## 2 Related Literature  
The VRPPD could be classified into three different categories [8; 9], which are as follows:  
Figure 1: Multiple readings of the same problem. * **Delivery first and pickup second**: vehicles perform a pickup operation after the delivery process. This category is called Vehicle Routing Problems with Backhauls (VRPB). * **Mixed pickup and delivery**: vehicles deliver or pickup in any sequence along their routes. This category is called Mixed Vehicle Routing Problem with Backhauls (MVRPB). * **Simultaneous Pickup and delivery**: vehicles simultaneously perform the delivery and pickup. This category is called Vehicle Routing Problems with Simultaneous Pickup and Delivery (VRPSPD). The majority of published VRPPD models assume that each customer is visited only once [10]. Some exceptions have considered multi-customer visits, such as in [11] where the authors developed a large-scale model, allowing two visits per customer for a many-to-many pickup and delivery routing problem. In [12; 13], the authors considered a VRPSPD involving the delivery of full bottles and the collection of empty ones. The authors assumed that such a problem is classified among reverse logistics operations. Several real-life applications encountered in the beverage industry are described in [14]. For example, in [15], authors considered a truck scheduling problem for container transportation in a local area with multiple depots and terminals. They proposed an approach based on an integer programming heuristic that determines pickup and delivery sequences for daily drayage operations while ensuring a minimum transportation cost. In the same context, the authors in [16] demonstrated that drayage operations could be considered as a multi-stop VRPB. More details regarding VRPB and VRPPD can be found in two comprehensive overviews provided in [17; 18], respectively. The problem of container drayage has been considered by other research work. For example, in [19], authors have developed models capable of minimizing both present and future operating costs. The authors in [20] modeled the container drayage problem as a pickup and delivery problem and proposed Lagrangian relaxation to solve the problem. In [21], the authors proposed three approaches for the container movement problem with time windows at origins and destinations. These approaches are based on an asymmetric multiple traveling salesman problem. Some researchers have considered a single vehicle while modeling the VRPPD. For example, the single-vehicle VRPPD with deterministic demands and predetermined customer visit sequence has been considered in [22]. Authors in [22] have developed the routing of a single-vehicle that delivers multiple products under stochastic demand. Other researchers, such as [23; 24], have considered a VRP with mixed pickup and delivery, called (VRPM), where pickups are made before deliveries. Recently, [PERSON] et al. [25] introduced a new VRP variant which encourages the reuse of collected items. They developed a segment-based evaluation procedure to reduce the computation time. They provided a mathematical formulation and a metaheuristic algorithm, and analyzed several features of the problem. In [26], a hybrid heuristic algorithm for the 3L-PDP problem is extended by using two key improvements: the first is the usage of a tabu strategy for enlarging the local search space, the second is the employment of complex block generation and depth-first heuristics for incrementally finding one proper box at a time in the packing phase. The experimental results show that the improved hybrid heuristic algorithm outperforms its origin regarding total travel distance on benchmark state-of-the-art instances. More variants of VRPPD including MRVRP, VRPP, SDVRP, SVRP, VRPSF, and VRPTZ can be found detailed in [27; 28]. Finally, we recall the main contributions of this paper. We have been motivated by the large number of studies that tackled the VRPTD.