## 2 Literature Review
### Classical Cross-Docking Terminals  
Optimizing the cross-docking operations was widely addressed in the literature [8]. Several literature reviews and classifications were conducted concerning cross-docking optimization problems. The reader can refer to [8; 9; 17] for detailed classifications and reviews. Many papers addressed the cross-dock scheduling with single receiving and shipping dock with different approaches. For instance, [PERSON] and [PERSON] [18] formulated the problem mathematically as a Mixed-Integer Programming model (MIP) to minimize the makespan. The problem was then solved using a heuristic. Later, many authors suggested different approaches to solve the single door cross-dock truck scheduling problem using Genetic Algorithm [19], Hybrid Particle Swarm Optimization [20] and other various meta-heuristics [21; 22]. Other researches addressed the problem considering different uncertainties in various situations (taking into account the breakdown of the trucks [23], the availability of cross-dock resources such as handling systems and dock doors [24], unknown trucks' arrival time [25], etc.).  
In multiple-door cross-dock scheduling problem, which consists on assigning trucks to the inbound and outbound docks on a time horizon, various mathematical models were developed [8; 26]. In a recent study, [PERSON] et al. [27] proposed eight mathematical formulations for the cross-docking assignment problem in addition of three existing models in the literature. Then, a comparative analysis was performed on the proposed models on benchmark instances from the literature. For solving approaches, many meta-heuristics were suggested: Population based meta-heuristics (Differential Evolution [28; 29], Diploid Differential Evolution [30], Genetic algorithm [25], Particle Swarm Optimization [31], etc.) and single solution based meta-heuristics (Tabu search [32], Variable Neighborhood Search [33], Simulated Annealing [33; 34], etc.).  
In the multi-objective context, [PERSON] et al. [35] proposed a formulation of the inbound truck scheduling as a bi-objective and also as bi-level mixed integer programming model to minimize the total service time and the delayed completion which are conflicting objectives. Then, the two formulations were compared. A genetic algorithm and k-th best algorithm were proposed because of the complexity of the problem. Authors in [23] proposed a bi-objective mathematical formulation for cross-dock truck scheduling to minimize the total tardiness and weighted completion time while considering trucks' breakdown. The problem was then solved using three multi-objective meta-heuristics: Non-dominated Sorting Genetic Algorithm, Multi-Objective Simulated Annealing and Multi-objective Differential Evolution. [PERSON] et al. [36] developed a mathematical model in which the objective is to minimize the makespan, transportation cost and the number of truck trips. They proposed two population based meta-heuristics: Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Multi-Objective Particle Swarm Optimization (MOPSO). The results show that the NSGA-II outperforms MOPSO. In [22], authors addressed the multi-criteria cross-dock scheduling through a unified objective function minimizing both earliness and tardiness of trucks. The authors proposed three population based meta-heuristic: Genetic Algorithm, Particle Swarm Optimization and Differential Evolution. The results showed that Differential Evolution is the most robust algorithm since it is less sensitive to the size of the problem. Other studies considered uncertainties with multi-objective optimization and proposed bi-objective bi-level approach to solve the cross-dock truck scheduling with unknown truck arrival time [37].