sustainability

Article Optimal Project Planning for Public Rental Housing in

Jae Ho Park 1, Jung-Suk Yu 2,* and Zong Woo Geem 3,* 1 Department of Social Housing, Gyeonggi Urban Innovation Corporation, 16556, Korea; [email protected] 2 School of Urban Planning & Real Estate Studies, Dankook University, 16890, Korea 3 College of IT Convergence, Gachon University, 13120, Korea * Correspondence: [email protected] (J.-S.Y.); [email protected] (Z.W.G.)

 Received: 22 December 2019; Accepted: 13 January 2020; Published: 14 January 2020 

Abstract: Although Korea has made notable progress in the availability of public rental housing, Korea’s public rental housing representing 6.3% of the country’s total housing is still below the 8% OECD average from 2016. The Metropolitan Area (composed of Seoul City, City, and ) has nearly 50% of the country’s population, but 11% of the nation’s territory, meaning the area suffers from an acute shortage of public rental housing. This is a serious problem which is hampering the sustainability of Korean society in general. We will examine the possibility of improving this public housing problem using certain algorithms to optimize decision making and resource allocation. This study reviews two pioneering studies on optimal investment portfolio for land development projects and optimal project combination for urban regeneration projects, and then optimizes a public housing investment combination to maximize the amount of public rental houses in Gyeonggi province using optimization techniques. Through the optimal investment combination, public rental houses were found to be more efficiently and sustainably planned for the community.

Keywords: public rental house; sustainability; optimal project combination; genetic algorithm; branch & bound method

1. Introduction Korea’s record for improving access to quality housing has been significant. This has been partially due to the introduction of minimum living standards (e.g., the number of rooms and floor space being differentiated by the size and composition of households) and by direct government support for housing construction. However, although the long-term public rental housing inventory has been steadily rising over the last decade, its share (6.3%) of total housing in 2016 is still below the OECD average (8%) according to the Korean Ministry of Land, Infrastructure, and Transport [1,2]. South Korea aims to increase the share of public rental housing to 9% by 2022 [1]. The scarcity of developable land for residential purposes in South Korea is more problematic in urban areas such as Seoul. The Seoul Metropolitan Area (SMA) —composed of Seoul city, Incheon city, and Gyeonggi province—represents 11% of Korea’s territory and accommodates almost 50% of the national population. As a result, housing demand in SMA is very high [2]. Strong demand, geographical constraint, and extensive land use regulation, such as greenbelt policy, may be leading to high house prices in SMA. Young, senior, and low-income households are particularly affected by soaring house prices in this region. The supply of public rental housing helps to solve this problem by expanding the stock of affordable housing, and it also indirectly contributes by keeping a lid on private rent prices. According to Housing Welfare Road map [1], total housing stock increased by 3.58 million (22.0%) from 16.3 million in 2007 to 19.88 million in 2016 but housing prices increased by 24.9%, meaning it is

Sustainability 2020, 12, 600; doi:10.3390/su12020600 www.mdpi.com/journal/sustainability Sustainability 2020, 12, 600 2 of 14 not easy for ordinary people to buy houses. The Price to Income Ratio (PIR) is 5.6 and the PIR for the lowest-income group is 9.8 in South Korea. So far, researchers have performed useful studies in the field of land-project optimization and public rental housing supply using optimization techniques such as the genetic algorithm (GA) and branch and bound method (B&B). The genetic algorithm is useful tool which has been used to find the spatial optimization of multi-objective and multi-site land use allocation [3], to forecast the private housing demand in Hong Kong [4], to search for optimal solutions to a land use allocation problem with multiple objectives and constraints in case of Tongzhou Newtown in Beijing, China [5], to formulate and develop municipal land use plans in Galicia, Spain [6], and to undertake land-use spatial optimization in Gaoqiao Town, Zhejiang Province, China [7]. The genetic algorithm has also been used to maximize land prices and reduce incompatibility among land uses of an area for urban planners [8], enhance real estate appraisal forecasting with ridge regression [9], optimize transportation infrastructure planning in Provo, Utah, USA [10] or urban land-use allocation in the case study of Dhanmondi Residential Area, Dhaka, Bangladesh [11], search for a spatial multi-objective land use optimization model [12], solve multi-objective land use planning in the Netherlands [13], and support simulating multi-objective spatial optimization allocation of land in Changsha, Zhuzhou, Xiangttan city in China [14]. While the above studies used GA in real estate problems, other researchers have used other intelligent techniques. Jin and Yu [15] analyzed the risk of housing rearrangement projects using the technique of fuzzy theory [16], and Bae and Yu [17] predicted apartment housing prices using the technique of machine learning [18]. There are two pioneering studies in real estate optimization for South Korean projects. The first one considered the optimal investment portfolio for land development projects [19], and the second one considered the optimal project combination for urban regeneration projects [20]. Both studies used both the genetic algorithm and the branch and bound method to obtain combinatorial optimization solutions in real estate cases. Park et al. [21] also proposed an optimization model for another type of real estate problem involving investment scheduling for public rental housing projects. However, their initial study has the limitation of not considering real-world cases. Thus, this study aims to focus more on practical approach in investment optimization for public rental housing projects by considering real-world project data in South Korea.

2. Methodologies The genetic algorithm is the optimal problem-solving method, and it involves using the natural selection phenomenon together with genetics-related operators such as crossover, mutation, and reproduction. The branch and bound method is a technique used for discrete and combinatorial optimization problems.

2.1. Genetic Algorithm The Genetic algorithm was first introduced by John Holland in the 1960s [21]. GA is a technique for moving from one population of ‘chromosomes’ to a new population using selection operators such as crossover, mutation, and inversion. Each chromosome is composed of ‘genes (digital bits)’, and each gene is filled with a particular ‘allele (zero or one)’. In the selection operation, a group of chromosomes that are allowed to be reproduced is selected in the population, and the fitter chromosomes have a higher chance to produce offspring. Crossover exchanges subparts of two chromosomes, generally mimicking biological recombination between two chromosome organisms. Afterwards, mutation arbitrary changes the values of some places in the chromosomes and inversion reverses the order of an adjacent section of the chromosome, thus rearranging the order in which genes are spread. Sustainability 2020, 12, 600 3 of 14

2.2. Branch and Bound Method The Branch and Bound method (B&B) was developed independently by Land and Doig in 1960 and by Murty, Karel, and Little in 1962 [19]. B&B is an analytical approach for discrete optimization problems. Unlike continuous optimization problems, discrete optimization problems are not smooth functions because integer restrictions are placed on (at least some of) the relevant variables. Discrete optimization problems are solved by enumerative methods that investigate the feasible solution set. B&B is an attractive partial enumeration strategy for optimization problems because it analyzes each subgroup with a lower bound or upper bound (branching and bounding) and deletes some groups with no feasibility (pruning), thus finding optimal combination in remaining groups (retracting). Therefore, B&B has four steps as follows: (1) branching, (2) bounding, (3) pruning, and (4) retracting.

3. Optimization for Land Development Projects One of pioneering studies in public real estate optimization in South Korea focused on land development planning [19]. The summary of the study can be reviewed as follows. Government-owned public companies often have a chance to decide the most reasonable investment portfolio from a number of new projects under a limited budget. Here, the limited budget can be a major constraint in this study. Another constraint in land development problems is the balance between profitability and public interest. If a public company chooses projects with a high profit margin but low public interest in order to maximize the total return on investment, its role for public good is likely to be reduced. The third constraint in land optimization is the equitability in each region. If a project is concentrated on a specific region, it may be criticized for not focusing on regionally balanced development. The fourth constraint is the balance among land use purposes, such as new town, public rental housing, and industrial complexes. There is a minimally required amount constraint for each purpose. The fifth constraint involves efficient allocation of human resources. Regarding human resources, it is necessary to minimize unassigned employees in order to maintain employment. The sixth constraint is the possibility of joint investment from cooperated companies. While there are some projects that can be jointly performed with a shared budget and risk, there are other projects that must be solely completed by a single company. It is very important to find the best investment combination that will allow public companies to properly allocate financial resources and maximize return on investment among many new projects while meeting the constraints described above. It is not easy to rationally derive the optimal business combination that maximizes the return on investment among many new projects or maximizes the public interest while meeting the minimum profit goal because there is currently no customized methodology for achieving this in South Korea. As such, we must rely on the optimal business combination (combinatorial optimization) that maximizes the return on investment while meeting multiple constraints from a group of new project candidates that have different characteristics. In line with the above-mentioned factors (return on investment maximization, budget limitation, public interest consideration, regional balance, land purpose balance, human resource management, joint investment possibility), an optimal land development model was proposed as follows: P - Objective function: Max (R X ): maximization of the return on investment (R is the return i i · i i on investment (%) for project i) 10 - Decision variable: Xi: the investment amount on project i (unit: 10 KRW) P 10 - Constraint 1. i Xi 110: the total investment amount is equal to or less than 110 10 KRW P ≤ P × - Constraint 2. X 0.3 X , k Set of non-for-profit projects: the investment for non-for-profit k k ≥ i i ∈ projects is equal to or more than 30% of total investment P P - Constraint 3. X 0.4 X , k {East, West, North, South}: the investment in each area is k k ≤ i i ∈ equal to or less than 40% of total investment Sustainability 2020, 12, 600 4 of 14

P P - Constraint 4. X 0.2 X , k {New Town, Public Housing, Industrial Complex}: investment k k ≥ i i ∈ in each business division is equal to or more than 20% of total investment P - Constraint 5. N Sgn(X ) 250: total employees in active projects are equal to or more than i i · i ≥ 250 (Ni is the number of employees for performing project i; Sgn() is a sign function representing the sign (0 or 1) of Xi) Upper Upper - Constraint 6. 0 X X and X is an integer if i is a joint project. X = 0 or X = X if i ≤ i ≤ i i i i i is not a joint project. Projects that cannot be jointly invested such as E, F, G, H, M, N, O, P, S, and T have only two selections such as no investment or whole investment, while projects that can be jointly invested such as A, B, C, D, I, J, K, L, Q, and R have a partial investment option. Park et al. [19] also provided a dataset of 20 new candidate projects in South Korea, as shown in Table1. Each project has di fferent characteristic in terms of investment amount, profit, public interest, investment area, business division, number of employees participated, and joint investment possibility.

Table 1. Candidate Land Development Projects.

Investment Partnership Profit Type Project ROI * Profit Type *** Region Biz Division Personnel (108 KRW) ** **** A 2% 1000 Non-for-profit East New town Possible 30 − Low profit B 1% 800 Non-for-profit West New town Possible 24 C 1% 600 Non-for-profit South New town Possible 18 − D 5% 400 For-profit North New town Possible 12 High profit E 6% 200 For-profit East New town Impossible 6 Industrial F 5% 1000 For-profit West Impossible 30 complex Industrial G 2% 800 Non-for-profit South Impossible 24 complex Low profit Industrial H 1% 600 Non-for-profit North Impossible 18 complex Industrial I 2% 400 Non-for-profit East Possible 12 − complex Industrial J 5% 200 For-profit West Possible 6 complex High profit K 6% 1000 For-profit South Housing Possible 30 L 5% 800 For-profit North Housing Possible 24 M 2% 600 Non-for-profit East Housing Impossible 18 − Low profit N 1% 400 Non-for-profit West Housing Impossible 12 O 2% 200 Non-for-profit South Housing Impossible 6 − P 5% 1000 For-profit North New town Impossible 30

High profit Q 6% 800 For-profit East New town Possible 24 Industrial R 5% 600 For-profit West Possible 18 complex Industrial S 1% 400 Non-for-profit South Impossible 12 Low profit complex T 2% 200 Non-for-profit North Housing Impossible 6 − * ROI was assumed based on real project performances. ** Total investment amount is 1.2 trillion KRW, which is over the total investment budget of 1.1 trillion Korean Won (KRW). *** Non-for-profit: New town projects that are not for profit but are for regional balance development; Public rental housing and Industrial complex projects that are not for profit but are for regional balance development. / For-profit: New town projects in attractive location; Public sale housing and Industrial complexes in attractive locations. **** Local government-owned company may invest with other public land development companies to reduce financial burden and business risk if partnerships are possible.

This optimization model has 20 decision variables, each of which has an integer or binary number, and the total number of possible candidate solutions is 3.3 1011, which requires a considerable × computation process. Sustainability 2020, 12, 600 5 of 14

After computation, this land development planning model found an optimal profit of 3.58 (1010 KRW), as shown in Table2, which also satisfies the constraints as follows:

Table 2. Result of Land Development Optimization.

Project Area Business Division Investment Project Non-for- Profit (10 Industrial Person Amount Profit East West South North New Town Housing billion KRW) Complex A ------B 8 8 - 8 - - 8 - - 24 0.08 C ------D 4 4 - - - 4 4 - - 12 0.2 E 2 - 2 - - - 2 - - 6 0.12 F 10 - - 10 - - - 10 - 30 0.5 G 8 8 - - 8 - - 8 - 24 0.16 H 6 6 - - - 6 - 6 - 18 0.06 I ------J 2 - - 2 - - - 2 - 6 0.1 K 10 - - - 10 - - - 10 30 0.6 L 8 - - - - 8 - - 8 24 0.4 M ------N 4 4 - 4 - - - - 4 12 0.04 O ------P 10 - - - - 10 10 - - 30 0.5 Q 8 - 8 - - - 8 - - 24 0.48 R 6 - - 6 - - - 6 - 18 0.3 S 4 4 - - 4 - - 4 - 12 0.04 T ------Total 90 30 10 30 22 28 32 36 22 270 3.58

- Total investment amount: 90 (1010 KRW) which is less than 110 (1010 KRW). - Non-for-profit ratio: 33% which is more than 30% of total investment. - Investment area: East (10), West (30), South (22), North (28). Each area has less than 36 (1010 KRW) which is 40% of total investment. - Investment division: new town (32), industrial complex (36), public housing (22). Each division is more than 18 (1010 KRW), which is 20% of total investment. - Number of employees: 270 which is more than 250.

4. Optimization for Urban Regeneration Projects Another pioneering study in public real estate optimization in South Korea is urban regeneration planning [20]. The summary of this study can be reviewed as follows. According to Lee and Lim [22], urban growth in South Korea has reached its limit, and urban areas have started to decline. Urban decline has resulted in critical issues such as outflow of the population, ageing infrastructure, loss of economic capacity, etc. Thus, the ‘urban regeneration’ can be a new strategy in South Korea’s national urban policy for maintaining sustainable urban circumstances and revitalizing enervated communities. This concept of urban regeneration is not only for city planning-oriented approaches which can develop sustainable economic and physical city environments, but also for social and governance-oriented practices which can accumulate social capital. Thus, South Korea’s urban regeneration policy is highly related to the idea of urban sustainability. There are various models such as the ‘Downtown model (DM)’, ‘Economic support model (ESM)’, and ‘Public company proposal model (PCPM)’ for urban regeneration projects. The DM is a project model used to support the recovery of public functions and the vitalization of commerce through cooperation with historical, cultural, and traveling resources in old downtown areas where the decline Sustainability 2020, 12, 600 6 of 14 of public services and the decline of commerce are severe. The ESM is a project model that creates new industrial complexes to increase jobs in areas where urban decline is severe. The PCPM has been proposed by public companies as a plan for urban regeneration in certain cities, while other models were proposed by local governments. Each project can be evaluated based on various criteria and correspondingly earned certain scores, as shown in Table3.

Table 3. Evaluation Criteria and Score for Urban Regeneration Projects [23].

Evaluation Criteria Score Points Detail Evaluation Criteria Score Points Urgency of project (Region deterioration, Safety) 15 Urgency and Necessity 30 of project Necessity of project (Community participation) 15 Local government’s organization for project 5 40 Relevance of project plan 10 Feasibility of project plan Plan of land acquisition and finance for project 15 Community participation and empowerment training 10 Housing welfare and improvement of quality of life 10 30 Job creation effect 10 Effect of project Social integration and sustainability 5 Countermeasure towards side-effects of the real 5 estate market

The South Korean central government plans to choose 13 DM projects, 2 ESM projects, and 10 PCPM projects from a total of 66 projects developed by 16 local governments based on the evaluation of the Urban Regeneration Special Committee. Here, each local government can apply for a maximum of four projects. If the central government selects projects with respect to project effects themselves, there will be unselected regions, which will violate the principle of regionally balanced development. For this reason, a combinatorial optimization model was proposed and could provide optimal solutions while satisfying various constraints. The model for optimally selecting urban regeneration projects can be formulated as follows: P - Objective function: Max (S X ): maximization of urban regeneration effect (S is earned i i · i i score for project i) - Decision variable: X 0, 1 : investment decision for project i (1 means investment; and 0 means i ∈ { } no investment) P - Constraint 1. k Xk = 13, k Set of downtown-focused projects P ∈ - Constraint 2. k Xk = 2, k Set of industry-oriented projects P ∈ - Constraint 3. k Xk = 10, k Set of public-corporation-proposed projects P ∈ - Constraint 4. 1 X 3, j Set of non-Gyeonggi province projects (Projects should be ≤ j j ≤ ∈ selected in each local government from a minimum of one project to a maximum of three for regionally balanced development) P - Constraint 5. 2 X 4, j Set of Gyeonggi province projects (Because Gyeonggi province ≤ j j ≤ ∈ has lots of urban regeneration demand, projects should be selected from a minimum of two projects to a maximum of four) Total number of candidate solutions for this combinatorial problem including constraint-violated ones is 266 ( 7.38 1019), which actually requires a major computation process. ≈ × The results of this optimal project combination problem using GA and B&B are shown in Tables4–6. The total score (2198) from B&B as shown in Table5 is slightly better than that (2173) of GA as shown in Table4, and Table6 shows the overall result from B&B. Here, stands for Busan Metropolitan City, stands for Daegu Metropolitan City, Incheon stands for Incheon Metropolitan City, stands for Gwangju Metropolitan City, stands for Daejeon Metropolitan City, stands for Sustainability 2020, 12, 600 7 of 14

Ulsan Metropolitan City, Jeju stands for the Jeju Special Self-governing Province, and Sejong stands for the Sejong Special Self-governing City.

Table 4. Selected Projects of Urban Regeneration Planning using GA.

Project Model (Number) Project Name DM (13) B1, C1, E1, F2, G3, H1, J2, K1, M1, M2, N1, O1, P1 ESM (2) A4, B4 PCPM (10) C3, D3, F3, G4, H2, I2, J3, K2, L3, M3

Table 5. Selected Projects of Urban Regeneration Planning using B&B.

Project Model (Number) Project Name DM (13) B1, C1, E1, F2, G2, G3, H1, K1, L2, N1, O1, P1, P2 ESM (2) D4, K4 PCPM (10) A3, H2, I2, J3, K2, L3, M3, N2, O2, P3

Table 6. Overall Result of Urban Regeneration Planning using B&B.

Local Govt. Project Project Score of Local Govt. Project Project Score of (Number) Name Model Evaluation (Number) Name Model Evaluation A1 DM 74 I1 DM 73 A2 DM 76 Chungcheong I2 PCPM 89 Busan (1) A3 PCPM 86(North) (1) I3 ESM 84 A4 ESM 83 I4 ESM 76 B1 DM 83 J1 DM 79 B2 DM 83Chungcheong J2 DM 82 Daegu (1) B3 PCPM 80 (South) (1) J3 PCPM 91 B4 ESM 83 J4 ESM 79 C1 DM 88 K1 DM 88 C2 DM 73 Jeolla (North) K2 PCPM 94 Incheon (1) C3 PCPM 86(3) K3 ESM 79 C4 ESM 75 K4 ESM 86 D1 DM 74 L1 DM 81 D2 DM 73 Jeolla (South) L2 DM 85 Gwangju (1) D3 PCPM 84 (2) L3 PCPM 92 D4 ESM 83 L4 ESM 79 E1 DM 92 M1 DM 79 E2 DM 84Gyeongsang M2 DM 82 Daejeon (1) E3 PCPM 83 (North) (1) M3 PCPM 92 E4 ESM 82 M4 ESM 78 F1 DM 73 N1 DM 85 F2 DM 86 Gyeongsang N2 PCPM 89 Ulsan (1) F3 PCPM 85(South) (2) N3 ESM 84 F4 ESM 77 N4 ESM 84 G1 DM 80 O1 DM 87 G2 DM 82 O2 PCPM 90 Jeju (2) Gyeonggi (2) G3 DM 86 O3 ESM 81 G4 PCPM 85 O4 ESM 80 G5 ESM 81 P1 DM 87 G6 ESM 83 P2 DM 83 Sejong (3) H1 DM 95 P3 PCPM 90 Gangwon (2) H2 PCPM 89 P4 ESM 77 H3 ESM 81 H4 ESM 83 Sustainability 2020, 12, x FOR PEER REVIEW 8 of 15

(2) G2 DM 82 O2 PCPM 90 G3 DM 86 O3 ESM 81 G4 PCPM 85 O4 ESM 80 G5 ESM 81 P1 DM 87 G6 ESM 83 P2 DM 83 Sejong (3) H1 DM 95 P3 PCPM 90 H2 PCPM 89 P4 ESM 77 Sustainability 2020Gangwon, 12, 600 8 of 14 (2) H3 ESM 81 H4 ESM 83 5. Optimal Project Combination for Public Rental Housing 5. Optimal Project Combination for Public Rental Housing While previous real estate optimization studies [19,20] were based on artificial examples on investment amount,While previous return onreal investment, estate optimization the evaluation studies [19,20] score forwere a urbanbased regenerationon artificial examples project, on etc., this studyinvestment focused amount, on a real-world return on caseinvestment, of a new the townevaluation project score in for South a urban Korea. regeneration We planned project, to etc., find this study focused on a real-world case of a new town project in South Korea. We planned to find a a optimal public housing investment combination to maximize the amount of public rental houses optimal public housing investment combination to maximize the amount of public rental houses in in Gwanggyo, which is one of the second-stage new towns. Gwanggyo new town is a planned city Gwanggyo, which is one of the second-stage new towns. Gwanggyo new town is a planned city surroundingsurrounding part of part Suwon of Suwon city and city partand part of Yongin of Yongin city. city. It isIt is located located 25 25 km km southsouth from Seoul, Seoul, as as shown withshown a red with rectangle a red rectangle in Figure in Figure1. In 2004,1. In 2004 Gwanggyo, Gwanggyo new new town town was was designated designated byby GyeonggiGyeonggi Province,Province, Suwon Suwon city, Youngin city, Youngin city, and city, by and a local-government-ownedby a local-government-owned real-estate real-estate companycompany named named GyeonggiGyeonggi Urban InnovationUrban Innovation Corporation Corporation (GICO). (GICO) Gwanggyo. Gwanggyo new new town, town, which which willwill accommodate more thanmore 31,000 than households,31,000 households, was not was only not only intended intend fored for the the purpose purpose of of providing providing increasedincreased housing housing supply butsupply also but for severalalso for regionalseveral regional purposes purposes suchas such a local-government as a local-government office, office, convention convention center, center, and commercialand zone.commercial zone.

Gwanggyo

FigureFigure 1. Map 1. of Map Gwanggyo of Gwanggyo New New Town Town (Google (Google and and Naver Naver map). map).

The percentageThe percentage of public of public rental rental housing housing investment investment from from 2008 2008 to to 2018 2018 byby GICO was was very very low, low, and during this period the housing investment for public sale occupied most of relevant company and during this period the housing investment for public sale occupied most of relevant company activities, as seen in Table 7 (the data was extracted from an internal report). activities, as seen in Table7 (the data was extracted from an internal report).

Table 7. The Public Sale and Rental House Construction Record of GICO.

Type Housing Project Construction Period Investment (108 KRW) Detail of Investment Sub Total 30,345 -Yangchon 2008.4~2010.12 437 Land price +Construction cost Gwanggyo Edu-town 12 2009.11~2012.11 2613 Construction cost (GICO’s land) Gwanggyo Edu–town 13–15 2009.12~2012.12 2225 Construction cost (GICO’s land) Sales Housing Gimpo-Hangang Ab–1 2009.12~2013.2 2617 Land price +Construction cost Gimpo-Hangang Ab–7 2009.12~2013.2 3028 Land price +Construction cost Wirye A2–11 2014.4~2016.9 6758 Land price +Construction cost Wirye A2–2 2015.4~2017.9 4661 Land price +Construction cost Namyangju-Dasan B2 2015.4~2017.11 2166 Construction cost (GICO’s land) Namyangju-Dasan B4 2015.4~2017.11 2938 Construction cost (GICO’s land) Namyangju-Dasan S1 2015.12~2018.6 2902 Construction cost (GICO’s land) Rental Housing Gimpo-Hangang Ab-2 2012.1~2013.2 1091 Land price +Construction cost Sustainability 2020, 12, 600 9 of 14

On the other hand, all the public rental houses located in Gwanggyo New Town were supplied by the Korea Land Housing Corporation (KLHC), which is the central government-owned company with more than 32 trillion KRW of capital as of the first half of 2019 (www.lh.or.kr). GICO, who had about 1.6 trillion KRW of capital as of the first half of 2019 (www.gico.or.kr), did not build any public rental houses in Gwanggyo New Town. Because GICO had more than 4 trillion KRW of loans resulting from land acquisition and development expense with regard to Gwanggyo New Town from 2012 to 2014, it had to sell land for public rental housing to KLHC rather than construct and operate public rental houses. Table8 shows the list of public rental house projects developed by KLHC and the corresponding construction costs. But it would be more desirable for GICO to supply some public rental houses to satisfy its mission statement. If the GICO had used 3034.5 billion won, which was originally invested for the 10 public sale house projects from 2008 to 2018, to construct rental houses and sales houses instead, it would have been a better decision that met the purpose of public interest.

Table 8. Estimated Cost of Public Rental House Projects.

Total Area (m2) Estimated Construction Total Construction Cost Site Name Number of Houses ConstructionCompletion (A) Cost (KRW) per m2 (B) (108 KRW) of GICO Total 6956 804,656 8673 A10 701 2013.11 111,002 1196 A11 637 2013.11 102,334 1103 A16 224 2014.7 34,680 374 A19 1373 2011.11 112,4581,077,893 1212 A23 258 2014.2 39,979 431 A24 394 2014.2 54,883 592 A25 146 2011.10 13,091 141 A26 1132 2013.12 172,477 1859 A30 2091 2011.12 163,752 1765

According to a study on housing policy in South Korea [24], Korean housing authorities focused on the expansion of state-developed housing for sale rather than the provision of rental accommodation. In order to obtain adequate housing for poor and disadvantaged groups, adequate rental accommodation is needed to ensure legal security of tenure protection from discrimination and equal access to adequate housing for all persons and their families. Here, the total number of combinations with 10 sales of housing sites and 10 rental housing sites (one rental housing project was developed by GICO as seen in Table7 and nine projects were developed by KLHC as seen in Table8) was 2 20 because we had to decide whether or not to select each of 20 housing projects. Thus, instead of total enumeration, we utilized optimization techniques such as GA and B&B to find an optimal solution. The objective function and constraints for this housing combinatorial problem were as follows: P - Objective function: Max (N X ): Maximization of the number of supplied public rental i i · i houses (Ni is the number of supplied houses from project i) - Decision variable: X 0, 1 : investment decision for project i (1 means investment; and 0 means i ∈ { } no investment) P - Constraint 1: (B X ) 3034.5: Total investment amount should be less than 3034.5 billion i i · i ≤ KRW, which is the total investment amount for public sale house projects from 2008 to 2018 (Bi is budget for project i) P - Constraint 2. X = 9, k Set of public sale house projects: By slightly reducing the number of k k ∈ public sale house projects from 10 to 9, GICO can increase public rental houses more.

5.1. Public Rental Housing Planning by Arbitrary Selection #1 GICO usually invests two public sale house projects per one new town, for example Gimpo-Hangang Ab-1 and Ab-7 in Gimpo-Hangang new town, Wirye A2-2, and Wirye A2-11 Sustainability 2020, 12, x FOR PEER REVIEW 10 of 15

Here, the total number of combinations with 10 sales of housing sites and 10 rental housing sites (one rental housing project was developed by GICO as seen in Table 7 and nine projects were developedSustainability by KLHC 2020as seen, 12, x inFOR Table PEER 8)REVIEW was 2 20 because we had to decide whether or not to select 10 of 15 each of 20 housing projects. Thus, instead of total enumeration, we utilized optimization techniques such as GA andHere, B&B theto find total an number optimal of solution. combinations with 10 sales of housing sites and 10 rental housing sites The objective(one rental function housing and projectconstraints was for developed this housing by GICOcombinatorial as seen problemin Table were 7 and as ninefollows: projects were developed by KLHC as seen in Table 8) was 220 because we had to decide whether or not to select - Objective function: Max ∑( 𝑁 ∙𝑋): Maximization of the number of supplied public rental houses (𝑁 is the numbereach of of supplied 20 housing houses projects. from Thus, project instead i) of total enumeration, we utilized optimization techniques such as GA and B&B to find an optimal solution. - Decision variable: 𝑋 ∈ {0,1}: investment decision for project i (1 means investment; and 0 means no investment)The objective function and constraints for this housing combinatorial problem were as follows: - Objective function: Max ∑(𝑁 ∙𝑋): Maximization of the number of supplied public rental houses (𝑁 - Constraint 1: ∑( 𝐵 ∙𝑋) ≤ 3034.5: Total investment amount should be less than 3034.5 billion KRW, whichis the is thenumber total ofinvestment supplied housesamount from for public project sale i) house projects from 2008 to 2018 (𝐵 is Sustainability 2020, 12, 600 10 of 14 budget for project- Dec i) ision variable: 𝑋 ∈ {0,1}: investment decision for project i (1 means investment; and 0 means no investment) - Constraint 2. ∑ 𝑋 =9, k ∊ Set of public sale house projects: By slightly reducing the number of public sale house- Constraint projects 1 from: ∑( 𝐵 10 ∙𝑋 to) 9,≤ GICO 3034.5 can: Total increase investment public rental amount houses should more. be less than 3034.5 billion in Wirye new town for their businessKRW, which portfolio. is the total Gimpo-Yangchon investment amount for (one public project) sale house and projects Namyangju-Dasan from 2008 to 2018 (𝐵 is budget for project i) (three projects) are exceptional5.1. Public Rental cases. Housing Therefore, Planning by weArbitrary excluded Selection #1 the biggest public sale house project, - Constraint 2. ∑ 𝑋 =9, k ∊ Set of public sale house projects: By slightly reducing the number GICO usually invests two public sale house projects per one new town, for example Gimpo- Namyangju-Dasan B4 among threeof public Namyangju-Dasan sale house projects from projects. 10 to 9, GICO Then, can increase we redistributed public rental houses that investmentmore. Hangang Ab-1 and Ab-7 in Gimpo-Hangang new town, Wirye A2-2, and Wirye A2-11 in Wirye new amount of Namyangju-Dasan B4 (293,800 million KRW) to select public rental house projects. The town for their5.1. Public business Rental portfolio. Housing PlanningGimpo-Yangch by Arbitraryon (one Selection project) #1 and Namyangju-Dasan (three result of arbitrary selectionprojects) #1 are is shownexceptional in cases. Table Therefore,9. we excluded the biggest public sale house project, Namyangju-DasanGICO B4 usually among invests three two Namyangju-Da public sale housesan projects. projects perThen, one we new redistributed town, for example that Gimpo- investmentHangang amount Ab-1of Namyangju-Dasan and Ab-7 in Gimpo-Hangang B4 (293,800 newmillion town, KRW) Wirye to A2-2,select andpublic Wirye rental A2-11 house in Wirye new projects. Thetown Tableresult for oftheir 9. arbitraryResult business selection of Arbitraryportfolio. #1 is shownGimpo-Yangch Selection in Table #1. 9.on (one project) and Namyangju-Dasan (three projects) are exceptional cases. Therefore, we excluded the biggest public sale house project, Number of Investment Number of Investment Name of Site Namyangju-Dasan B4Table among 9. Result three of Arbitrary Namyangju-DaSelection Selection san#1. projects. Then, we redistributed that Houses Amount (100m.) Selected Houses Amount (100m.) investment amount of Namyangju-Dasan B4 (293,800 million KRW) to select public rental house Number Gwanggyo A10 701 1196Investment X -Investment - projects. The result of arbitrary selection #1 is shown in Table 9. of Name of Site Number of Houses Amount Selection Amount Gwanggyo A11 637 1103 XSelected - - (100m.) (100m.) Gwanggyo A16 224 374Table 9. Result of X Arbitrary SelectionHouses #1. - - Gwanggyo A10 701 1196 X - - Gwanggyo A19 1373 1212 X -Number - Rental house Gwanggyo A11 637 1103 InvestmentX - - Investment (10) of Gwanggyo A23Gwanggyo 258Name A16 of Site 431224 Number of Houses374 X AmountX Selection - - Amount - Selected (100m.) (100m.) Gwanggyo A24Gwanggyo 394 A19 5921373 1212 XX - Houses - - Gwanggyo A23 Gwanggyo A10258 701 431 1196X - X - - - Gwanggyo A25Rental house 146 141 X - - Gwanggyo A24 Gwanggyo A11394 637 592 1103X - X - - - (10) Gwanggyo A26Gwanggyo 1132 A25 Gwanggyo A16 1859146 224 141 X374 X - X - - - Gwanggyo A30Gwanggyo 2091 A26 Gwanggyo A19 17651132 1373 1859 O1212X 2091- X - - 1765 - Gimpo Ab-2Gwanggyo 559 A30 Gwanggyo A23 10912091 258 1765 X431 O 2091 -X 1765 - - Rental house Gimpo Ab-2 Gwanggyo A24559 394 1091 592 X - X - - - (10) Sub Total 7515Sub Total Gwanggyo A25 97647515 1461 site9764 selected 1 site141 selected 2091X 1765 - 1765 - Gimpo-Yangchon Gwanggyo A26743 1132 437 1859O 743X 437 - - Gimpo-YangchonGwanggyo-Edutown 743 12Gwanggyo A30 4371764 2091 2613 O1765O 7431764O 2613 2091 4371765 Gwanggyo-Edutown 12Gwanggyo-Edutown 1764 13~1Gimpo5 Ab-2 2613 1173 559 2225 O1091O 17641173X 2225- 2613 - Gwanggyo-Edutown 13~15 Gimpo-Hangang1173 Ab-1 Sub Total 2225 1167 7515 2617 O9764O 1 1173site 1167 selected 26172091 22251765 Gimpo-Hangang Ab-7Gimpo-Yangc hon 1382 743 3028 437O 1382O 3028743 437 Sales house Gimpo-Hangang Ab-1Sales house 1167 2617 O 1167 2617 Wirye A2-11Gwanggyo-Edutown 1540 12 1764 6758 2613O 1540O 67581764 2613 (10) (10) Gimpo-Hangang Ab-7 1382Wirye A2-2Gwanggyo-Edutown 30281413 13~1 5 1173 4661 O2225O 1382 1413O 46611173 30282225 Wirye A2-11Namyangju-Dasan 1540Gimpo-Hangang B2 6758 Ab-1 1186 1167 2166 O2617O 1540 1186O 2166 1167 6758 2617 Namyangju-DasanGimpo-Hangang B4 Ab-7 1615 1382 2938 3028X - O - 1382 3028 Wirye A2-2Sales 1413 house 4661 O 1413 4661 Namyangju-Dasan S1Wirye A2-11 1685 1540 2902 6758O 1685O 2902 1540 6758 Namyangju-Dasan B2 1186(10) 2166 O 1186 2166 Sub Total Wirye A2-2 13,668 1413 30,345 9 sites4661 selected 12,053O 27,407 1413 4661 Namyangju-Dasan B4Total 1615 Namyangju-Dasan 293821,183 B2 1186 40,109 X 102166 sites selected 14,144 -O 29,172 1186 2166 - Namyangju-Dasan S1 1685Namyangju-Dasan 2902 B4 1615 O2938 1685X - 2902 - Namyangju-Dasan S1 1685 2902 O 1685 2902 Sub Total 13,668 30,345 9 sites selected 12,053 27,407 Sub Total 13,668 30,345 9 sites selected 12,053 27,407 Total 21,183Total 40,109 21,18310 sites selected40,109 1014,144 sites selected 14,144 29,172

As observed in Table9, Constraint 1 is satisfied because total investment amount is 2,917,200 million KRW, which is less than 3,034,520 million KRW. Also, Constraint 2 is satisfied because only Namyangju-Dasan B4 was excluded. The result of the objective function (maximization of the number of suppled public rental houses) is 2091. If GICO also includes Gwanggyo A19, the biggest remaining public rental house project, the total investment amount would be 3,384,000 million KRW which violates Constraint 1 ( 3,034,500 ≤ million KRW).

5.2. Public Rental Housing Planning by Arbitrary Selection #2 GICO excludes Wirye A2-11 (whose investment amount was the biggest) to supply more public rental houses. Then, GICO redistributes that investment amount of Wirye A2-11 (675,800 million KRW) in order to maximize the number of selected houses. The result of arbitrary selection #2 is as shown in Table 10. As observed in Table 10, Constraint 1 is satisfied because total investment amount is 2,961,900 million KRW which is less than 3,034,520 million KRW. Also, Constraint 2 is satisfied because only Wirye A2-11 is excluded. The result of objective function (maximization of the number of suppled public rental houses) is 5297. If GICO also includes Gwanggyo A11, the biggest remaining public rental house project, Sustainability 2020, 12, x FOR PEER REVIEW 11 of 15

As observed in Table 9, Constraint 1 is satisfied because total investment amount is 2,917,200 million KRW,Sustainability which 2020 is less, 12, xthan FOR 3,034,520PEER REVIEW million KRW. Also, Constraint 2 is satisfied because only 11 of 15 Namyangju-Dasan B4 was excluded. The resultA ofs observedthe objective in Table function 9, Constraint (maximization 1 is ofsatisf the iednumber because of suppled total investment public rental amount houses) isis 2,917,200 2091. If GICOmillion also KRW,includes which Gwanggyo is less A19,than the 3,034,520 biggest millionremaining KRW. public Also, rental Constraint house project,2 is satisfied the total because only investmentNamyangju-Dasan amount would be B4 3,384,000 was excluded million. KRW which violates Constraint 1 (≤3,034,500 million Sustainability 2020, 12, 600 KRW). The result of the objective function (maximization of the number of suppled public rental11 houses) of 14 is 2091. If GICO also includes Gwanggyo A19, the biggest remaining public rental house project, the total 5.2. Publicinvestment Rental Housing amount Planning would by beArbitrary 3,384,000 Selection million #2 KRW which violates Constraint 1 (≤3,034,500 million KRW). total investment amountGICO would excludes be 3,722,000Wirye A2-11 million(whose investment KRW, amount which was violates the biggest) Constraint to supply more 1 ( public3,034,500 rental houses.5.2. Public Then, Rental GICO Housing redistributes Planning that by investmentArbitrary Selection amount #2 of Wirye A2-11 (675,800 million≤ million KRW). KRW) in order to maximize the number of selected houses. The result of arbitrary selection #2 is as shown in TableGICO 10. excludes Wirye A2-11 (whose investment amount was the biggest) to supply more public rentalTable houses. 10. Then,Result GICO of Arbitraryredistributes Selection that investment #2. amount of Wirye A2-11 (675,800 million KRW) in order to maximizeTable 10. the Result number of Arbitrary of selected Selection houses. #2. The result of arbitrary selection #2 is as shown in NumberTable 10. of Investment Number of Investment Name of Site Selection Number Houses Amount (100m.) Investment Selected HousesInvestmentAmount (100m.) of Name of Site NumberTable of Houses 10. ResultAmount of Arbitrary Selection Selection #2. Amount Gwanggyo A10 701 1196 OSelected 701 1196 (100m.) (100m.) Gwanggyo A11 637 1103 XHouses - Number - Investment Investment Gwanggyo A10 701 1196 O 701 1196of Gwanggyo A16 224Name of Site 374 Number of Houses XAmount Selection - Amount - Gwanggyo A11 637 1103 X - Selected - Gwanggyo A19 1373 1212 O(100m.) 1373(100m.) 1212 Rental house Gwanggyo A16 224 374 X - Houses - (10) Gwanggyo A23Gwanggyo 258 A19Gwanggyo A10 431 1373 701 1212 X 1196 O 1373 O - 1212701 1196 - Gwanggyo A11 637 1103 X - - Gwanggyo A24Gwanggyo 394 A23 592258 431 X X - - - Rental house Gwanggyo A16 224 374 X - - Gwanggyo A25Gwanggyo 146 A24 141394 592 X X - - - (10) Gwanggyo A19 1373 1212 O 1373 1212 Gwanggyo A26Gwanggyo 1132 A25 1859146 141 O X 1132 - - 1859 Gwanggyo A23 258 431 X - - RentalGwanggyo house A26 1132 1859 O 1132 1859 Gwanggyo A30 2091Gwanggyo A24 1765 394 O592 2091 X - 1765 - Gwanggyo(10) A30 2091 1765 O 2091 1765 Gimpo Ab-2 559Gwanggyo A25 1091 146 X141 X- - - Gimpo Ab-2 559 1091 X - - Gwanggyo A26 1132 1859 O 1132 1859 Sub TotalSub 7515 Total 97647515 4 sites9764 selected 4 sites selected 5297 6032 6032 Gimpo-YangchonGwanggyo A30 743 2091 437 1765O 7 O43 2091437 1765 Gimpo-Yangchon 743 437 O 743 437 Gwanggyo-EdutownGimpo 12 Ab-2 1764 559 26131091 O 1764 X 2613 - - Gwanggyo-Edutown 12Gwanggyo-Edutown 1764 13~1Sub5 Total 26131173 7515 2225 O9764 O 4 sites 17641173 selected 5297 2225 26136032 Gwanggyo-Edutown 13~15 Gimpo-Hangang1173Gimpo-Yang Ab-1 chon 2225 1167 743 2617 O437 O 1173 1167O 2617743 2225437 Gwanggyo-Edutown 12 1764 2613 O 1764 2613 Sales house Gimpo-Hangang Ab-1Gimpo-Hangang 1167 Ab-7 2617 1382 3028 O O 1167 1382 3028 2617 Sales house Gwanggyo-Edutown 13~15 1173 2225 O 1173 2225 (10) Gimpo-Hangang Ab-7Wirye 1382 A2-11 30281540 6758 O X 1382 - - 3028 (10) Gimpo-Hangang Ab-1 1167 2617 O 1167 2617 Wirye A2-2 1413 4661 O 1413 4661 Wirye A2-11 1540Gimpo-Hangang 6758Ab-7 1382 X3028 O - 1382 3028 - Namyangju-DasanSales house B2 1186 2166 O 1186 2166 Wirye A2-2 1413Wirye A2-11 46611540 O6758 1413 X - 4661 - Namyangju-Dasan(10) B4 1615 2938 O 1615 2938 Wirye A2-2 1413 4661 O 1413 4661 Namyangju-Dasan B2Namyangju-Dasan 1186 S1 2166 1685 2902 O O 1186 1685 2902 2166 Namyangju-Dasan B2 1186 2166 O 1186 2166 Namyangju-Dasan B4Sub 1615 Total 293813,668 30,345 O 9 sites selected 12,128 1615 23,587 2938 Namyangju-Dasan B4 1615 2938 O 1615 2938 Namyangju-Dasan S1Total1685 290221,183 40,109 O 13 sites selected 17,42 16855 29,619 2902 Namyangju-Dasan S1 1685 2902 O 1685 2902 Sub Total 13,668 30,345 9 sites selected 12,128 23,587 As observed in Table 10, ConstraintSub Total 1 is satisf13,668ied because total30,34 5investment 9 sites selected amount 12,128 is 2,961,90023,587 Totalmillion KRW which is 21,183 less thanTotal 3,034,520 40,109 million KRW.21,18313 sites Also, selected Constraint40,109 13 2sites17,425 is selected satisfied 17,42 because5 29,619 only Wirye A2-11 is excluded. SustainabilityThe 2020 result, 12, Asx of FOR observedobjective PEER REVIEW functionin Table (maximization10, Constraint of 1 theis satisf numberied ofbecause suppled total public investment rental houses) 12amount of is 155297. is 2,961,900 5.3. Public Rental HousingIf GICO Planning alsomillion includes KRW Determined Gwanggyo which isA11, less by the than the biggest 3,034,520 Branch remaining million and public Bound KRW. rental MethodAlso, house Constraint project, 2total is satisfied investment because only amountThe result wouldWirye of thebe A2-11 3,722,000Branch is excluded. and million Bound KRW, Me whichthod is violates shown Constraint in Table 11. 1 ( ≤As3,034,500 observed million in Table KRW). 11, The result of theConstraint Branch 1 is satisfied andThe result Bound because of objective total Method investment function is shownamount (maximization is in2,929,800Table of the millionnumber 11. KRW, of As suppled observed which public is less rental inthan houses) Table is 11 5297., 3,034,5205.3. Public millionIf Rental GICO KRW. Housingalso Also, includes Planning Constraint Gwanggyo Determined 2 is A11, satisfied the by biggest the because Branch remaining onlyand BoundWirye public Method A2-11 rental is excluded.house project, total investment Constraint 1 is satisfiedThe because resultamount of objective total would investment function be 3,722,000 (maximization million amount KRW, of is the which 2,929,800 number violates of millionsuppled Constraint pu KRW,blic 1 ( rental≤3,034,500 which houses) million is is less KRW). than 3,034,520 million KRW.5187. Also, Constraint 2 is satisfied because only Wirye A2-11 is excluded. 5.3. Public Rental Housing Planning Determined by the Branch and Bound Method Table 11. Result of Branch & Bound Method. Table 11. Result of Branch & Bound Method. Number Investment Investment Number of Investment Numberof of Investment Name of Site Name of Site Number of Houses AmountSelection Selection Amount Houses Amount (100m.) SelectedSelected Houses Amount (100m.) (100m.) (100m.) Gwanggyo A10 701 1196 OHouses 701 1196 Gwanggyo A11Gwanggyo A10 637 701 1103 1196 X O 701 - 1196 - Gwanggyo A16Gwanggyo A11 224 637 374 1103 O X 224 - - 374 Rental house Gwanggyo A19Gwanggyo 1373A16 224 1212 374 O O 1373 224 374 1212 (10) Gwanggyo A23Gwanggyo A19 258 1373 431 1212 O O 1373258 1212 431 Gwanggyo A23 258 431 O 258 431 GwanggyoRental hous A24e 394 592 O 394 592 Gwanggyo A24 394 592 O 394 592 Gwanggyo(10) A25 146 141 O 146 141 Gwanggyo A25 146 141 O 146 141 Gwanggyo A26 1132 1859 X - - Gwanggyo A26 1132 1859 X - - Gwanggyo A30 2091 1765 O 2091 1765 Gwanggyo A30 2091 1765 O 2091 1765 Gimpo Ab-2 559 1091 X - - Gimpo Ab-2 559 1091 X - - Sub TotalSub Total 7515 7515 9764 79764 sites selected 5187 5711 5711 Gimpo-Yangchon 743 437 O 743 437 Gwanggyo-Edutown 12 1764 2613 O 1764 2613 Gwanggyo-Edutown 13~15 1173 2225 O 1173 2225 Gimpo-Hangang Ab-1 1167 2617 O 1167 2617 Gimpo-Hangang Ab-7 1382 3028 O 1382 3028 Sales house Wirye A2-11 1540 6758 X - - (10) Wirye A2-2 1413 4661 O 1413 4661 Namyangju-Dasan B2 1186 2166 O 1186 2166 Namyangju-Dasan B4 1615 2938 O 1615 2938 Namyangju-Dasan S1 1685 2902 O 1685 2902 Sub Total 13,668 30,345 9 sites selected 12,128 23,587 Total 21,183 29,298 Sustainability 2020, 12, x FOR PEER REVIEW 12 of 15

The result of the Branch and Bound Method is shown in Table 11. As observed in Table 11, Constraint 1 is satisfied because total investment amount is 2,929,800 million KRW, which is less than 3,034,520 million KRW. Also, Constraint 2 is satisfied because only Wirye A2-11 is excluded. The result of objective function (maximization of the number of suppled public rental houses) is 5187.

Table 11. Result of Branch & Bound Method. Number Investment Investment of Name of Site Number of Houses Amount Selection Amount Selected (100m.) (100m.) Houses Gwanggyo A10 701 1196 O 701 1196 Gwanggyo A11 637 1103 X - - Gwanggyo A16 224 374 O 224 374 Gwanggyo A19 1373 1212 O 1373 1212 Sustainability 2020, 12, 600 12 of 14 Gwanggyo A23 258 431 O 258 431 Rental house Gwanggyo A24 394 592 O 394 592 (10) Gwanggyo A25 146 141 O 146 141 Table 11. Cont. Gwanggyo A26 1132 1859 X - -

NumberGwanggyo of A30 Investment 2091 1765 NumberO of 2091 Investment1765 Name of Site Selection HousesGimpo Ab-2 Amount (100m.)559 1091 SelectedX Houses -Amount - (100m.) Gimpo-Yangchon 743Sub Total 4377515 O9764 7435187 5711 437 Gwanggyo-Edutown 12Gimpo-Yangchon 1764 2613743 O437 O 1764 743 2613437 Gwanggyo-Edutown 13~15 Gwanggyo-Edutown1173 12 22251764 O2613 O 1173 1764 22252613 Gwanggyo-Edutown 13~15 1173 2225 O 1173 2225 Sales house Gimpo-Hangang Ab-1 1167 2617 O 1167 2617 (10) Gimpo-Hangang Ab-7Gimpo-Hangang 1382 Ab-1 3028 1167 O2617 O 1382 1167 3028 2617 Gimpo-Hangang Ab-7 1382 3028 O 1382 3028 Wirye A2-11Sales house 1540 6758 X - - Wirye A2-11 1540 6758 X - - Wirye A2-2(10) 1413 4661 O 1413 4661 Wirye A2-2 1413 4661 O 1413 4661 Namyangju-Dasan B2 1186 2166 O 1186 2166 Namyangju-Dasan B2 1186 2166 O 1186 2166 Namyangju-Dasan B4 1615 2938 O 1615 2938 Namyangju-Dasan B4 1615 2938 O 1615 2938 Namyangju-Dasan S1 1685 2902 O 1685 2902 Namyangju-Dasan S1 1685 2902 O 1685 2902 Sub Total 13,668 30,345 9 sites selected 12,128 23,587 Sub Total 13,668 30,345 9 sites selected 12,128 23,587 TotalTotal 21,183 40,109 21,183 16 sites selected 17,315 29,298

The result ofSustainability objective 2020 function, 12, x FOR PEER (maximization REVIEW of the number of suppled public13 rental of 15 houses) is 5187. 5.4. Public SustainabilityRental Housing 2020, Pl12,anning x FOR PEER by Genetic REVIEW Algorithm 13 of 15 5.4. Public Rental HousingThe result5 Planning.4. Public of the Rental Genetic by GeneticHousing Algorithm Pl Algorithmanning is shown by Genetic in Table Algorithm 12. As observed in Table 12, Constraint 1 is satisfied because total investment amount is 3,025,900 million KRW which is less than 3,034,520 The result of the Genetic Algorithm is shown in Table 12. As observed in Table 12, Constraint 1 million KRW. Also, Constraint 2 is satisfied because only Wirye A2-11 is excluded. The result of the Geneticis satisfied Algorithm because total is investment shown in amount Table is 123,025,900. As observedmillion KRW inwhich Table is less 12 than, Constraint 3,034,520 The result of objective function (maximization of the number of suppled public rental houses) is million KRW. Also, Constraint 2 is satisfied because only Wirye A2-11 is excluded. 1 is satisfied because5773. total investment amount is 3,025,900 million KRW which is less than 3,034,520 million KRW. Also, ConstraintThe 2 result is satisfied of objective because function (maximization only Wirye of A2-11 the number is excluded. of suppled public rental houses) is 5773. Table 12. Result of the Genetic Algorithm. Investm Table 12. Result ofTable the Genetic12. Result of Algorithm. the Genetic Algorithm.Number Investment ent of Investm Name of SiteNumber of NumberInvestment of Houses Amount Selection Number ofAmounNumberInvestment Name of Site SelectionInvestment Selected ent Houses Amount (100m.) (100m.) Selected Houses t of Amount (100m.) Name of Site Number of Houses Amount SelectionHouses Amoun Gwanggyo A10 701 1196 X -(100m.)Selected - (100m.) t Gwanggyo A11Gwanggyo A10 637 70 11031 1196 OX 637 -Houses - 1103 (100m.) Gwanggyo A11 637 1103 O 637 1103 Gwanggyo A16 224Gwanggyo A10 374701 X1196 X - - - Gwanggyo A16 224 374 X - - Rental house Gwanggyo A19 1373Gwanggyo A11 1212637 O1103 1373 O 637 1212 1103 (10) Gwanggyo A19 1373 1212 O 1373 1212 Gwanggyo A23 258Gwanggyo A16 431224 X374 X - - - Gwanggyo A23 258 431 X - - GwanggyoRental hous A24e 394Gwanggyo A19 5921373 O1212 394 O 1373 1212592 Gwanggyo A24 394 592 O 394 592 Gwanggyo(10) A25 146Gwanggyo A23 141258 O431 146 X - 141 - RentalGwanggyo house A25 146 141 O 146 141 Gwanggyo A26 1132Gwanggyo A24 1859394 O592 1132 O 394 1859 592 (10)Gwanggyo A26 1132 1859 O 1132 1859 Gwanggyo A30 2091Gwanggyo A25 1765146 X141 O - 146 141 - Gwanggyo A30 2091 1765 X - - Gimpo Ab-2 559Gwanggyo A26 10911132 X1859 O - 1132 1859 - Gimpo Ab-2 559 1091 X - - Gwanggyo A30 2091 1765 X - - Sub TotalSub Total 7515 7515 9764 59764 sites selected 5773 6672 6672 Gimpo Ab-2 559 1091 X - - Gimpo-Yangchon 743 437 O 743 437 Gimpo-Yangchon 743Sub Total 4377515 O9764 7435773 6672 437 Gwanggyo-Edutown 12 1764 2613 O 1764 2613 Gwanggyo-Edutown 12 1764Gimpo-Yangchon 2613743 O437 1764O 743 2613437 Gwanggyo-Edutown 13~15 1173 2225 O 1173 2225 Gwanggyo-Edutown 13~15 Gwanggyo-Edutown1173 12 22251764 O2613 1173O 1764 22252613 Gimpo-Hangang Ab-1 1167 2617 O 1167 2617 Gimpo-Hangang Ab-1Gwanggyo-Edutown 1167 13~1 26175 1173 O2225 1167O 1173 26172225 Sales house Gimpo-Hangang Ab-7 1382 3028 O 1382 3028 (10) Sales house Gimpo-Hangang Ab-1 1167 2617 O 1167 2617 Gimpo-Hangang Ab-7Wirye A2 1382-11 1540 30286758 OX 1382- - 3028 (10) Gimpo-Hangang Ab-7 1382 3028 O 1382 3028 Wirye A2-11Sales houseWirye A2 1540-2 1413 6758 4661 XO 1413 - 4661 - Wirye A2-11 1540 6758 X - - Wirye A2-2Namyangju-Dasan(10) 1413 B2 118 46616 2166 OO 14131186 2166 4661 Wirye A2-2 1413 4661 O 1413 4661 Namyangju-DasanNamyangju-Dasan B2 1186 B4 1615 2166 2938 O O 1186 1615 2938 2166 Namyangju-Dasan B2 1186 2166 O 1186 2166 Namyangju-DasanNamyangju-Dasan B4 1615 S1 1685 2938 2902 O O 1615 1685 2902 2938 Namyangju-Dasan B4 1615 2938 O 1615 2938 Namyangju-Dasan S1Sub Total 1685 13,668 2902 30,345 O 9 sites selected 12,128 1685 23,587 2902 Namyangju-Dasan S1 1685 2902 O 1685 2902 Sub TotalTotal 13,66821,183 30,345 940,109 sites selected 14 sites selected 12,12817,901 30,259 23,587 Sub Total 13,668 30,345 9 sites selected 12,128 23,587 Total 21,183Total 40,109 21,18314 sites selected40,109 14 sites17,901 selected 17,901 30,259 Table 13 is the comparison of each method. The result from the genetic algorithm is superior to those from arbitrary selection #1 and #2. Also, the result of the branch the bound method is not better Table 13 is the comparison of each method. The result from the genetic algorithm is superior to than that of arbitrary selection #2. The result of objectivethose function from arbitrary (maximization selection #1 and #2. of Also, the the number result of ofthe suppledbranch the bound public method rental is not houses) better than that of arbitrary selection #2. is 5773. Sustainability 2020, 12, 600 13 of 14

Table 13 is the comparison of each method. The result from the genetic algorithm is superior to those from arbitrary selection #1 and #2. Also, the result of the branch the bound method is not better than that of arbitrary selection #2.

Table 13. Comparison of the Supplied Number of Public Rental Houses.

Arbitrary Arbitrary Branch & Genetic Method Selection #1 Selection #2 Bound Method Algorithm Number of Public Rental 2091 5297 5187 5773 Houses

6. Conclusions This study reviewed the optimal land development planning model and optimal urban regeneration planning model in South Korea. Then, it proposed an optimal project selection model to maximize the number of total supplied public rental houses with real-world project data. There is a trade-off between the investment profit and investment amount needed to supply public rental houses. We applied a couple of optimization techniques such as the genetic algorithm and the branch and bound method to this combinatorial problem. The genetic algorithm obtained a superior result to those from arbitrary selections or the branch and bound method. We think that this optimization model is a useful and practical planning tool for real estate investment projects while meeting various constraints including budget limitations, regional balance, and profit and welfare balance. Because real estate projects have no divisibility, we must decide whether or not to select any specific project. The genetic algorithm and branch and bound methods are useful tools for this kind of discrete optimization problems in real estate investment. Our optimization model may be applied to government-level infrastructure development plan in all over the country. With a limited budget, governments would select infrastructure (e.g., expressways, high-speed rail, facilities for disaster prevention, etc.) development projects which have different project effect, investment amount, and project location. The model also can be applied to financial investment decisions with different returns of investment and risk among lots of bond, stock, commodities like gold or real estate. Investors would find an optimal investment portfolio obtaining objective profits under affordable risks with this model. The model saves considerable enumeration time with the trial and error method and proposes a reasonable basis for decisions. Our research was limited by the amount of data available, thus we could not do a more detailed comparison between the various methods. If more data becomes available to us in the future, we can revisit this study and provide more precise comparisons between the different methods.

Author Contributions: J.H.P. proposed the idea, performed computation, and wrote the paper. J.-S.Y. supervised the research on real estate investment. Z.W.G. supervised the research on optimization formulation and algorithms. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the Energy Cloud R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT (2019M3F2A1073164). Conflicts of Interest: The authors declare no conflict of interest.

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