# Optimizing Perishable Product Supply Chain Network Using Hybrid Metaheuristic Algorithms
## 1 Introduction  
In recent decades, there has been a significant increase in the demand for perishable products in various markets. At the same time, customers in different countries have become more and more concerned about the freshness of these products. However, perishable products, including vegetables, fruits, and milk, are prone to deterioration shortly after production. The global issue of food waste is particularly severe in the United States, with approximately 15% of perishable products spoiling during transportation and sales each year. Additionally, perishable product sales constitute half of the overall retail industry [1], while about 10% of perishable goods are wasted before being purchased by customers [2; 3]. In China, over 25% of fruits and vegetables deteriorate during transportation, storage, and sales [4; 5]. The rates of fresh produce deterioration in inventory and transportation in China are approximately 15% for fruits, 8% for vegetables, and 10% for meat and aquatic products [5]. To address these challenges, it is crucial to implement effective inventory control, optimize transportation routes, and enhance operational efficiency within the perishable product supply chain. The period between the manufacturing date and the final delivery to the end customers holds significant importance for both producers and traders of perishable products. The vulnerability of perishable items to damage and spoilage introduces specific constraintson various aspects of the supply chain, including facility location, distribution planning, inventory management, and routing arrangements. Undoubtedly, considering the unique nature of perishable goods, this issue becomes even more critical. Therefore, there is an urgent requirement to develop a specialized and comprehensive optimal supply chain network model that caters to the specific needs of perishable products [6; 7]. Additionally, ensuring cost effectiveness poses a significant challenge in the management of goods with a limited shelf life. To minimize the economic cost of the PPSCN, this study develops a novel model that considers the perishable characteristics of the products. The LIRP model involves the integrated optimization of facility location, inventory management, and routing arrangement within the supply chain network. This integration tackles the logistics LIRP, which poses a comprehensive optimization challenge for the entire logistics system [8]. The purpose of this study is to provide an optimized solution for supply chain managers or practitioners, empowering them to efficiently manage the PPSCN and achieve cost effectiveness. Since the LIRP is characterized by its size, complexity, and nonlinear nature, it is not always feasible to obtain an optimal solution using exact methods. Nowadays, metaheuristic algorithms have been commonly used globally for their simple structure and other advantageous qualities, such as adaptability and flexibility [9]. GA has the advantage of providing feasible solutions that are close to optimal, even in scenarios where the problem's constraints or objective function are non-continuous and do not necessitate a linear formulation. The proposed metaheuristic algorithms in this paper comprise HGA-VNS and HMPGA-VNS, where GA and MPGA are, respectively, hybridized with VNS. Hybrid metaheuristic algorithms leverage the strengths of different algorithms while mitigating their weaknesses [10; 11]. GA and MPGA contribute global information and search guidance to VNS, while VNS enhances the search diversity and global search capability of GA and MPGA. The field of PPSCN has gained significant attention in recent years. A predominant research focus is designing a supply chain network for perishable goods while addressing the uncertainties associated with their perishability. This paper's modeling and solution approach is inspired by previous research conducted in the field of PPSCN. In the subsequent section, we provide a concise overview of these studies.