sajjad rahmanzadeh - School of Industrial Engineering, Iran university of Science and Technology, Tehran, Iran
amin shahmardan - Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
Mir Saman Pishvaee - School of Industrial Engineering, Iran university of Science and Technology, Tehran, Iran
amin jabarzadeh - School of Industrial Engineering, Iran university of Science and Technology, Tehran, Iran

Nowadays, cross docking plays an important role in the supply chain networks especially in transportation systems. According to the cross dock system advantages such as reducing transportation costs, lead times, and inventories, scheduling in a cross-dock center would be more complicated by increasing the number of suppliers, customers and product types. Considering the cross dock limited capacities (equipment, storage space, work force, and etc.), sometimes it is not possible to deliver the supplier s products tocustomers in the right times. Thus, suppliers pay more tardiness penalties for scheduling problems in the cross dock centers. The current paper aims to propose an integer programming mathematical model that enables the suppliers to choose appropriate transportation paths according to amount of products delivered and moreover considering cross docks scheduling time constraints. In fact, cross dock centers present the list of outbound trucks departure times and suppliers reserve certain capacity based on their tardiness, transportation and inventory holding costs. Moreover, in this paper, a Lightening search algorithm (LSA) is developed to solve the proposed model. Additionally, to develop the solving procedure, a heuristic algorithm is proposed and compared with the LSA.

Cross dock, Scheduling, Heuristic, Lightening search algorithm, network;