## 1 Introduction  
The need for designing networks in a supply chain has been attracting a lot of attention in recent years; a result of the booming development of industrial commerce. A practice in traditional commerce is that customers can return the unsatisfactory products they bought within a given certain period of time. This process is called the reverse logistics by which the products are returned for proper planning of their disposal [1]. Reverse logistics can also be defined as the process of moving goods for capturing value. Efficient reverse logistics can reduce cost especially transportation cost, shipping cost, and inventory cost. Besides that, it also improves the service by offering a fast response to the demands and returns from customers. By implementing reverse logistics in supply chain network design, the expectation of a gain in both profit and increased customer retention can be expected, benefiting both from the economic and social factor of the economy respectively [2]. Reverse logistics is necessary for various reasons; such as the increasing trend in customers' returns, product lifecycles, and demanding customers [3]. To maintain a high level of customer satisfaction and quickly respond to the complaints, some industries are willing to handle those returns on their own and thus strive to provide an efficient logistics system to accommodate this. Hence, one can argue that it is necessary for the reverse logistics network and logistics process to be integrated. Nowadays, a large number of organizations are experiencing high volumes of product returns. Managing product returns in reverse logistics depends on detailed planning, especially when the volume of return flow had increased considerably [4]. The returned products can be re-entered into the market to be resold either with or without some refurbish process depending on the condition of the products. Returned products can be categorized into two categories which are defect or non-defect products. The non-defect products will be re-sold in the next batch while the defect products will need to go through the process of refurbishing before re-entering the market [5]. In supply chain network design, besides facility location and vehicle routing, inventory control is also considered an important part of the whole process of optimization. Designing a distribution network consists of the three sub-problems which is essential to drive the key performance for the overall productivity and profitability. Looking at previous works from literature, most of the studies done focused on the integration of only two sub-problems such as location-routing problem (LRP), Inventory-Routing Problem (IRP), or Location-Inventory Problem (LIP). We found work on the integration of all three sub-problems, i.e., Location-Inventory-Routing Problem (LIRP) to be very limited especially those utilising the Economic Production Quantity (EPQ) model. There is a body of literature with regards to the EOQ model. The EOQ model determines the optimal order quantity a company should purchase from other companies to minimize inventory cost. On the other hand, the EPQ model determines the optimal production quantity for manufacturing. The main difference between these two models is that the EPQ model assumes the company will produce its own quantity, therefore the orders are available in an incremental manner while the products are being produced. While the EOQ model assumes the order quantity arrives complete and immediately after ordering, meaning that the parts are produced by another company and are ready to be shipped when the order is made. Since the EPQ model is less researched despite being a practice of most companies in the industry, we propose the LIRP utilizes the EPQ model for defect and non-defect items in reverse logistics. The problem is solved by a hybrid harmony search-simulated annealing (HS-SA) algorithm.