers offered a very interesting approach with the possibility of performing direct delivery from the suppliers (origin nodes) to customers (destination nodes) |

Developing cross-docking studies related to transportation problem is very challenging and important for the companies. Yet there are only few studies discussing about that particular matter. Musa et. al and Chen et al proposed a development of cross docking and they have successfully developed the transportation network. Chen et. al proposed a study with the objective of minimizing transportation cost and fixed cost of vehicles and time windows were considered as the constraint in their study. Tabu search was employed as a solution and 2.52%...
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