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Cross-docking is the main operation of unloading products from incoming trucks, regrouping products in relation to their destination, and loading directly onto shipping trucks, reducing warehousing, picking, transportation costs, and delivery times. This is the intended logistics technology. In this paper, we present a new bi-objective mixed-integer mathematical model for truck scheduling problems in cross-docking systems. The goal of the proposed mixed-integer mathematical model is to minimize the total operation time (makespan) and cost of moving cargo within the terminal. The performance of the proposed model is compared with that of the available model to solve small instances. The results showed that in solving small size of problem, the proposed model in this study is more efficient and we found better solutions. An evolutionary algorithm called the nondominated sorting genetic algorithm (NSGA-II) has been proposed to solve larger instances due to computational complexity. To evaluate the proposed algorithm, a comparative analysis of benchmark instances was performed and the efficiency of the above algorithm was compared to the nondominated ranked algorithm (NRGA) based on the index designed in the literature. The statistical hypothesis testing (t-test) is used for determining the best algorithm based on the average runtime and average number of Pareto solutions. Using the Taguchi method, the proposed algorithms are tuned. Considering a temporary storage space and the multiple receiving and shipping docks is the main contribution of the paper. Finally, for evaluating algorithms, multicriteria decision-making (MCDM) technique and statistical method are used. The results show the suitable performance of presented model. [ABSTRACT FROM AUTHOR]