Efficient Expansion Algorithm of Urban Logistics Network for Medical Products Considering Environmental Impact

Abstract

As society continues to age, people are becoming more concerned about their health care. This has led to an increase in the demand for medical products in urban areas, emphasizing the need for regular and prompt deliveries. However, the existing logistics centers are located in the suburbs of Seoul, a metropolitan city, which makes it challenging to ensure timely delivery. To address this issue, this study aims to establish new logistics centers in urban areas, particularly in Seoul, while minimizing CO₂ emissions from delivery vehicles in alignment with sustainability efforts. The scientific gap addressed in and the novelty of this paper is that the input parameters are prepared based on actual data from a medical company in Korea to reflect reality, and the mathematical model-based optimization technique is applied to determine the optimal location of a new logistics center. The genetic algorithm is developed to solve the proposed mathematical model by deriving optimal or near-optimal solutions. Furthermore, the numerical experiment examined the impact of establishing a new logistics center in one of the candidate areas of local governments in Seoul by considering environmental impact. As a result, the new logistics network can reduce CO₂ emissions by approximately 66.74% compared to the existing logistics network.

1. Introduction

The demand for medical products such as dietary supplements has globally increased because many people have become interested in health care and improving their immunity against infectious diseases due to the advent of the COVID-19 pandemic [1]. In addition, good health has generally been considered an essential basis of life. As a result, the medical product industries such as those for vitamins, minerals, herbs or other botanical products, and health examinations have also grown [2]. According to a survey conducted by the Korea Health Functional Food Association, it is expected that the annual growth rate of the health functional food market would be 10.8% on average [3]. Moreover, with the growth of the medical product industry, the logistics industry has grown because of an increase in demand for online shopping due to COVID-19 as well. Various national policies such as social distancing were implemented during the period of the COVID-19 pandemic, and it caused consumers to depend on online shopping, particularly for food [4].

The trend in logistics networks is changing along with the growth of the logistics industry. One of the prominent changes is the expansion of the Micro-fulfillment Center (MFC). MFCs are small-scale logistics centers located in urban areas, unlike large logistics centers located in suburban areas [5], and enable same-day delivery and efficient logistics management [6]. As a result, customer satisfaction and repurchase rates can increase because of fast delivery, and delivery costs can be reduced by shorter distances between consumers to urban logistics centers. Moreover, a reduction in delivery distance leads to a decrease in CO₂ emissions from delivery vehicles, which has a positive environmental impact. Several countries operate MFCs in urban areas. For example, the food/logistics company ‘Coupang’ in South Korea offers the ‘Rocket Delivery’ service, which uses an urban logistics center to deliver products within 24 h. As shown in Figure 1, the health/beauty company ‘CJ Olive Young’ in South Korea also offers the ‘O Neul Dream’ service, which means delivery tonight, and uses an urban logistics center to deliver products within 3 h. In other countries such as the United States, Whole Foods Market uses urban logistics centers to enhance logistics efficiency and provide fast delivery services within two hours for Amazon Prime customers [7]. Approximately 7% of global carbon emissions originate from the logistics industry. In countries like the United States, where long-distance delivery is common due to the vastness of the territory, 20–30% of CO₂ emissions are attributed to transportation. Consequently, environmental issues related to the logistics industry are recognized as significant concerns [8]. In summary, urban logistics centers are gaining attention as alternatives to traditional large logistics centers due to the great advantage of fast and sustainable delivery. In this situation, the purpose of this study is to reduce the CO₂ emissions of the ‘L’ medical company by constructing a new logistics center in an urban area. A new logistics center is to be constructed in one of the 25 candidate sites in Seoul, and the candidate site with the lowest total CO₂ emissions from vehicles will be determined. The company sells powdered medical products that are effective for hydration in South Korea. The ‘L’ medical company has four large logistics centers located in the suburban areas of Seoul, and each logistics center only processes orders received from pharmacies, home shopping, online platforms, and military marts. According to the data analysis in Section 5, the proportion of pharmacy orders is 44.65% around Seoul including suburban cities. Therefore, it seems that the logistics network can be improved by reducing delivery distance when an urban logistics center is built in Seoul, in addition to the existing logistics center in Gunpo. Furthermore, the company will surely be able to increase its economic benefits and improve customer satisfaction by reducing delivery costs and time by using an urban logistics center from a long-term perspective [9]. Thus, a strategy for determining the optimal location of an urban logistics center in Seoul is proposed to reduce CO₂ emissions by minimizing the delivery distances of the ‘L’ medical company’s logistics network.

The logistics network of the ‘L’ medical company can be improved by determining the optimal location for the urban logistics center through a developed mathematical model-based optimization technique. The optimal solution solver and genetic algorithm are adopted to solve the proposed mathematical model by deriving an optimal or near-optimal solution. The scientific gap of this study is that the input parameters such as demands and capacities are derived from the ‘L’ medical company’s actual data for the practical and rational aspects. The delivery distance and time differ depending on the location of the urban logistics center constructed within Seoul. At this point, the candidate locations for constructing a logistics center with higher demands have a higher probability of being determined as the optimal location. It means that the accessibility of the candidate locations to the pharmacies is crucial. In summary, this study aims to find the optimal location in Seoul for the urban logistics center by using actual data such as the demand and capacity of medical companies and the actual distance between candidate locations and pharmacies and examines how many orders of the existing logistics center in Gunpo are assigned to the new urban logistics center in Seoul through the numerical experiment.

This paper is organized as follows. Section 2 presents a literature review related to the environmental impacts of logistics centers and vehicle routing problems. In Section 3, the problem description of this research is explained including the actual logistics networks of the ‘L’ medical company and the development of a mathematical model that can minimize the total CO₂ emissions of all vehicles. In Section 4, various methodologies for solving the mathematical model are introduced and how to apply them in this study is explained. In Section 5, the procedure of processing raw data is described and the numerical experiments for reasonable-size problems are conducted. Finally, the findings and insights from this study are presented as concluding remarks in Section 6.

2. Literature Review

The delivery and logistics industries have been striving to enhance customer satisfaction and reduce CO₂ emissions over the past few years. Generally, studies related to logistics centers have been conducted on topics such as location decision making for logistics centers, storage and inventory management, delivery staff scheduling, and transportation route optimization [10]. In this situation, many companies tried to locate logistics centers in urban areas close to customers to reduce CO₂ emissions by reducing delivery distance and time. Furthermore, many studies have been conducted to rationally determine the location of logistics centers. Kazançoğlu et al. [11] sought to determine the location of logistics centers in emerging countries using a hybrid multi-criteria decision-making method, which combines the fuzzy Analytic Hierarchy Process (AHP) and the Preference Ranking Organization Method for Enrichment Evaluations (PROMETHEE). As a result, 12 criteria were derived to select the location of the logistics centers in the Sivas region. Wang et al. [12] used a heuristic genetic algorithm to schedule the process of logistics centers and aimed to achieve improving the circulation efficiency of logistics networks and reducing the cost by recommending the number of vehicles and working hours. As a result, the goal of improving the circulation efficiency of the logistics center and reducing circulation fees was achieved by deriving the optimal number and path of picking carts. Cattaruzza et al. [13] performed a study that contributed to reducing traffic congestion and enhancing the mobility of freight transportation services in urban areas at a minimum cost by optimizing the vehicle routing of urban logistics centers. Consequently, the study found that vehicle routing optimization can indeed play a key role in the urban goods movement. Thus, the logistics network can be operated more efficiently by optimizing the routes and the number of vehicles that are used within the logistics center like picking carts and delivery vehicles for external customers. Based on this literature review, this study emphasized environmental and economic factors in the selection of logistics center locations. Furthermore, aiming to optimize the number of vehicles and delivery routes, a genetic algorithm was developed based on mathematical models.

The development of land transportation infrastructure and the increasing demands for delivery services have caused the adoption of eco-friendly management in the logistics industry [14]. Liu et al. [15] present a sustainable management aimed at reducing the carbon emissions of cold chain logistics companies. In this study, based on actual business data from 4 cold chain companies and 28 client firms, a Joint Distribution-Green Vehicle Routing Problem (JD-GVRP) model was constructed. Subsequently, the simulated annealing (SA) algorithm was applied to optimize the routing of cold chain vehicles. As a result, a joint logistics network effectively reduced the total costs and carbon emissions. Scaburi et al. [16] aimed to optimize the newspaper delivery process of a Brazilian printing company by applying a mathematical model-based VRP (Vehicle Routing Problem). Based on the results, the reduction in greenhouse gas emissions was assessed using the Greenhouse Gas Protocol calculation tool. Gupta et al. [17] implemented a vehicle routing problem in urban areas based on actual company data from Singapore. This study considered time windows at customer locations, simultaneous pickup and delivery demands, a heterogeneous fleet of vehicles, and the heterogeneity of traffic congestion levels in urban transportation networks and compared the results of various cases to derive the optimal route that minimizes CO₂ emissions. Numerous studies exist that effectively reduce CO₂ emissions through optimizing logistics networks. However, this study stands out as research focused on determining the location of logistics centers, considering both CO₂ emission reduction and economic factors such as real estate prices.

Various industries use the strategy for finding an optimal location that is used in this study. Ahmad et al. [18] conducted a study about the optimal location of electric vehicle charging facilities using mathematical models and genetic algorithms. This research set the cost, net benefit, power loss, distance, covered trip, and power supply moment balance index as objective functions and found the optimization strategies with the handling of uncertainty and integration of renewable energy sources. Subsequently, discussions on the optimal location of electric vehicle charging facilities were conducted through an evaluation of the distribution network and the environmental and economic impact. Ko et al. [19] used mathematical models and genetic algorithms to find the optimal location, capacity, and capability of emergency medical centers. The objective is to minimize costs while satisfying the functions and capacities of emergency medical centers considering the types of transportation that patients primarily use when visiting emergency medical centers and the types of diseases. The optimal solutions were derived from the proposed strategy in this research and were examined by the simulation studies at the stochastic scheme. Gavina et al. [20] proposed that strategically arranging the beehives in the situation of the limited availability of nectar and pollen near the beekeeping site leads to competition among bees and a scarcity of pollinators relative to the abundance of flowers, which could result in less-than-optimal crop pollination. In this situation, the research established a mathematical model aimed at maximizing objective functions such as the beekeeper’s variable preferences, the count of bee colonies that can be utilized, and the expected productivity of the flora surrounding them and utilized linear programming to derive conclusions. Similarly, in various industries such as charging facilities, emergency medical centers, and beekeeping, while the objectives may differ from those in the logistics industry, optimization techniques based on mathematical models are employed to find optimal locations.

The difference between the optimal location selection in the logistics industry and others is that the Vehicle Routing Problem is usually applied. The Vehicle Routing Problem (VRP) was first proposed by Dantzig and Ramser based on the issues of the transportation/logistics field [21]. The VRP plays a significant role in reducing costs in the transportation/logistics sector by 5% to 20%. Traditionally, the VRP in the logistics industry encompasses the process of planning the optimal routes for vehicles loading and displacing products within the logistics center, as well as for vehicles delivering products externally. The general objective of the traditional VRP is to search for the optimal route to satisfy various customer demands under given circumstances [22]. Ray et al. [23] proposed an ILP model to find the depot locations and vehicle routes for commodity delivery. They also suggested an efficient heuristic-based mechanism that can solve the model optimally. Moreover, vehicle routes were segmented by multiple depots. However, this strategy had a limitation in that it only assumed a situation where the total demand was less than the vehicle’s load, and it did not account for additional work after the vehicle returned to the logistics center. Wang et al. [24] proposed a low-carbon cold chain logistics distribution route optimization model that minimizes various costs such as transportation, cooling, and carbon emissions of cold chain logistics centers in China and derived the optimal solution by cycle evolutionary genetic algorithm (CEGA). However, the working time of vehicles considered only the delivery time, excluding the loading/unloading time, and the vehicles did not operate additional delivery tasks after returning to the cold chain logistics center.

Moreover, the study applying the VRP has been conducted beyond the logistics industry. Markov et al. [25] developed a mathematical model with the goal of minimizing waste transportation costs in the process of waste collection and disposal through vehicle operation. However, this study appeared to present an inefficient routing plan in that it assumes all available waste-collecting vehicles are operating simultaneously, and this previous study differed from the present study in that the departure and destination of the vehicles can be different. Zhou & Wu [26] introduced a Green Vehicle Routing Problems with Pick-up and Delivery (GVRPPD) model to establish an eco-friendly route that minimizes fuel emissions from vehicles. The results of the design experiment revealed that the GVRPPD model significantly reduced carbon emissions without reducing customer satisfaction. However, they had the limitations of not reflecting reasonable situations due to the problem design being based on only one depot for the delivery vehicles.

Studies related to the location selection of logistics centers have been prolongedly conducted. It is easy to find research that applies the VRP to select the location of logistics centers. This paper also uses the VRP considering demands and vehicle capacity and derives solutions by a mathematical model and a meta-heuristic algorithm. The development of the Internet has led to a vast amount of information about users, making it crucial to derive the direction of user preferences [27]. In this regard, this study can be seen as reflecting customer preference clearly and more empirical research because it sets the problems using several months of actual data from the ‘L’ medical company in South Korea. Furthermore, the health care provider currently operates multifaceted supply chains to reduce logistics costs and improve the quality and efficiency of medical products transport [28]. The way to consider features in real life to construct practical models is a challenge that has always received attention in VRP problem research [29]. Therefore, it is expected that this study would be evaluated as one of the practical strategies in a company’s decision-making process in that it treats the problem based on the actual data of the company.

3. Model Development

3.1. Problem Description

According to the World Health Organization, three-quarters of modern people are in a state of chronic dehydration. To address this health issue, the ‘L’ medical company has been selling oral rehydration solutions (ORS) as beverages since 2017, aiming to alleviate symptoms associated with dehydration. Last year, the ‘L’ medical company achieved sales of KRW 33.5 billion and an operating profit of KRW 3.3 billion. This year, the target is to reach sales of KRW 50 billion and an operating profit of KRW 5 billion. With this continuous growth, military marts, pharmacies, home shopping, and online platforms are the main sales channels of the ‘L’ medical company. As shown in Figure 2, logistics centers for each channel are located in suburban Seoul. However, the demand for pharmacies out of four channels is not evenly distributed throughout the country and is concentrated in large cities around Seoul, which accounts for around 50%. Accordingly, it could be more efficient to build an urban logistics center in Seoul to cover the demand for pharmacies in Seoul to improve the logistics network for the ‘L’ medical company. Then, it would be possible to reduce the CO₂ emissions for the demands within Seoul, and the existing logistics center can respond to the demands of other regions by distributing the demand previously handled by the existing logistics center to a newly constructed logistics center in Seoul. In this situation, the location of the urban logistics center affects the delivery routes and operation time of each vehicle. Furthermore, there is an appropriate number of vehicles needed based on the overall demand, and these vehicles are distributed between the urban logistics center and the existing logistics center.

Thus, this study aims to develop an algorithm that selects the optimal location for a new logistics center, which can minimize CO₂ emissions to pharmacies across different local governments in Seoul, when operated concurrently with an existing logistics center. There are a certain number of vehicles available to handle the demand of all pharmacies in Seoul, and the number of vehicles used by each logistics center varies depending on the location of the new logistics center. Additionally, if the number of remaining products in a vehicle is less than the demand of the next pharmacy, it can return to the logistics center to load additional products before continuing the delivery. Lastly, since the ‘L’ medical company has a limited budget for investing in the construction of a logistics center, the maximum volume of the logistics center that can be built varies according to the real estate prices in different local governments of Seoul.

3.2. Notations

A mathematical model-based optimization technique is applied in this study to decide the optimal location for an urban logistics center. Sets for index, decision variables, and system parameters are defined to develop the mathematical model below.

Sets
$I,J$	: Set of nodes for areas including logistics centers, $I,J=R\cup W$
$R$	: Set of nodes for areas
$W$	: Set of nodes for logistics centers
$F$	: Set of vehicles
$N$	: Set of delivery sequences
Decision Variable
$X_{rijfn}$	: Binary decision variable, 1 if vehicle $f$ moves from $i$ to $j$ in $n$th sequence when urban logistics center is located at $r$, 0 otherwise
$Y_{rijfn}$	: Number of products remaining in the vehicle when urban logistics center is located at $r$ and vehicle $f$ moves from $i$ to $j$ in $n$th sequence
$V_{rijfn}$	: Number of products unloading to node $i$ when urban logistics center is located at $r$ and vehicle $f$ moves from $i$ to $j$ in $n$th sequence
$G_r$	: Binary decision variable, 1 if urban logistics center is located in $r$, 0 otherwise
$A_{rfn}$	: Total operation time when urban logistics center is located at $r$ and vehicle $f$ moves in $n$th sequence
System Parameters
$d_{rij}$	: Distance between node $i$ to node $j$ when urban logistics center is located at $r$ (km)
$o_r$	: Demands of area $r$ (box)
$q_r$	: Time required for delivery to pharmacies in area $r$ (min)
$c_r$	: Number of products available for delivery when urban logistics center is located at $r$ (box)
$e$	: CO2 emissions of a vehicle (g/km)
$b$	: Maximum capacity of vehicle (box)
$p$	: Loading/unloading operation time per product (min/box)
$s$	: Speed of vehicle (km/min)
$mw$	: Maximum working time of vehicles (min)
$m$	: A large number

3.3. Mathematical Model

Equation (1) is the objective function that minimizes the total CO₂ emission of vehicles. CO₂ emissions are proportional to the delivery distance. The total delivery distances of the vehicles are calculated by summing the distances between nodes. The location of pharmacies is fixed, but the total delivery distances of vehicles become different depending on the location of the newly built urban logistics center.

$$Minimize\sum _{r\in R}\sum _{i\in I}\sum _{j\in J}\sum _{f\in F}\sum _{n\in N}{d}_{rij}·X_{rijfn}·G_r·e$$

(1)

Equations (2) to (6) define the relationship between decision variables. Equation (2) is the relationship between $X_{rijfn}$ and $Y_{rijfn}$. If the vehicles do not move from node $i$ and node $j$, then decision variable $Y_{rijfn}$ cannot have the value. Equation (3) is the relationship between whether a vehicle delivers, and the number of products delivered to a specific node. If the vehicles do not move from node $i$ and node $j$, then decision variable $V_{rijzn}$ cannot have the value. Equation (4) indicates that the number of products remaining in the vehicle should be larger than the demand at the next node. Equation (5) represents the number of unloading products equal to the node’s demand. Equation (6) defines the relationship between the remaining loads and the delivery amount for each delivery sequence.

$$m·X_{rijfn}\ge Y_{rijfn},\hspace{1em} \forall r\in R,\forall i\in I,\forall j\in J,\forall f\in F,\forall n\in N$$

(2)

$$m·X_{rijfn}\ge V_{rijfn},\hspace{1em} \forall r\in R,\forall i\in I,\forall j\in J,\forall f\in F,\forall n\in N$$

(3)

$${\sum }_{i\in I}{V}_{rjifn}\le {\sum }_{i\in I}{Y}_{rijfn-1},\hspace{1em} \forall r\in R,\forall j\in J,\forall f\in F,\forall n\in \{2,3,\dots ,N\}$$

(4)

$$V_{rijfn}=o_i·X_{rijfn},\hspace{1em} \forall r\in R,\forall i\in R,\forall j\in J,\forall f\in F,\forall n\in \{2,3,\dots ,N\}$$

(5)

$${\sum }_{i\in I}{Y}_{rjifn}={\sum }_{i\in I}{Y}_{rijfn-1}-{\sum }_{i\in I}{V}_{rjifn}, \forall r\in R,\forall j\in J,\forall f\in f,\forall n\in \{2,3,\dots ,N\}$$

(6)

Equations (7) and (8) show the constraints related to the loading amount of the delivery vehicles. Equation (7) means that the remaining capacity of the delivery vehicles is determined by the demands of the previously visited node. Equation (8) indicates that the vehicle’s remaining load capacity cannot exceed the maximum load capacity.

$${\sum }_{i\in I}{\sum }_{f\in F}{\sum }_{n\in \{2,3,\dots ,N\}}\left(Y_{rijfn-1}-Y_{rjifn}\right)\ge o_j,\hspace{1em} \forall r\in R,\forall j\in R$$

(7)

$$Y_{rijfn}\le b,\hspace{1em} \forall r\in R,\forall i\in I,\forall j\in J,\forall f\in F,\forall n\in N$$

(8)

Equations (9) to (14) indicate how vehicles move. Equation (9) prevents vehicles from moving between the same nodes. Equation (10) indicates that vehicles should depart from the logistics center. Equation (11) indicates that vehicles can deliver only one route in each delivery sequence. Equation (12) is the constraint that the vehicle should return to the logistics center from which it departed after finishing delivery. Equation (13) is a constraint related to the continuity of vehicle delivery sequence and indicates that a vehicle arriving at a node $i$ should depart from the same node $i$ when delivering in the next sequence. Equation (14) indicates that the vehicles cannot be assigned to the delivery sequence $n$ if the vehicles are not assigned to the delivery sequence $n-1$.

$$X_{riifn}=0,\hspace{1em} \forall r\in R,\forall i\in I,\forall f\in F,\forall n\in N$$

(9)

$${\sum }_{w\in W}{\sum }_{j\in J}{X}_{rwjf1}=1,\hspace{1em} \forall r\in R,\forall f\in F$$

(10)

$${\sum }_{i\in I}{\sum }_{j\in J}{X}_{rijfn}\le 1,\hspace{1em} \forall r\in R,\forall f\in F,\forall n\in N$$

(11)

$${\sum }_{i\in R}{\sum }_{n\in N}{X}_{rwifn}={\sum }_{i\in R}{\sum }_{n\in N}{X}_{riwfn},\hspace{1em} \forall r\in R,\forall w\in W,\forall f\in F$$

(12)

$${\sum }_{i\in I}{X}_{rijfn-1}={\sum }_{i\in I}{X}_{rjifn},\hspace{1em} \forall r\in R,\forall j\in R,\forall f\in F,\forall n\in \{2,3,\dots ,N\}$$

(13)

$${\sum }_{i\in I}{\sum }_{j\in J}{X}_{rijfn}\le {\sum }_{i\in I}{\sum }_{j\in J}{X}_{rijfn-1},\hspace{1em} \forall r\in R,\forall f\in F,\forall n\in \{2,3,\dots ,N\}$$

(14)

Equations (15) to (17) are constraints related to the working time of vehicles. Equation (15) means that the vehicle’s working time is determined by the sum of the moving time between nodes and the working (loading/unloading/moving) time at the nodes. Equation (16) represents the working time of vehicles in the first sequence. Equation (17) means that the total working time of vehicles cannot exceed the maximum working time. Equation (18) shows that an urban logistics center is established in only one area. Equations (19) and (20) ensure that the decision variables are not negative.

$$\begin{array}{}{A}_{rfn}=A_{rfn-1}+{\sum }_{i\in I}{\sum }_{j\in J}{X}_{rijfn}·d_{rij}÷s+\left|{\sum }_{i\in I}{\sum }_{j\in J}{V}_{rijfn}\right|·p+\sum _{i\in R}\sum _{j\in J}{X}_{rijfn}·q_i,& \forall r\in R,\forall f\in F,\forall n\in \{2,3,\dots ,N\}\end{array}$$

(15)

$$A_{rf1}={\sum }_{w\in W}{\sum }_{j\in R}{Y}_{rwjf1}·p+{\sum }_{w\in W}{\sum }_{j\in R}{X}_{rwjf1}·d_{rwj}/s, \forall r\in R,\forall f\in F$$

(16)

$$A_{rfn}\le mw,\hspace{1em} \forall r\in R,\forall f\in F,\forall n\in N$$

(17)

$${\sum }_{r\in R}{G}_r=1,$$

(18)

$$Y_{rijfn}\ge 0,\hspace{1em} \forall r\in R,\forall i\in I,\forall j\in J,\forall z\in Z,\forall n\in N$$

(19)

$$A_{rfn}\ge 0,\hspace{1em} \forall r\in R,\forall f\in F,\forall n\in N$$

(20)

4. Solution Procedure

An optimal solution solver and genetic algorithm (GA), one of the metaheuristic algorithms, are used to derive the optimal and near-optimal solution of the developed mathematical model. The optimal solution can be derived by using CPLEX version 22.1.1, which is one of the optimal solution solvers when the amount of data set and the size of the problem are relatively small. However, CPLEX requires a long computation time to find the optimal solution due to the increased complexity of problem solving when a reasonable-size problem is applied. In this study, it took over 48 h of computational time to obtain the optimal solution using CPLEX. To address the limitations of CPLEX, GA is developed, and the performance of GA is confirmed by comparing the results and computation time of CPLEX and GA. First, GA took about 2 h to derive the near-optimal solution, which represents a significant improvement in computational time compared to CPLEX. The comparison between the optimal solutions obtained by CPLEX and the results derived from GA was conducted. It was found that the discrepancy between the CPLEX and GA outcomes is less than 5%. Through this process, the validity and reliability of GA were confirmed.

4.1. Optimal Solution Solver

In this study, the optimal solution is derived using IBM’s ILOG CPLEX. IBM’s ILOG CPLEX is a sophisticated mathematical optimization tool designed to solve linear programming (LP), mixed-integer programming (MIP), and quadratic programming (QP) problems, among others [30]. It is widely recognized for its efficiency, reliability, and the ability to handle large-scale optimization problems. This makes CPLEX an invaluable tool in various fields such as logistics, finance, manufacturing, and research, where optimizing resources and decisions can significantly impact efficiency and outcomes.

4.2. Genetic Algorithm

GA is a metaheuristic algorithm inspired by the process of natural selection in biological organisms [31]. It is used to solve optimization and search problems by mimicking the process of natural evolution, reflecting the process of natural selection where the fittest individuals are selected for reproduction to produce offspring of the next generation. It is commonly used for optimization problems, such as vehicle routing, staff scheduling, engineering, and so on, to find a feasible solution to a complex problem for maximum efficiency. GA utilizes various operators during the search process. These operators include encoding schemes, crossover, mutation, and selection [32], as shown in Figure 3.

4.2.1. Chromosome Design

The chromosome is designed as shown in Figure 4, which is merely an example to explain the structure of the chromosome. The first gene of the chromosome represents the location of the candidate for the newly constructed logistics center and outputs a random number between 1 and 25. The genes from the 2nd to the 26th represent the demand region nodes, and 25 random numbers ranging from 0 to 59 are outputted. The last gene represents the number of vehicles, assigned to the newly constructed logistics center, and outputs a random number between 1 and 6. The 2nd to the 26th gene in the chromosome is composed of a random number ranging from 0 to 59. Genes 0–9 are assigned to Vehicle 1, 10–19 to Vehicle 2, 20–29 to Vehicle 3, 30–39 to Vehicle 4, 40–49 to Vehicle 5, and 50–59 to Vehicle 6. Subsequently, the genes assigned to each vehicle are sorted through the decoding process, which can be understood as shown in Figure 5. The first and last genes in the chromosome are the most crucial elements of the algorithm. Through the first gene, it is possible to explore all the possibilities of candidate locations, while the last gene allows for the exploration of all possibilities for vehicles allocated to the existing and new logistics centers.

Figure 5 illustrates the process of decoding the chromosome into delivery routes for each vehicle, based on the decoding result of the first chromosome example in Figure 4. In the first decoding process, the genes corresponding to the six vehicles are sorted in ascending order, and the route for each vehicle is set according to the order of nodes that match the gene that is sorted in ascending order. In the second phase, the beginning and end of the delivery routes for each vehicle are randomly assigned to either the existing logistics center or a new logistics center. At this time, the number of vehicles departing from the new logistics center is output to be the same as the number of the last gene of the chromosome and it is ensured that the logistics center from which a vehicle departs is the same as the one to which it returns.

4.2.2. Fitness Function, Selection, Crossover, and Mutation

After decoding the chromosome through a fitness function, the CO₂ emissions are calculated based on the total delivery distances of the vehicles. Subsequently, the processes of selection, crossover, mutation, and evaluation of fitness values are repeated until the termination criteria of the algorithm are met. Since the aim of this study is to minimize CO₂ emissions, chromosomes with lower CO₂ emission values have a higher probability of surviving into the next generation.

During the roulette wheel selection process, chromosomes that are selected are used to create the next generation through a crossover process. The crossover is performed using a two-point method to the gene from the 2nd to the 26th and a 1-point method to the first and last genes, as illustrated in Figure 6. If there are duplicate numbers within the gene from the 2nd to the 26th after the crossover, they are replaced with another number between 0 and 59. Subsequently, a one-point random mutation occurs, where a randomly selected gene within the chromosome is altered. These processes are repeated multiple times, inheriting chromosomes with lower fitness to the next generation, and each generation progressively produces routes that consume lower CO₂ emissions.

5. Numerical Experiment

In the existing logistics network, a logistics center located in Gunpo, which is a suburban area of Seoul, handled all of the demand in Seoul. However, there is a plan to construct a new logistics center within the Seoul urban area to reduce CO₂ emissions and establish an eco-friendly logistics network. Therefore, in the numerical experiments, the carbon emissions of the existing logistics network are compared with those of the new logistics network, and the location within Seoul that results in the lowest carbon emissions is selected for the logistics center. A total of six delivery vehicles are operated, and they are distributed to the existing and new logistics centers according to the optimal delivery routes. Additionally, since the company has a fixed budget for logistics center construction, the size of the new logistics center that can be built varies by local governments, based on the 2023 real estate prices in Seoul. This study only considers the routes between local governments and does not plan routes between each pharmacy within local governments. Therefore, delivery delay times are assigned based on the number of pharmacies in each local government. Furthermore, considering the circumstances of the ‘L’ medical company, 1-ton trucks are used, and the maximum operation time is based on the standard working hours per day in South Korea. Lastly, the operating time for each vehicle is calculated as the sum of the round-trip travel time from the logistics center to the demand area, the travel time between demand areas, the delay time at the demand area, and the unloading time for the number of demands. CO₂ emissions per kilometer are derived by considering the type of vehicle.

5.1. Data Analysis

The mathematical model in this study uses input parameters such as demands, locations of pharmacies in Seoul, capacity of vehicles, and volume of packaged products. The parameters above are derived from the actual data from the ‘L’ medical company in South Korea. Therefore, data analysis is conducted to derive insights and the input parameters for the developed mathematical model. The raw data are shown in Figure 7 to understand the demand of the pharmacy among various data. Seoul has a total of 25 local governments, and there are 958 pharmacies that receive products from the ‘L’ medical company. Additionally, the demand for products by the district is set based on the average value of the ‘L’ medical company’s actual data over one month.

The ‘L’ medical company uses 1-ton trucks due to the narrow roads when delivering. The maximum loading amount per vehicle is set according to the volume of the 1-ton truck and the size of the ‘L’ medical company’s product. As shown in Figure 8, each carton contains 40 boxes of products, and a vehicle can accommodate 40 cartons, which means a vehicle can carry a total of 1600 boxes. In addition, each vehicle cannot work on delivery tasks for more than 480 min a day, and the working time of the vehicle consists of the sum of delivery time and loading/unloading time.

5.2. Parameters Setting

The specific system parameter values are shown in

Table 1. System parameters.

Parameter	Value
$o_r$	{1100, 247, 165, 352, 591, 688, 157, 150, 427, 157, 180, 195, 300, 142, 472, 210, 232, 420, 300, 412, 180, 300, 375, 225, 135}
$q_r$	{68, 16, 10.5, 23, 24.5, 14.5, 10, 9.5, 28, 10, 11.5, 12.5, 20, 9, 31, 13.5, 15, 27.5, 19.5, 27, 11.5, 19.5, 24.5, 14.5, 8.5}
$c_r$	{4056, 7368, 8112, 8112, 8112, 6211, 8112, 8112, 8112, 8112, 8112, 6652, 6132, 7753, 4304, 5255, 8112, 5691, 6964, 6795, 5041, 8112, 7382, 7368, 8112}
$e$	1200
$b$	1600
$s$	1/3
$p$	0.1
$mw$	480
$m$	100,000

. Seoul has 25 local governments, and the demands of each local government’s pharmacies are given in the value of $o_r$. Although the delivery routes between the logistics center and the pharmacy demand areas are considered, the routes between each pharmacy are not. Therefore, vehicles will stay in the demand areas according to the number of pharmacies in local governments ($q_r$). Due to the real estate prices in Seoul, there are limitations on the size of logistics centers that can be constructed in each local government. Therefore, the maximum number of products that can be delivered is assigned through $c_r$. According to Jabali [33], the CO₂ emission rate per kilometer for a 1-ton truck is 1200 g. As described in Section 5.1, the capacity of the vehicle allows for 1600 products. Additionally, according to the Seoul Research Data Service, the average speed of vehicles in Seoul is about 20 km/h. Based on the standard working hours per day in South Korea, each vehicle cannot work for more than 480 min.

The genetic algorithm is evaluated by comparing the optimal solution derived by CPLEX. After this process, GA is applied to the actual situation, and parameters for the GA are set as shown in

Table 2. Parameters for the genetic algorithm.

Parameter	Value
Number of populations	1000
Number of generations	10,000
Probability of crossover	0.5
Probability of mutation	0.1

.

5.3. Results

Initially, this study compared the vehicle routes and CO₂ emissions for cases where logistics centers were constructed in the ‘Gangnam’, ‘Gwangjin’, and ‘Guro’ areas to verify the performance of the GA. CPLEX took over 48 h to find the optimal solution, which was considered an inefficient process. Subsequently, comparing the optimal solution from CPLEX with the results from the GA revealed a difference of less than 5%. The specific compared results of CPLEX and GA are shown in

Table 3. Compared results of CPLEX and GA.

Selected Location	$\mathit{F}$	Delivery Orders		Total CO2 Emissions (g/km)
		CPLEX	GA	CPLEX	GA
Gangnam	1	0-15-23-25-24-16-0	0-15-23-25-24-14-13-0	264,000	266,400
	2	1-19-3-7-17-1	1-19-3-7-17-1
	3	0-9-8-20-5-6-0	0-9-8-20-5-6-0
	4	0-21-14-22-13-0	0-21-22-16-0
	5	1-18-4-11-10-26-12-1	1-18-4-11-10-26-12-1
	6	1-2-1	1-2-1
Gwangjin	1	1-2-19-1	1-2-19-1	232,800	234,000
	2	1-7-3-1	1-7-3-1
	3	1-16-22-25-24-17-1	1-16-22-25-24-17-1
	4	0-14-15-23-5-20-8-0	0-14-15-23-5-20-8-0
	5	0-13-21-6-9-0	0-13-21-6-9-0
	6	1-12-18-4-11-10-26-1	1-12-26-18-4-11-10-1
Guro	1	1-17-7-3-19-1	1-17-7-3-19-1	214,800	217,200
	2	1-16-2-1	1-16-2-1
	3	1-13-6-9-1	1-13-6-9-1
	4	1-15-24-25-22-14-1	1-15-25-24-22-14-1
	5	1-8-20-5-21-1	1-8-20-5-21-1
	6	1-23-11-10-4-18-26-12-1	1-23-4-11-10-26-12-18-1

. Therefore, by utilizing the GA, this study aimed to find the most optimal location among the 25 local governments of Seoul, and the results can be found in

Table 4. Results of GA.

Selected Location (Node Number)	Total Delivery Distance (km)	Total CO2 Emissions (g/km)
Only Gunpo (0)	478	573,600
Gangnam (2)	222	266,400
Gangdong (3)	210	252,000
Gangbuk (4)	207	248,400
Gangseo (5)	233	279,600
Gwanak (6)	179	214,800
Gwangjin (7)	195	234,000
Guro (8)	181	217,200
Geumcheon (9)	201	241,200
Nowon (10)	226	271,200
Dobong (11)	225	270,000
Dongdaemun (12)	159	190,800
Dongjak (13)	187	224,400
Mapo (14)	210	252,000
Seodaemun (15)	188	225,600
Seocho (16)	263	315,600
Seongdong (17)	198	237,600
Seongbuk (18)	176	211,200
Songpa (19)	222	266,400
Yangcheon (20)	211	253,200
Yeongdeungpo (21)	198	237,600
Yongsan (22)	219	262,800
Eunpyeong (23)	207	248,400
Jongno (24)	176	211,200
Jung (25)	172	206,400
Jungnang (26)	205	246,000

.

Before the examination of cases, the existing logistics network of the ‘L’ medical company is examined. The company operates a logistics center that is only located in Gunpo, a suburb of Seoul, for deliveries to pharmacies. The six vehicles move until they meet the demand of pharmacies located in the 25 local governments within Seoul. Under the current logistics network environment, using only the logistics center located in Gunpo, the total CO₂ emissions amount to 577,360 g/km. Next, when comparing the CO₂ emissions resulting from the construction of logistics centers by local governments, constructing in Dongdaemun resulted in the lowest CO₂ emissions, at 190,800 g/km. Following Dongdaemun, the area with the next lowest CO₂ emissions is Jung, emitting 206,400 g/km. This means that compared to the existing logistics network, there is a 66.74% reduction in CO₂ emissions with the new logistics network. Dongdaemun and Jung are located in the heart of Seoul, offering excellent accessibility. Additionally, while Yongsan and Seocho are also located in the center of Seoul, the high real estate prices in these areas impose limitations on the size of logistics centers, leading to a larger allocation of vehicles to Gunpo and an increase in CO₂ emissions due to the increased travel distance. Therefore, the comparison is made between the existing logistics network, the optimal solution, and areas located in the center of Seoul, which have shown high carbon emissions, as in

Table 5. Three compared cases.

Logistics Network (Case Number)	$\mathit{F}$	Delivery Orders	Total CO2 Emissions (g/km)
Only Gunpo (1)	1	0 → 1→ 0 → 12 → 22 → 14 → 18 → 0	573,600
	2	0 → 7 → 19 → 15 → 0
	3	0 → 24 → 23 → 17 → 16→ 0
	4	0 → 2 → 9 → 10 → 3 → 0
	5	0 → 25 → 11 → 21 → 4 → 8 → 0
	6	0 → 20 → 5 → 0 → 13 → 6 → 0
Gunpo and Dongdaemun (2)	1	1 → 18 → 4 → 11 → 10 → 26 → 12 → 1	190,800
	2	1 → 13 → 6 → 9 → 8 → 15 → 23 → 1
	3	1 → 2 → 16 → 1
	4	1 → 24 → 25 → 1
	5	1 → 17 → 7 → 19 → 3 → 1
	6	1 → 22 → 14 → 21 → 20 → 5 → 1
Gunpo and Yongsan (3)	1	1 → 14 → 24 → 4 → 11 → 10 → 1	262,800
	2	1 → 16 → 19 → 3 → 1
	3	1 → 18 → 26 → 12 → 7 → 17 → 1
	4	0 → 2 → 0
	5	1 → 9 → 21 → 22 → 25 → 23 → 15 → 1
	6	0 → 6 → 13 → 8 → 20 → 5 → 0

.

Table 5 shows the comparison of 3 cases. In the first case, the existing logistics networks of the ‘L’ medical company are described, where all vehicles start from Gunpo, visit all demand points, and then return to Gunpo. In the second case, it represents the delivery routes based on the optimal results, where all vehicles start from the logistics center in Dongdaemun, to reduce CO₂ emissions according to delivery distance. In the case of Dongdaemun, the relatively low real estate prices allow for the construction of a logistics center large enough to accommodate the demands of all pharmacies in Seoul. This is why all vehicles were able to start from the Dongdaemun logistics center. The final case focuses on the results for Yongsan, an area located in the center of Seoul that has shown high CO₂ emissions despite its central location. Yongsan, being an area with high real estate prices, makes it challenging to build a logistics center large enough to accommodate the demand from all pharmacies in Seoul. As a result, while 4 vehicles start from the logistics center in Yongsan, 2 vehicles should start from Gunpo, leading to an increase in delivery distances and, consequently, higher CO₂ emissions.

6. Conclusions

This study proposed the optimal location for an urban logistics center to minimize the total CO₂ emissions to make the logistics network of the ‘L’ medical company sustainable. According to the numerical experiment results, the location with high accessibility and capacities was identified as the location that could minimize the total CO₂ emissions. Additionally, in areas adjacent to the optimal location, which have excellent accessibility but insufficient logistics center capacity due to high real estate prices, the increased delivery distance resulted in higher CO₂ emissions. These findings demonstrate that the CO₂ emissions were reduced by 66.74% compared to the existing logistics network of the ‘L’ medical company.

The contributions of this study can be divided into practical and theoretical implications. Firstly, this study proposes a mathematical model that can derive the optimal location of logistics centers to minimize the total CO₂ emissions from all vehicles. Selecting the location of a logistics center requires consideration of various factors, including economic, environmental, social, and political aspects. In this situation, the theoretical implication of this study is that it establishes a model for selecting the location of logistics centers based on the environmental aspects to construct a sustainable logistics network. The practical implications of this study are as follows. This study reflects the actual trends in the logistics industry and provides important insights for company decision making. The logistics industry is highly interested in constructing smart and green logistics infrastructure and the construction of MFC in urban areas as national projects [34]. In this situation, this study is meaningful in that it proposed the optimal location for a new logistics center using actual data from the ‘L’ medical company. It can be considered a highly realistic study as it incorporates actual data and reflects the logistics network currently in operation from the ‘L’ company. Recently, industries that provide delivery services by using land vehicles such as buses, taxis, and trucks are seeking to reduce environmental burdens by utilizing electric vehicles [35]. In this situation, the result in minimizing CO₂ emissions in the study is evaluated as one of the suitable methods to deal with environmental issues and enable a company to practice sustainable management.

This study only considered routing between logistics centers and demand areas and did not account for routing between pharmacies within demand areas. CO₂ emissions vary depending on the vehicle’s speed, the length of congested areas, and the road’s gradient. Therefore, future research plans to consider additional factors that can influence vehicle CO₂ emissions, as mentioned previously. Moreover, as these considerations increase, there is a possibility that the optimal location may shift to another location. Additionally, constructing a smaller-scale logistics center implies the need for multiple logistics centers in Seoul. Thus, research can be conducted to determine the optimal number of logistics centers and their optimal locations. Moreover, factors for selecting the location of urban logistics centers may include not only environmental factors but also various economic, social, and political factors. Therefore, future studies will address practical considerations for logistics center location selection by integrating factors such as infrastructure, geographical connectivity, transportation costs, and market demand [36]. Also, this study has set a single objective of minimizing CO₂ emissions and utilized heuristic algorithms to derive insights. However, future studies will design reward functions that assign weights to multiple optimization objectives such as equilibrium in delivery volume per vehicle and suitability for government regulations [37]. These multi-objective functions will be used in reinforcement learning to address the problem [38]. Furthermore, the study aiming to ensure sustainable management of resources and contribute to environmental protection and public health through the implementation of green logistics systems is actively underway [39]. Therefore, future studies also aim to explore optimizing the network of waste collection vehicles in urban areas or optimizing systems that bundle delivery tasks to adjacent destinations for execution.