Purpose The cross-docking strategy has a significant influence on supply chain and logistics efficiency. This paper aims to investigate the most suitable and efficient way to schedule the transfer of logistics activities and present a meta-heuristic method of the truck scheduling problem in cross-docking logistics. A truck scheduling problem with products time window is investigated with objectives of minimizing the total product transshipment time and earliness and tardiness cost of outbound trucks. Design/methodology/approach This research proposed a meta-heuristic method for the truck scheduling problem with products time window. To solve the problem, a lower bound of the problem is built through a novel two-stage Lagrangian relaxation problem and on account of the NP-hard nature of the truck scheduling problem, the novel red deer algorithm with the mechanism of the heuristic oscillating local search algorithm, as well as adaptive memory programming was proposed to overcome the inferior capability of the original red deer algorithm in the aspect of local search and run time. Findings Theory analysis and simulation experiments on an industrial case of a cross-docking center with a product’s time window are conducted in this paper. Satisfactory results show that the performance of the red deer algorithm is enhanced due to the mechanism of heuristic oscillating local search algorithm and adaptive memory programming and the proposed method efficiently solves the real-world size case of truck scheduling problems in cross-docking with product time window. Research limitations/implications The consideration of products time window has very realistic significance in different logistics applications such as cold-chain logistics and pharmaceutical supply chain. Furthermore, the novel adaptive memory red deer algorithm could be modified and applied to other complex optimization scheduling problems such as scheduling problems considering energy-efficiency or other logistics strategies. Originality/value For the first time in the truck scheduling problem with the cross-docking strategy, the product’s time window is considered. Furthermore, a mathematical model with objectives of minimizing the total product transshipment time and earliness and tardiness cost of outbound trucks is developed. To solve the proposed problem, a novel adaptive memory red deer algorithm with the mechanism of heuristic oscillating local search algorithm was proposed to overcome the inferior capability of genetic algorithm in the aspect of local search and run time.

<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>