## 2 Literature Review
### Physical Internet Cross-Docking Hubs  
PI Cross-Docking Hubs are a cornerstone in the Physical Internet network. Several functional designs were suggested for different PI Cross-Docking Hubs. [PERSON] et al. [15] presented a functional design for a Road-based transit center in which the PI-containers are transferred between inbound and outbound trucks. Another functional design was proposed by [PERSON] et al. [16] for Road-Rail PI-hubs with various key performance indicators from the customer's and PI-hub operator's perspective. As mentioned in the introduction, our focus is on the PI-hubs, and more precisely, the Road-Rail PI-hub which is considered as a PI-node in the Physical Internet network. As illustrated in Figure 1 Road-Rail PI-hubs are composed mainly of PI-sorters, maneuvering area, and storage areas.  
Many researches were conducted to study various control and optimization problems related the Road-Rail PI-hubs. The PI-sorters, which are used for the routing of the PI-containers, occupies a large area of Road-Rail PI-hub. Thus, several researchers addressed the PI-containers routing problem with different approaches. Most authors focused on intelligent reactive approaches, usually exploiting multi-agent systems. One of the first papers dealing with this issue belongs to [PERSON] et al. [38] in which a multi-agent model is developed for the routing process and grouping of PI-containers into the outgoing trucks in a Rail-Road cross-docking PI-hub. Different grouping strategies of the PI-containers were proposed to minimize the evacuation time and the tardiness of trucks loading the grouped PI-containers. One of the cornerstones of the Physical Internet paradigm is using standardized autonomous modular PI-containers that are easy to route in the PI-hubs and over the PI transportation network. In this context, an activeness concept of the PI-containers was introduces by [PERSON] et al. [39] considering PI-container as autonomous and active products able to make decisions such as choosing the optimal routing path and to optimize the handling and moving operations especially in the cross-docking PI-hubs. Hybrid control architectures were addressed in several papers, such as in [40] by evaluating the performance of the Rail-Road PI-hub using simulation while considering both internal and external disruptions. An Optimized and Reactive hybrid Control Architecture (ORCA) was suggested by [PERSON] et al. [41] through a simulation study for the PI-containers routing in a perturbed environment using different predictive and reactive strategies. Authors in [42] proposed a simulated annealing based meta-heuristic to allocate the PI-containers to the trucks while minimizing the distance. In order to consider uncertainties, a reactive approach based on multi agent systems is suggested to handle possible perturbations in the Rail-Road PI-hub. Several papers proposed mathematical formulations of the Rail-Road PI-hub problems such as PI-containers routing and truck scheduling and allocation of PI-containers to the outgoing trucks or trains' wagons. For instance, in [43], authors studied the truck assignment and proposed a mathematical formulation of the PI-containers allocation and outbound trucks scheduling in the Rail-Road section of the PI-hub. The objective is to minimize the distance traveled by the PI-containers in the PI-sorters to reach the outgoing trucks. Then, in order to find a solution within a reasonable time, a four steps heuristic is proposed. A mathematical model was suggested in [44] for the truck assignment in the Road-Rail section of the PI-hub. The model was then solved using a Tabu Search meta-heuristic.