## 2 Literature Review  
The basic formula for two-echelon vehicle routing problem (2 EVRP) variants, introduced by [PERSON] [13], is based on the two-echelon capacitated vehicle routing problem (2E-CVRP). The study proposed a mathematical model for the 2E-CVRP. This model was developed based on the classical capacitated vehicle routing problem (CVRP), considering that the delivery is made from the depot to the customer through an intermediary facility in a two-echelon system. Like the CVRP problem, 2E-CVRP is also NP-Hard [14]. Later, [PERSON] [15] introduced a two-echelon route problem model with cover options denoted by 2 EVRP-CO. The study considered cargo bicycles to deliver goods and locker facilities, becoming intermediary facilities. Furthermore, the results of the 2 EVRP-CO model showed that the mileage of the cargo bike can be reduced by 60.4%. [PERSON] [15] introduced a two-echelon vehicle route problem with a time window denoted by 2E-VRPTW. The 2E-VRPTW formulation separated urban vehicle routes from urban transport routes as a distinct component of the problem. The study reported that the approach successfully and efficiently solved instances with five satellites and 100 customers. [PERSON] [16] proposed a 2 EVRP model taking into account work constraints. The goal was to obtain a valid lower bound that breaks 2 EVRP into a finite set of multi-depot vehicle routing problems. The study showed promising results with the 2 EVRP which can solve the 2 EVRP benchmark problem better than in earlier studies. Furthermore, the results showed that the algorithm optimally solves 144 of 153 experimental institutions. The 2 EVRP has been extended to many variants. [PERSON] [17] developed a mathematical model and used a branch-and-cut algorithm to solve a two-echelon capacity vehicle route with grouping constraints denoted by 2E-CVRPGC. This study examined the comparison of the optimal solution between the 2E-CVRP and 2E-CVRPGC models. The results showed that the difference between the optimal solutions was quite significant, with a percentage difference of 38%. In addition, for clustered instances, the difference between 2E-CVRP and 2E-CVRPGC is 55%. [PERSON] [18] developed two-echelon vehicle routing problem models with simultaneous delivery and retrieval (2E-VRPSPD). In the study, a mathematical model for the problem was proposed and was strengthened using valid and adaptable inequalities from the literature. The study used a hybrid heuristic based environment variable descent  
Figure 1: Illustration of reverse logistics using drop box facilities. and a local search algorithm called VND-LS. The result showed effectiveness in finding a good solution for 2 EVRPSPD. The application of the parcel locker in logistics activities has been modelled as a network design or routing optimization problem. [PERSON] and [PERSON] (2018) developed a packet locker network design problem to solve the last mile distribution problem, selecting the best number, location, and size of intermediate facilities. This study aimed to find the maximum total system profit. The total profit was made up of the revenue from the end customer using the service, deducting the fixed costs and the costs of setting up facilities, discounted shipping costs for the customers, and the potential loss of customers who do not wish to use facilities. Research conducted by [PERSON] (2018) developed a two-echelon vehicle route problem model by considering the locker facility denoted by 2E-VRPLF. The study compared the results of the 2E-VRPLF calculation with the home-delivery method, indicating that 2E-VRPLF can reduce transportation costs by 70.4%. In solving the 2E-CVRP problem, there are various approaches, such as exact approaches, heuristic methods or a combination of both ([PERSON] et al., 2018). The column generation technique has been generally used in the exact approach ([PERSON] et al., 2018). Examples of this technique are branch and bound or branch and prices ([PERSON] et al., 2018).