## 1 Introduction  
E-commerce, also known as electronic commerce, refers to the buying and selling of goods or services using the Internet, and the transfer of money and data to execute these transactions. E-commerce sales worldwide amounted to 1.86 trillion US dollars and projected to grow to 4.48 trillion US dollars in 2021 [1]. The growth of e-commerce has evolved to make products easier to purchase through online retailers and marketplaces. Small businesses and large corporations have all benefitedfrom e-commerce, which enables them to sell their goods and services at a scale that was not possible with traditional offline retail. Moreover, the growth of e-commerce is associated with an increasing number of packages delivered to individual customers. Thus, the last mile distribution plays a vital role in serving customers.  
The last mile distribution are commonly used home delivery (HD) methods, and the packages are delivered directly to the recipients' site. However, it is seen as a cost-ineffective approach for goods distribution. It is because this approach often met unfortunate condition such as heavy traffic and environmental issues, especially in the urban area. Therefore, the last mile distribution is regarded as the most expensive, most polluting, and the least efficient part of the e-commerce supply chain [2]. Moreover, there are occasional unattended deliveries that can raise the re-delivery cost.  
Customer pickup (CP) is an option for the customers that is considered to be a less time-consuming and less costly process than the HD. In CP, customers are allowed to pick up or deliver the packages via intermediate facilities located nearby the customers' home or office. The customer pickup locations are usually located in a public area that is easy to be accessed. A more traditional form of parcel locker is seen in the implementation of a reception box which is a fixed locker to receive a package that is installed outside a consumer's home. [PERSON] et al. [3] showed that the utilization of a reception box can reduce the cost of home delivery by 42%. [PERSON] et al. [4] found that 15% of the customer tends to have more intention to use the lockers if it is located near to their home.  
Reverse logistics is a logistics network that consists of activities such as there are flows of product goes at least one step back in the supply chain. Business activities consist of moving goods from the customer to the retailer, the retailer to the distributor, and the distributor to the manufacturer. The purpose of those activities is varied from proper disposal at the end of the product life cycle, refurbish, product recall, to become a part of the green supply chain. These activities are beneficial for a company image which involved a trade-off with the cost required to support the process. Therefore, to unlock the full benefits of reverse logistics activities, the use of a parcel locker network needs to be further investigated.  
Our proposed research concerns on how to conduct reverse logistics activities such as product return, refurbish, and product recall by utilizing parcel locker network. The problem is addressed as an optimization model that formulated into an integer linear programming model denoted as the two-echelon vehicle routing problem with locker facilities (2 EVRP-LF). The objective is to minimize the cost of transportation with regards to the vehicle travelling cost to pick up the product from locker facilities/intermediate facilities, and the additional cost to compensate the customer that needs to travel to access the locker. Figure 1 shows the illustration of 2 EVRP-LF.  
Figure 1: The illustration of reverse logistics using parcel locker network facilities.  
The remainder of this paper is organized as follows: In Section 2 we listed the literature review related to the study. Section 3 shows the formulation of the two-echelon VRP-LF model. We demonstrate the numerical experiments of this problem in Section 4. Finally, the conclusion and future research direction are discussed in Section 5.