Lagrangian relaxation algorithm for the truck scheduling problem with products time window constraint in multi-door cross-dock

<p style='text-indent:20px;'>Cross-docking is a kind of process that products are unloaded in front of the inbound doors, consolidated based on the downstream demand, and then directly transferred to the outbound doors without a long storage process during the transportation. In this paper, a multi-door cross-dock truck scheduling problem is investigated in which the scheduling and sequencing assignment of trucks need to be considered, with the objectives of minimizing the inner transportation cost in the cross-dock and the total truck waiting cost. The major contribution of this paper is that a novel product-related time window constraint and the temporary storage area are firstly introduced to adapt to different physical conditions of goods considering real-world requirements. Then, a Lagrangian relaxation algorithm is proposed which aims to decompose the relaxed problem into several easy-to-be-solved sub-problems. Besides, a subgradient algorithm is used at each iteration to further deal with these sub-problems. Finally, theory analysis and simulation experiments of different problem scales are carried out during the comparison with a Greedy algorithm to evaluate the performance of the proposed algorithm. Results indicate that the Lagrangian relaxation algorithm is able to achieve more satisfactory near-optimal solutions within an acceptable time.</p>