Optimized Supply Chain Management of Rice in South Korea: Location–Allocation Model of Rice Production

: Planning for optimized farming with the aim of providing ideal site and cultivar selection is critical for a stable and sustainable supply of rice with sufﬁcient quantity and quality to customers. In this study, a range of morphological characteristics and yield of eight rice cultivars that are commonly cultivated in Korea were investigated from 2005 to 2020. All morphological characteristics were signiﬁcantly different among the eight rice cultivars. The dataset of morphological characteristics and yield was used to isolate groups of similar rice cultivars. The k -means clustering method was used to group the rice cultivars. Three groups (Group 1, Group 2, and Group 3) were created. Most cultivars were in Group 1. High-yielding rice cultivars were in Group 2, while the rice cultivars in Group 3 had the lowest rice grain yield. After grouping these rice cultivars, ideal farming locations for all three rice cultivar groups were identiﬁed to reduce transportation cost using an optimized location–allocation model. Simulation results suggested the following: (1) Group 1 should be produced in Jellanam-do (south west region), (2) Group 2 should be produced in Chungcheongnam-do (central west region), and (3) Group 3 should be mainly produced in the central west region of South Korea. Simulation results showed the potential to reduce transportation cost by around 0.014%. This can also reduce 21.04 tons of CO 2 emission from a freight truck. Because these eight cultivars only make up 19.76% of the total rice production in South Korea, the cost reduction proportion was only 0.014% of total revenue. In future studies, more rice cultivars should be investigated to increase the efﬁciency of the model performance. selecting clusters location–allocation


Introduction
In most Asian countries, including South Korea, rice has been the most important crop for thousands of years. In South Korea, rice is the stable crop of farms, accounting for about 85% of total grain production and over 49% of total agricultural income [1]. For the last few decades, rice yield has been increased through selection of high-yield varieties that are better suited for the Korean climate and taste [1]. Rice yield sharply increased between 1960 and 1977 and then gradually increased after 1981 [2]. However, since 1990, total rice production has been continuously decreasing due to decreasing rice harvesting areas [2]. Due to growing urbanization and climate change, arable areas for crops in South Korea have been continuously decreasing. This might lead to an increase in food shortage and food prices in the future. Moreover, due to limited available arable land in South Korea, most of the agricultural land is currently situated in the southern regions, thus requiring long distance transportation to deliver agricultural products to urban areas, which are

Modeling Framework Design
This study was conducted in three steps: (1) field experiment, (2) identification of cultivar groups via k-means clustering, and (3) location-allocation of cultivar groups to ideal farming sites. Figure 1 shows an overview of the proposed research framework. Data for morphological characteristics and yield of the subject crop cultivars were collected from a field study (see Section 2.2 for more detail). The subject cultivars were classified into different cultivar groups via k-means clustering based on their morphological similarity. Initially, the clustering algorithm assigned the subject cultivars to k cultivar groups. After evaluating the initial classification, the algorithm updated centroids of each cultivar group and assigned cultivars to new cultivar groups according to the morphological similarity between a cultivar and a centroid of each cultivar group. This new classification was evaluated and compared with the evaluation result of the previous classification. This process continued until there was no enhancement in the evaluation. Section 2.3 shows in detail the equations used in the clustering process. The finalized cultivar groups were sent to the location-allocation process. In this process, multiple alternatives were considered until the optimization algorithm found the ideal farming location in terms of the total transportation cost of a supply chain. The generalized reduced gradient (GRG) nonlinear algorithm written in JAVA was used for the optimization. Detailed explanation of the optimization is given in Section 2.4.
Agronomy 2021, 11, x FOR PEER REVIEW 3 of 15 characteristics is organized to isolate groups of similar rice cultivars through k-means clustering analysis. Finally, a location-allocation model is developed for selecting the ideal farming site and rice cultivar group to minimize transportation cost.

Modeling Framework Design
This study was conducted in three steps: (1) field experiment, (2) identification of cultivar groups via k-means clustering, and (3) location-allocation of cultivar groups to ideal farming sites. Figure 1 shows an overview of the proposed research framework. Data for morphological characteristics and yield of the subject crop cultivars were collected from a field study (see Section 2.2 for more detail). The subject cultivars were classified into different cultivar groups via k-means clustering based on their morphological similarity. Initially, the clustering algorithm assigned the subject cultivars to k cultivar groups. After evaluating the initial classification, the algorithm updated centroids of each cultivar group and assigned cultivars to new cultivar groups according to the morphological similarity between a cultivar and a centroid of each cultivar group. This new classification was evaluated and compared with the evaluation result of the previous classification. This process continued until there was no enhancement in the evaluation. Section 2.3 shows in detail the equations used in the clustering process. The finalized cultivar groups were sent to the location-allocation process. In this process, multiple alternatives were considered until the optimization algorithm found the ideal farming location in terms of the total transportation cost of a supply chain. The generalized reduced gradient (GRG) nonlinear algorithm written in JAVA was used for the optimization. Detailed explanation of the optimization is given in Section 2.4.

Field Experiment
A field experiment was conducted at Jeollanamdo Agricultural Research and Extension Center in Jeollanam-do, South Korea, during the growing seasons of 2005-2020 (35 • 1 19.35 • N, 126 • 38 29.65 • E). A total of eight different medium to late maturing rice (Oryza sativa subsp. Japonica) cultivars, namely Ilmi, Donjin-1, Dongan, Nampyoung, Saegehwa, Hopyoung, Mipum, and Hyunpum, were used in this experiment. These cultivars were selected because they are commonly grown by farmers in the southern regions of South Korea. The characteristics of each rice cultivar are summarized in Table 1. The cultivars were arranged in a completely randomized design. Due to the limited size of the field, each cultivar was planted in different years; only Ilmi was planted during 2005-2020.

Mipum
Mipum is mainly cultivated in inland plains south of Chungnam, South Korea. This variety has high rice quality and is resistant to stripped leaf blight disease.

2012-2020
Hyunpum Hyunpum is mainly cultivated in the southwest coastal area and plains south of Pyeongtak in South Korea. This rice cultivar has high eating quality and resistance to white leaf blight and stripped leaf blight diseases.

2015-2020
According to the National Institute of Agricultural Science, Rural Development Administration (RDA) (available online at http://soil.rda.go.kr/soil/soilmap/characteristic. jsp), the soil type is Deogpyeong (silt loam). During the rice growing season (June-August) of 2005-2020, the average temperature and total rainfall were 25.04 • C and 1165 mm, respectively. The average temperature and total rainfall during the rice growing season (June-August) of each year are shown in Figure 2.
were selected because they are commonly grown by farmers in the southern regions of South Korea. The characteristics of each rice cultivar are summarized in Table 1. The cultivars were arranged in a completely randomized design. Due to the limited size of the field, each cultivar was planted in different years; only Ilmi was planted during 2005-2020.

2009-2018
Mipum Mipum is mainly cultivated in inland plains south of Chungnam, South Korea. This variety has high rice quality and is resistant to stripped leaf blight disease.

2012-2020
Hyunpum Hyunpum is mainly cultivated in the southwest coastal area and plains south of Pyeongtak in South Korea. This rice cultivar has high eating quality and resistance to white leaf blight and stripped leaf blight diseases.

2015-2020
According to the National Institute of Agricultural Science, Rural Development Administration (RDA) (available online at http://soil.rda.go.kr/soil/soilmap/characteristic.jsp), the soil type is Deogpyeong (silt loam). During the rice growing season (June-August) of 2005-2020, the average temperature and total rainfall were 25.04 °C and 1165 mm, respectively. The average temperature and total rainfall during the rice growing season (June-August) of each year are shown in Figure 2.  Seeds were sown in a seedling nursery box, and the seedlings were transplanted to a paddy field. Then, 25-day-old seedlings were transplanted with one pot seedling per hill using a planting density of 30 cm × 14 cm (23.8 hills m −2 ) on June 5. During the growing season, fertilizer was applied twice (mid-June and mid-July). The total rate of fertilizer applied to the plot was 90/45/57 kg of N/P/K ha −1 .
All morphological measurements were done in three replicates. The size of each replicate differed according to the type of measurement. Total plant height and number of stems per m 2 were measured at 10 (mid-June), 35 (early July), 50 (mid-July), 65 (early August), and 80 (mid-August) days after transplanting. Plant height was measured as the length from ground level to the bottom of the plant's panicle. The length of the panicle was measured as the length from the bottom to the top of the plant's panicle. Total plant height was measured as the sum of the plant height and length of the panicle. Heading date, plant height, and length of panicle were measured between mid-August and mid-September. Heading date was determined as the date of observing 40% of flowering panicles. The number of days from transplanting to the flowering date was recorded for further analysis. The fertility rate was measured 20 days after the flowering date. The fertility rate was calculated using the number of filled spikelets and total number of spikelets (panicles of one plant per replicate). Spikelets were squeezed using the index finger and thumb together to determine if they were filled or not. Both completely and partially filled spikelets were considered as fertile grains. Matured rice plants in m 2 were harvested from three random places within each plot between early and mid-October. At harvest, the yield components, including the number of spikelets, weight of 1000 spikelets, rate of ripened grain, and rice yield, were measured. Harvested grain were hand threshed and oven dried at 45 • C until the final moisture content was 14-15%. After drying the samples, rough grains were subjected to a series of milling process. Two different rice milling machines were used in each step. In the first step of the milling process, a SY88-TH (Ssang Yong, South Korea) was used. A MC-90A (Toyorice Co. Ltd., Japan) was used in the second step. The first step of the milling process removed husk from the whole grain or paddy to obtain the whole brown rice grain (BR). Brown rice contains an outer bran layer that is brown in color. The second step of the milling process was to remove the brown layer and to obtain polished or white rice (WR). The number of spikelets was counted for each harvested panicle. The rate of ripened grain was measured to test grain filling. It was determined by counting the number of rice grains that sank in water after the water settled. Regression analysis was conducted to test the effect of cultivars on measured morphological characteristics and yield. Correlation between morphological characteristics and yield of eight rice cultivars were tested using Pearson's correlation analysis.

k-Means Clustering Analysis
The clustering method was used to organize multivariate dataset collected from field research into isolated groups of similar rice cultivars. Morphological characteristics, including days from transplanting date to flowering date, number of panicles per m 2 , number of spikelets per panicle, number of spikelets per m 2 , plant height, length of panicle, fertility rate, rate of ripened grain, unhulled rice yield, BR yield, and WR yield, were used to identify groups of similar rice cultivars. Note that the production cost (or price) of each cultivar was not considered in this study because it is not useful to identify groups with similar morphological characteristics. In other words, the morphological characteristics of cultivar groups can vary even if their prices are the same. The economic aspect will be considered in Section 2.4. Equation (1) represents the k-means clustering algorithm used to identify k groups based on the morphological characteristics [13,14] . . , z n ] T ; and µ i is a centroid (or mean value) of cluster i. Note that C represents a cluster set, and z is a vector with normalized scores of n cultivars. The normalized score z j was computed with Equation (2).
where x jl is the value of morphological characteristic l for cultivar j; µ l is the mean of morphological characteristic l over cultivars; and σ l is the standard deviation of morpholog- ical characteristic l over cultivars. The clustering was conducted over multiple iterations, and it was stopped if the current iteration did not have any significant improvement in Equation (1) compared to the previous iteration. In other words, the clustering was stopped if the improvement of the value of Equation (1) was smaller than threshold θ.

Optimized Location-Allocation Model for Ideal Farming Site
The k clusters identified in Section 2.3 were allocated based on a location-allocation model for minimizing transportation cost. Table 2 and Equation (3) show the definition of symbols and the devised optimization model, respectively.

Symbol Definition C
A set of cultivar clusters (or cultivar groups), c ij Unit transportation cost from cluster i to market j, i ∈ C and j ∈ M.
q ij Attractiveness from cluster i to market j, i ∈ C and j ∈ M, 0 ≤ q ij ≤ 1.
f ij Transportation quantity (or material flow) from cluster i to market j, i ∈ C and j ∈ M.
Euclidean distance between cluster i and market j, i ∈ C and j ∈ M.
Equation (3) was used to compute total transportation cost between k clusters (or groups) and markets. Because the equation tends to identify locations of cultivar clusters (i.e., V 1 , . . . , V k ) with the minimum total transportation cost to markets, we can find cost-effective locations. However, unlike the location-allocation problem for general commodities, finding a field close to market may result in inappropriate allocation of rice fields. A farmer may want to cultivate a certain type of rice due to its environmental adaption or specific needs (e.g., weather condition, soil quality, land lease fee, etc.). Considering the preference of farmers, this study devised an attractiveness weight w ij from cluster i to market j. Note that w ij is between 0 and 1. Attractiveness can be achieved by conducting a survey of farmer preferences. Alternatively, it can also be computed based on the proportion of existing harvested area of each group in the entire harvested area in each field. In this case, we assumed that farmers preferred to determine existing locations of rice paddy fields. In fact, farmers consider multiple factors, such as climate, harvesting skill (or familiarity), soil type, and production and logistic costs, to determine harvesting fields. Because the objective function tended to minimize transportation cost, the attractiveness weight was subtracted from 1 (i.e., penalty on the transportation cost). By doing this, the objective function increased as the attractiveness weight decreased. Equation (4) is a constraint to only consider available fields for cluster i. Note that potential sites in P i were determined by environmental factors, such as weather, temperature, soil type, geography, etc.

Morphological Characteristic Evaluation
Total plant heights (sum of plant height and length of panicle) of all eight rice cultivars were measured at transplantation date, mid-June, early July, mid-July, early August, and flowering date (mid-August) (Figure 3). Most cultivars showed similar growth patterns. Plant growth rates at 10, 25, 40, and 55 days after transplantation were 16-18, 19-28, 35-42, 63-74, and 81-87% of total plant heights of full-growth plants, respectively (data not shown). Unlike other cultivars, Hopyoung showed a big increase in total plant height between mid-July (45% of total plant height) and early August (81% of total plant height).
Euclidean distance between cluster i and market j, ∈ and ∈ .

Morphological Characteristic Evaluation
Total plant heights (sum of plant height and length of panicle) of all eight rice cu vars were measured at transplantation date, mid-June, early July, mid-July, early Augu and flowering date (mid-August) (Figure 3). Most cultivars showed similar growth p terns. Plant growth rates at 10, 25, 40, and 55 days after transplantation were 16-18, 1 28, 35-42, 63-74, and 81-87% of total plant heights of full-growth plants, respectively (d not shown). Unlike other cultivars, Hopyoung showed a big increase in total plant hei between mid-July (45% of total plant height) and early August (81% of total plant heigh The morphological characteristics and yield of eight rice cultivars are summarized Tables 3 and 4, respectively. All morphological characteristics were significantly differ by cultivar. The number of days from transplanting date to flowering date varied from to 80 days (Table 3)   The morphological characteristics and yield of eight rice cultivars are summarized in Tables 3 and 4, respectively. All morphological characteristics were significantly different by cultivar. The number of days from transplanting date to flowering date varied from 73 to 80 days (Table 3) Among the cultivars, Ilmi had the highest percentage of fertility rate (92.71%) and ripened grains (90.53%) ( Table 4), while Dongan had the lowest fertility rate. Donjin-1ho and Saegehwa had lower percentage of ripened grains. Hopyoung had the lowest unhulled rice grain yield (6.84 Mg ha −1 ), while Dongan had the highest unhulled rice grain yield (7.38 Mg ha −1 ). Saegehwa had the second highest unhulled rice yield (7.35 Mg ha −1 ) after Dongan. However, it had the highest yield of brown rice (6.18 Mg ha −1 ) and white rice (5.68 Mg ha −1 ). Dongan had the second highest yield of white rice (5.60 Mg ha −1 ) after Saegehwa. Correlation between morphological variables and yield were tested, and the results are shown in Table 5. The number of spikelets per m 2 was positively and moderately correlated with yield of brown rice and white rice. The number of spikelets and the length of panicle were positively correlated with each other, and the length of panicle was also positively and moderately correlated with grain yield. The number of filled spikelets per m 2 was positively and moderately correlated with white rice yield. It was observed that Saegehwa had the largest number of filled spikelets. Its white rice grain yield was highest among the cultivars. Similar results were reported by Li et al. [15] who found a strong positive relationship between filled grain number and grain yield. Plant height was negatively correlated with the number of panicles per m 2 . Similar results were reported by Li et al. [15] who found that the yield of japonica hybrid was negatively correlated with its plant height. However, plant height was positively correlated with the yield for indicas and japonica inbred. Based on these results, breeders focusing on the eight cultivars (japonica) used in this study might need to consider decreasing the plant height to improve yield potential. The rate of ripened grain was negatively correlated with yield. This might be because the number of spikelets was negatively correlated with the rate of ripened grain.

k-Means Clustering Analysis
Grouping the data of morphological characteristics and yield of rice collected from the field experiment of 2005-2020 with the k-means clustering algorithm resulted in three clusters, as shown in Figure 4. The result was achieved by conducting four iterations with the object value of 10.3633 (see Equation (1)). The threshold (θ) of the clustering was 12.00. Initial values of µ_1, µ_2, and µ_3 were 0.4364 (median between normalized max and normalized min), 8.1662 (normalized max), and −7.2935 (normalized min), respectively. Based on the results of data processing with k-means clustering, five rice cultivars were included in Group 1: Ilmi, Dongan, Nampyoung, Hopyoung, and Mipum. DongJin-1 and Saegehwa were in Group 2, while Hyunpum was in Group 3. Each group was significantly different at α = 0.10. The p-values of significance between Groups 1 and 2, between Groups 2 and 3, and between Groups 1 and 3 were 0.083, 0.083, and 0.085, respectively. Note that the numbers in Figure 4 show centroids of the three clusters.
Morphological characteristics and yield for all three clusters are summarized in Tables 6 and 7   Group 3 had the highest fertility rate (91.94%), while Group 2 had the lowest fertility rate (90.19%). Group 1 had the highest percentage of ripened grain (88.64%). Group 2 had the largest grain yield of unhulled rice (7.37 Mg ha −1 ), brown rice (6.17 Mg ha −1 ), and white rice (5.66 Mg ha −1 ), while Group 3 had the lowest grain yield.

Location-Allocation of Cultivar Groups
Based on the results from Section 3.2, ideal locations for cultivating the three cultivar groups where transportation cost could be reduced were identified via the optimization model addressed in Section 2.4. Note that Jeju-do in South Korea was ignored in this study

Location-Allocation of Cultivar Groups
Based on the results from Section 3.2, ideal locations for cultivating the three cultivar groups where transportation cost could be reduced were identified via the optimization model addressed in Section 2.4. Note that Jeju-do in South Korea was ignored in this study because it only has 43 ha to produce all types of rice. As of 2020, the total harvested area of rice was 726,732 ha with production quantity of 3,631,000 tons in South Korea [16]. Selected cultivars accounted for 23.84% of total production. As mentioned in the Introduction, most harvested areas are located in Jeollanam-do, which is far from the metropolitan area (i.e., Gyeonggi-do) with 50.24% of total consumption (see Table 8). As shown in Table 8, Jeollanam-do is the furthest province from the metropolitan area, with an average distance of 238.38 km. Jeollanam-do produces 356,122 Mg year −1 of white rice (see Table 9). Its estimated transportation cost is $123,089,666, which accounts for 14.14% of the total revenue of $870,439,707. On the other hand, Chungcheongbuk-do with the minimum average travel distance of 145.25 km produces 11,507.86 Mg year −1 of white rice (see Table 9), and its transportation cost is $2,423,670, which only accounts for 8.62% of the total revenue of $28,127,784. These values imply that the transportation cost in existing locations of rice fields might be too high. Distance, unit transportation cost, and harvested area data (shown in Table 8) were used to determine optimal locations of the three cultivar groups.   Table 9 shows the attractiveness weight and demand for rice paddy fields in South Korea. The attractiveness was computed based on the proportion of existing harvested area of each group in the entire harvested area in each field. This study assumed that existing locations of rice paddy fields were determined by farmers who considered multiple factors, such as climate, soil type, and production and logistic costs, to maximize their profit (see Section 2.4). Group 1 (C1) is the most popular cultivar group in Gyeonggi-do (F1), Chungcheong-nam-do (F4), Jeollabuk-do (F5), Jeollanam-do (F6), and Gyeongsangnamdo (F8). On the other hand, Group 2 (C2) is a popular cultivar group in Gangwon-do (F2), Chung-cheongbuk-do (F3), and Gyeongsangbuk-do (F7). Group 3 is not a popular cultivar group in any province. In addition, according to Hong and Kwon [16], each Korean individual consumes about 59.2 kg of rice per year. Thus, the demand can be estimated by multiplying the population by an individual's rice consumption. The population in each province is shown in Figure 5.
sangnam-do (F8). On the other hand, Group 2 (C2) is a popular cultivar group in Gangwon-do (F2), Chung-cheongbuk-do (F3), and Gyeongsangbuk-do (F7). Group 3 is not a popular cultivar group in any province. In addition, according to Hong and Kwon [16], each Korean individual consumes about 59.2 kg of rice per year. Thus, the demand can be estimated by multiplying the population by an individual's rice consumption. The population in each province is shown in Figure 5.   Figure 5a shows the distribution of rice paddy and other fields in South Korea. An area with yellow color represents rice paddy field, and an area with pink color represents other farming field. The estimated objective value of existing fields is approximately $13,648,336. The location-allocation result is shown in Figure 5b with an objective value of $13,406,015. Because the proposed approach tends to find locations of rice paddy fields depending on transportation cost to markets, it can reduce $242,321.34 from the existing objective value.
The results revealed that each group was fully allocated to a certain area with major markets to minimize the transportation cost of rice. For example, in the solution, Jellanamdo was calculated as producing 353,782.56 Mg year −1 of rice, and its transportation cost was $122,281,405, which is a reduction of $808,260 from $123,089,666 (Table 10). Rice paddy fields in Chungcheongnam-do and Jeollabuk-do were popular due to their accessibility to markets (i.e., Gyeonggi-do and Gangwon-do). In fact, these provinces are located in the middle of South Korea, so they have low average transportation costs. In addition, they have large rice paddy fields (i.e., 16,255.2 ha in Chungcheongnam-do and 18,745.1 ha in Jeollabuk-do). As shown in Table 10, Group 1 (C1) was mainly located in Jeollanam-do (63.87%) and Gyeongsangnam-do (34.99%) because of their attractiveness, travel distance to markets, and size of harvested area (see Tables 8 and 9). Due to similar reasons, Group 2 (C2) was mainly located in Chungcheongnam-do (27.03%) and Jeollabuk-do (29.57%), while Group 3 (C3) was mainly located in Chungcheongnam-do (33.75%), Jeollabuk-do (33.06%), and Jeollanam-do (33.03%). Although Gyeonggi-do (i.e.,  Figure 5a shows the distribution of rice paddy and other fields in South Korea. An area with yellow color represents rice paddy field, and an area with pink color represents other farming field. The estimated objective value of existing fields is approximately $13,648,336. The location-allocation result is shown in Figure 5b with an objective value of $13,406,015. Because the proposed approach tends to find locations of rice paddy fields depending on transportation cost to markets, it can reduce $242,321.34 from the existing objective value. The results revealed that each group was fully allocated to a certain area with major markets to minimize the transportation cost of rice. For example, in the solution, Jellanamdo was calculated as producing 353,782.56 Mg year −1 of rice, and its transportation cost was $122,281,405, which is a reduction of $808,260 from $123,089,666 (Table 10). Rice paddy fields in Chungcheongnam-do and Jeollabuk-do were popular due to their accessibility to markets (i.e., Gyeonggi-do and Gangwon-do). In fact, these provinces are located in the middle of South Korea, so they have low average transportation costs. In addition, they have large rice paddy fields (i.e., 16,255.2 ha in Chungcheongnam-do and 18,745.1 ha in Jeollabuk-do). As shown in Table 10, Group 1 (C1) was mainly located in Jeollanam-do (63.87%) and Gyeongsangnam-do (34.99%) because of their attractiveness, travel distance to markets, and size of harvested area (see Tables 8 and 9). Due to similar reasons, Group 2 (C2) was mainly located in Chungcheongnam-do (27.03%) and Jeollabuk-do (29.57%), while Group 3 (C3) was mainly located in Chungcheongnam-do (33.75%), Jeollabuk-do (33.06%), and Jeollanam-do (33.03%). Although Gyeonggi-do (i.e., metropolitan area in South Korea) was popular in Group 2 (98.22%), its size of rice paddy fields was way too small. Similarly, Gangwon-do is a mountainous area without enough rice paddy fields.
The total transportation cost of the proposed solution was $250,564,489, which is lower than the total transportation cost of $250,867,873 for the existing fields. In addition, the proposed solution can save annual travel distance of 209,203.4 km, which can potentially reduce 21.04 tons of CO 2 emission from a freight truck [17]. Because certain fields are only able to cultivate a specific rice group (or cluster) due to weather or soil characteristics, the difference was only $303,384.03. This is 0.014% of the total revenue of $2,024,187,746. However, this study only considered eight cultivars that account for only 19.76% of the entire rice fields in South Korea. Thus, the impact of the proposed approach can be significant if we consider more cultivars. In addition, by having rice paddy fields close to their major markets, consumers are able to cook fresh rice with better taste.

Conclusions
A range of morphological characteristics and yield of eight rice cultivars that are commonly grown in South Korea were investigated at Jeollanamdo Agricultural Research and Extension Center in Jeollanam-do, South Korea, during the growing seasons of 2005-2020. Based on morphological analysis, the number of spikelets and the length of panicle were positively and moderately correlated with rice yield. Among the eight cultivars, Saegehwa and DongJin-1 produced high grain yield attributed to the higher number of spikelets per m 2 . Based on the dataset of measured morphological characteristics and yield, groups of similar cultivars were isolated using the k-means clustering method. Three groups (Group 1, Group 2, and Group 3) were created. High-yielding cultivars Saegehwa and DongJin-1ho were in Group 2. Hyunpum was the only cultivar in Group 3. Hyunpum was the cultivar with the lowest number of spikelets per panicle and the lowest number of spikelets per m 2 . Thus, Group 3 had lower yield than the other groups. Through field measurements and k-mean clustering, some useful characteristics of rice cultivars were identified. These might play a critical role in rice breeding. An optimized location-allocation model was developed to determine ideal location for cultivating the three cultivar groups so that transportation cost could be reduced. Based on simulation results, the southern region (i.e., Jeollanam-do and Gyeongsangnam-do) was appropriate for Group 1 and the central region (i.e., Chungcheongnam-do and Jeollabuk-do) was appropriate for Group 2. Group 3 was evenly distributed over the west central and southern regions (i.e., Chungcheongnamdo, Jeollabuk-do, and Jeollanam-do) in South Korea. These results could reduce $303,384.03 from the existing transportation cost of $250,867,873. In particular, Jeollabuk-do is the most popular province not only because it is close to the metropolitan area (i.e., Gyeonggi-do) with 50.14% of the total demand in South Korea but also because it is close to large cities in the southern regions. Moreover, unlike metropolitan areas, agriculture is a major industry in this province, so it should have enough rice paddy fields in the future.
The proposed location-allocation approach can contribute to enhancing farming profits and implementation of precision agriculture in practice. In addition, this approach can be applied to other countries. In most developed and developing countries, urban areas cannot meet their own demands for food crops and must rely on crop production in rural areas and transportation of food crops to the cities. Thus, this approach can be easily modified using information such as known cultivar characteristics, crop cost, cost incurred during transportation, and available agricultural land from interested countries and used for their supply chain management planning.
The aims of this study were to (1) identify some useful morphological characteristics that could increase rice yield potential, (2) identify rice cultivars using k-mean clustering, and (3) reduce transportation cost by selecting ideal farming locations for all rice clusters using an optimized location-allocation model. Results from this study can increase economic benefit for all beneficiaries of the rice supply chain. However, the simulation model developed in this study has some limitations. The production of the eight cultivars used in this study only accounts for 19.76% of the total rice production in South Korea. In addition, the yield data used in the model development was only estimated for Jeollanam-do. In future studies, the number of cultivars should be increased to improve efficiency of the model performance. Their yield characteristics should also be investigated in multiple locations in South Korea.