Urban Land-Use Allocation with Resilience: Application of the Lowry Model

Abstract

The Resilient Cities Network initiated by the Rockefeller Foundation advocates achieving the goal of comprehensive resilient urban development through land-use planning, but the implementation of resilience must be achieved through a vulnerability analysis. The Lowry Model is the earliest and most used land-use integrated transportation allocation model. Its operation is mainly based on accessibility indicators to allocate population and employment opportunities, and the results of the allocation can be used as a basis for urban development. Accessibility is a unique feature of the Lowry Model, in which accessibility is a function of employment opportunities and physical distance. However, it builds non-resilient cities. A city is a system that is vulnerable and suffers the most when change occurs. A city with a high density of population, although it has location convenience, is relatively vulnerable to disasters and security threats. Ignoring resilience makes the city lose its adjustment mechanism to avoid disasters and make the city less resilient, less safe, and even less efficient. This paper takes Taoyuan City, Taiwan, as the case study area, uses the data to implement a resilience-oriented allocation of land use, and compares the results with a non-resilient land-use allocation. The results show that the resilience-oriented Lowry Type Model can indeed allocate population and service employment opportunities to districts with higher resilience and lower vulnerability, can meet the threshold standard constraints of the economies of scale, and can obeythe population density scale constraints to maintain an adequate level of quality of life. This paper offers positive conclusions that can support the application of the resilience-oriented Lowry Type Model to Taiwan and even other cities that expect resilient planning.

1. Introduction

The fields of urban modelling have sprung from many disciplines which are applied to solve land-use allocation with emerging data sources. They can be divided into three traditions of models, including the effective and practical models, the general equilibrium of the spatial economy models, and the spatial effects and economies of scale models. For a fully practical urban policy, urban governance goes through these decisions, including the timing and developmental trajectories of growth, trade, transport, and location, which are mutually dependent. The main urban models to be used as reference for political decisions since Lowry (1964) [1] are built on Lowry-type spatial interaction models. Accessibility and employment opportunities of cities attract rural immigrants, but hidden behind these benefits are unpredictable risks, including low-lying disaster-prone landscapes being scattered on major urban roads, concentrated living of vulnerable populations, and rapid spread of diseases. In past land-use plans that lacked the consideration of vulnerability and hazard-prone factors, dangers and crises in the process of urban development often made the assignment results contradictory. During the COVID-19 pandemic, many high-density areas, which are the most vulnerable parts of cities, are the places with the largest number of people infected. The applicability of modifying the Lowry model for the land-use allocation of Taiwan should be reconsidered. A revised Lowry-type model, which incorporates resilience factors, is introduced to adjust the original equation.

Resilience is to maintain the maximum flexibility of a city to govern it. For example, when the COVID-19 pandemic spread and paralysed the medical system, all reconstruction seemed to be slow. The flexible setting of Central Park as an emergency medical base was indeed a very effective method to meet the urgent needs. To incorporate this concept into the Lowry model, social vulnerability can be included in the gravity equation in the present study. The gravity equation of the original Lowry model is used to calculate the employment and shopping accessibility indicators of a district as a probability of distributing the population [2,3,4,5]. The allocation results are based on the principle of accessibility, and vulnerability and resilience are ignored in the model [6,7,8]. Table 1 illustrates a comparison of the vulnerability indicators and resilience definition on the panel for a discussion of this empirical study.

This study uses resilience as an assignment index to conduct land-use and population allocation. Low income; disabilities; illiteracy; unemployment; young and old age; government subsidy recipients [9,10,11]; renting [12,13,14,15,16]; and work in certain industries, such as mining and the low-paying service sector [17,18,19] are vulnerability indicators that are often used in the literature [20,21]. Indicators of vulnerable areas include low numbers of hospitals per person, long-term fallow land, high numbers of vacant houses, households without tap water, amount of garbage generated, and area of nonurban land.

In the resilience-oriented Lowry-type model (ROLTM), the basic industry is regarded as an exogenous variable, and the basic multiplier of economic basic theory is used to obtain the total employed population. The total population is then calculated according to the dependency ratio to obtain the population employed in the service sector by using service sector demand parameters. Finally, the total increase in employment according to the employment multiplier is calculated. The allocation must meet the upper limits of density and the lower limit of economies of scale in service sectors.

Table 1. Comparison of vulnerability indicators and resilience definition in the literature.

Author, Time	Title	Model	Vulnerability Indicators	Resilience Definition	Summary
Cutter, Susan L.; Barnes, L.; Berry, M.; Burton, C.; Evans, E.; Tate, E.; Webb, J., 2008 [14]	A place-based model for understanding community resilience to natural disasters	Disaster resilience of place (DROP)model.	Some research argues that vulnerability arises from underlying social conditions that are often remote from the initiating event. Here, exposure is treated as given, and research under this perspective searches for patterns of differential access to resources or differential susceptibility to loss. A second perspective within vulnerability research explains causality by modeling potential exposure to hazard events. This view assumes vulnerability is simply a function of proximity to the source of risk or hazard. A third theme in vulnerability research integrates both the biophysical and social perspectives. In this view, vulnerability is a function of biophysical risk and social response and how this manifests itself locally, or in the hazardousness of place.	Wetlands acreage and loss erosion rates. % Impervious surface. Biodiversity. Demographics (age, race, class, gender, and occupation). Social networks and social embeddedness. Community values—cohesion. Faith-based organizations. Employment. Value of property. Wealth generation. Municipal finance/revenues. Participation in hazard reduction programs (NFIP, Storm Ready) and hazard mitigation plans. Emergency services. Zoning and building standards; emergency response plans; interoperable communications; and continuity of operations plans. Lifelines and critical infrastructure, and transportation network. Residential housing stock and age. Commercial and manufacturing establishments. Local understanding of risk, and counseling services. Absence of psychopathologies (e.g., alcohol, drug, and spousal abuse), and health and wellness (e.g., low rates mental illness and stress-related outcomes). Quality of life (high satisfaction).	This paper provides a new framework, the disaster resilience of place (DROP) model, designed to improve comparative assessments of disaster resilience at the local or community level.
Vale, Lawrence J., 2014 [22]	The politics of resilient cities: whose resilience and whose city?	Criticism and discourse	Vulnerable population	Resilience, in one sense, is an anticipatory venture. Resilience is a complex concept to transfer to the built environment because it operates in these two distinct modes: proactive/preventive resilience and reactive/restorative resilience.	Due to cities and city-regions being organized in ways that both produce and reflect underlying socio-economic disparities, some parts are much more resilient than others and, therefore, vulnerability is often linked to both topography and income. Uneven resilience threatens the ability of cities to function economically, socially, and politically.
Bergstrand, K.; Mayer, B.; Brumback, B.; Zhang, Y., 2015 [20]	Assessing the relationship between social vulnerability and community resilience to hazards	Factor analysis	Percent Asian. Percent of households earning >$200,000 annually. Per capita income. Median house value. Median rent. Percent black. Percent of children living in married couple families. Percent poverty. Percent female headed household. Percent with <12th grade education. Percent of housing units with no car. Percent of population under 5 years or 65 and over. Median age. Percent of households receiving social security. People per unit. Percent female participation in labor force. Percent Hispanic. Percent speaking English as a second language with limited English proficiency. Percent of population without health insurance. Population density. Percent urban population. Percent renters. Percent mobile homes. Percent of population 65 and over in group quarters. Hospitals per capita. Percent of population with a disability. Percent civilian unemployment. Percent employed in extractive industry. Percent employment in service industry. Percent native American.	Economic Development Index (1) Employment. (2) Income. (3) Occupations. (4) Taxes. (5) Resource equity. (6) Social Capital Index. (7) Household composition. (8) Civic organizations. (9) Voting behaviours. (10) Religious adherence. (11) Migration. (12) Crime.	It measures community resilience and social vulnerability in counties across the United States and finds a correlation between high levels of vulnerability and low levels of resilience, indicating that the most vulnerable counties also tend to be the least resilient.
Chang, Stephanie E.; Yip, Jackie Z. K.; van Zijll de Jong, Shona L.; Chaster, R.; Lowcock, A., 2015 [23]	Using vulnerability indicators to develop resiliencenetworks: a similarity approach	This article proposes a similarity measure that is adapted from Gower’s general similarity coefficient SGower, which was originally proposed by Gower and has been widely used for mixed data types.			The method developed here quantifies vulnerability profiles for the purposes of identifying places that are similarly vulnerable.
Da, Silva J., 2016 [24]	City resilience index- understanding and measuring city resilience	Scored on a linear scale between 1 and 5, based upon a consideration of the ‘best case’ and ‘worst case’ scenarios relevant to a particular area of city performance. Scored on relevant city data in a specific unit as a globally applicable metrics of resilience. A score from 1 to 5 is then automated, based on a standardized performance scale.		Resilience of a city relates to four key dimensions: (1). Health and well-being. (2). Economy and society. (3). Infrastructure and environment, manmade. (4). Leadership and strategy. Research to develop the Framework and Index has identified 52 indicators. The indicators add further definition to the 12 indicators and identify the critical factors that contribute towards the resilience of urban systems. (1). Safe and affordable housing. (2). Adequate affordable energy supply. (3). Inclusive access to safe drink water. (4). Effective sanitation. (5). Sufficient affordable food supply. (6). Inclusive labour policies. (7). Relevant skills and training. (8). Local business environment. (9). Supportive financing mechanisms. (10). Diverse protection of livelihoods following a shock. (11). Robust public health systems. (12). Adequate access to quality healthcare. (13). Emergency medical care. (14). Effective emergency response services. (15). Local community support. (16). Cohesive communities. (17). Strong city-wide identity and culture. (18). Actively engaged citizens. (19). Effective systems to deter crime. (20). Proactive corruption prevention. (21). Competent policing. (22). Accessible criminal and civil justice. (23). Well-managed public finances. (24). Comprehensive business continuity planning. (25). Diverse economic base. (26). Attractive business environment. (27). Strong integration with regional and global economies. (28). Comprehensive hazard and exposure mapping. (29). Appropriate codes, standards. and enforcement. (30). Effectively managed protective ecosystems. (31). Robust protective infrastructure. (32). Effective stewardship of ecosystems. (33). Flexible infrastructure. (34). Retained spare capacity. (35). Diligent maintenance and continuity. (36). Adequate continuity for critical assets and services. (37). Diverse and affordable transport networks. (38). Effective transport operation and maintenance. (39). Reliable communications technology. (40). Secure technology networks. (41). Appropriate government decision-making. (42). Effective co-ordination with other government bodies. (43). Proactive multi-stakeholder collaboration. (44). Comprehensive hazard monitoring and risk assessment. (45). Comprehensive government emergency management. (46). Adequate education for all. (47). Widespread community awareness and preparedness. (48). Effective mechanisms for communities to engage with the government. (49). Comprehensive city monitoring and data management. (50). Consultative planning process. (51). Appropriate land use and zoning. (52). Robust planning approval process.	The Index measures relative performance over time rather than comparison between cities. It does not deliver an overall single score for comparing performance between cities, neither does it provide a world ranking of the most resilient cities. However, it provides a common basis for measurement and assessment to better facilitate dialogue and knowledge sharing between cities.

Table 1. Comparison of vulnerability indicators and resilience definition in the literature.

Author, Time	Title	Model	Vulnerability Indicators	Resilience Definition	Summary
Cutter, Susan L.; Barnes, L.; Berry, M.; Burton, C.; Evans, E.; Tate, E.; Webb, J., 2008 [14]	A place-based model for understanding community resilience to natural disasters	Disaster resilience of place (DROP)model.	Some research argues that vulnerability arises from underlying social conditions that are often remote from the initiating event. Here, exposure is treated as given, and research under this perspective searches for patterns of differential access to resources or differential susceptibility to loss. A second perspective within vulnerability research explains causality by modeling potential exposure to hazard events. This view assumes vulnerability is simply a function of proximity to the source of risk or hazard. A third theme in vulnerability research integrates both the biophysical and social perspectives. In this view, vulnerability is a function of biophysical risk and social response and how this manifests itself locally, or in the hazardousness of place.	Wetlands acreage and loss erosion rates. % Impervious surface. Biodiversity. Demographics (age, race, class, gender, and occupation). Social networks and social embeddedness. Community values—cohesion. Faith-based organizations. Employment. Value of property. Wealth generation. Municipal finance/revenues. Participation in hazard reduction programs (NFIP, Storm Ready) and hazard mitigation plans. Emergency services. Zoning and building standards; emergency response plans; interoperable communications; and continuity of operations plans. Lifelines and critical infrastructure, and transportation network. Residential housing stock and age. Commercial and manufacturing establishments. Local understanding of risk, and counseling services. Absence of psychopathologies (e.g., alcohol, drug, and spousal abuse), and health and wellness (e.g., low rates mental illness and stress-related outcomes). Quality of life (high satisfaction).	This paper provides a new framework, the disaster resilience of place (DROP) model, designed to improve comparative assessments of disaster resilience at the local or community level.
Vale, Lawrence J., 2014 [22]	The politics of resilient cities: whose resilience and whose city?	Criticism and discourse	Vulnerable population	Resilience, in one sense, is an anticipatory venture. Resilience is a complex concept to transfer to the built environment because it operates in these two distinct modes: proactive/preventive resilience and reactive/restorative resilience.	Due to cities and city-regions being organized in ways that both produce and reflect underlying socio-economic disparities, some parts are much more resilient than others and, therefore, vulnerability is often linked to both topography and income. Uneven resilience threatens the ability of cities to function economically, socially, and politically.
Bergstrand, K.; Mayer, B.; Brumback, B.; Zhang, Y., 2015 [20]	Assessing the relationship between social vulnerability and community resilience to hazards	Factor analysis	Percent Asian. Percent of households earning >$200,000 annually. Per capita income. Median house value. Median rent. Percent black. Percent of children living in married couple families. Percent poverty. Percent female headed household. Percent with <12th grade education. Percent of housing units with no car. Percent of population under 5 years or 65 and over. Median age. Percent of households receiving social security. People per unit. Percent female participation in labor force. Percent Hispanic. Percent speaking English as a second language with limited English proficiency. Percent of population without health insurance. Population density. Percent urban population. Percent renters. Percent mobile homes. Percent of population 65 and over in group quarters. Hospitals per capita. Percent of population with a disability. Percent civilian unemployment. Percent employed in extractive industry. Percent employment in service industry. Percent native American.	Economic Development Index (1) Employment. (2) Income. (3) Occupations. (4) Taxes. (5) Resource equity. (6) Social Capital Index. (7) Household composition. (8) Civic organizations. (9) Voting behaviours. (10) Religious adherence. (11) Migration. (12) Crime.	It measures community resilience and social vulnerability in counties across the United States and finds a correlation between high levels of vulnerability and low levels of resilience, indicating that the most vulnerable counties also tend to be the least resilient.
Chang, Stephanie E.; Yip, Jackie Z. K.; van Zijll de Jong, Shona L.; Chaster, R.; Lowcock, A., 2015 [23]	Using vulnerability indicators to develop resiliencenetworks: a similarity approach	This article proposes a similarity measure that is adapted from Gower’s general similarity coefficient SGower, which was originally proposed by Gower and has been widely used for mixed data types.			The method developed here quantifies vulnerability profiles for the purposes of identifying places that are similarly vulnerable.
Da, Silva J., 2016 [24]	City resilience index- understanding and measuring city resilience	Scored on a linear scale between 1 and 5, based upon a consideration of the ‘best case’ and ‘worst case’ scenarios relevant to a particular area of city performance. Scored on relevant city data in a specific unit as a globally applicable metrics of resilience. A score from 1 to 5 is then automated, based on a standardized performance scale.		Resilience of a city relates to four key dimensions: (1). Health and well-being. (2). Economy and society. (3). Infrastructure and environment, manmade. (4). Leadership and strategy. Research to develop the Framework and Index has identified 52 indicators. The indicators add further definition to the 12 indicators and identify the critical factors that contribute towards the resilience of urban systems. (1). Safe and affordable housing. (2). Adequate affordable energy supply. (3). Inclusive access to safe drink water. (4). Effective sanitation. (5). Sufficient affordable food supply. (6). Inclusive labour policies. (7). Relevant skills and training. (8). Local business environment. (9). Supportive financing mechanisms. (10). Diverse protection of livelihoods following a shock. (11). Robust public health systems. (12). Adequate access to quality healthcare. (13). Emergency medical care. (14). Effective emergency response services. (15). Local community support. (16). Cohesive communities. (17). Strong city-wide identity and culture. (18). Actively engaged citizens. (19). Effective systems to deter crime. (20). Proactive corruption prevention. (21). Competent policing. (22). Accessible criminal and civil justice. (23). Well-managed public finances. (24). Comprehensive business continuity planning. (25). Diverse economic base. (26). Attractive business environment. (27). Strong integration with regional and global economies. (28). Comprehensive hazard and exposure mapping. (29). Appropriate codes, standards. and enforcement. (30). Effectively managed protective ecosystems. (31). Robust protective infrastructure. (32). Effective stewardship of ecosystems. (33). Flexible infrastructure. (34). Retained spare capacity. (35). Diligent maintenance and continuity. (36). Adequate continuity for critical assets and services. (37). Diverse and affordable transport networks. (38). Effective transport operation and maintenance. (39). Reliable communications technology. (40). Secure technology networks. (41). Appropriate government decision-making. (42). Effective co-ordination with other government bodies. (43). Proactive multi-stakeholder collaboration. (44). Comprehensive hazard monitoring and risk assessment. (45). Comprehensive government emergency management. (46). Adequate education for all. (47). Widespread community awareness and preparedness. (48). Effective mechanisms for communities to engage with the government. (49). Comprehensive city monitoring and data management. (50). Consultative planning process. (51). Appropriate land use and zoning. (52). Robust planning approval process.	The Index measures relative performance over time rather than comparison between cities. It does not deliver an overall single score for comparing performance between cities, neither does it provide a world ranking of the most resilient cities. However, it provides a common basis for measurement and assessment to better facilitate dialogue and knowledge sharing between cities.

2. Materials and Methods

Urban resilience comprises infrastructural, institutional, economic, and social resilience [25,26,27,28,29]. Resilience is different from the vague concepts of “sustainability”, “development”, “continuity”, and “maintenance” [22]. Da Silva proposed that resilience encompasses four aspects: (1) health and well-being, (2) economy and society, (3) facilities and environment, and (4) leadership and strategy [24]. Chang et al. concluded that natural disasters experienced around the world continue to highlight that certain groups within society are more vulnerable to the impacts of disasters than other groups [23]. Low income, lack of insurance, and poor housing quality are believed to intensify the impact of natural hazards on people. Beban and Gunnell reported that land-use planning has a key role in reducing exposure and susceptibility to hazards through the management of activity locations and planning [30].

Papilloud and Keiler proposed that vulnerability should be a key factor in determining an accessibility index. Moreover, they proposed that vulnerability should affect the parameters of the distance function in an accessibility index [31]. They pointed out that vulnerability can be measured by the degree of accessibility reduction. The present study developed a similar concept, namely that the allocation of industry and population should be calculated using a resilience index that is a function of accessibility and vulnerability. A city with flexible design and planning is the resilient city defined in this article. The meaning of flexibility does not lie in the pursuit of location convenience without caring about the existence of risks. Flexibility also does not mean that there should be no risks at all; rather, it means that there should be planning and design to avoid the risks from vulnerability. In other words, resilience is about recognizing risks and coexisting with them. Vulnerability and accessibility can be measured by a combination of different variables. Furthermore, resilience can be measured by the combination of vulnerability and accessibility. The advantage of this approach is that it can be further investigated through variable combinations to estimate vulnerability. Because climate changes and extreme weather events in the past half century were not as obvious and frequent as they are now, for planning justice, the Lowry model must be adapted to make it more focused on resilience. Past planning that applied the Lowry model only considered socioeconomic spatial costs and benefit factors when allocating land use. To avoid the location fallacy caused by ignoring the resilience criterion, this study developed a land-use allocation model by incorporating the concept of resilience into the original Lowry model.

This study developed the ROLTM by incorporating two crucial urban economic theories—the economic basic theory and the gravity model—to allocate land use for Taoyuan City.

2.1. Land Use

Urban land use is divided into three categories: basic industry, service industry, and residential. The scale and distribution of the basic industries are determined by policy variables. Service industry use is divided into the neighborhood, city, and metropolitan sectors according to their scope of service. Service industry land use and residential land use are regarded as endogenous variables.

2.2. Economic Base Theory

Cities develop with the expansion of the basic industries, which triggers housing demand. This phenomenon induces a multiplier effect on the increase in demand for the service industry.

2.3. Assumptions

The following information is given exogenously: the basic industry activities in each district; the developable land area of each district; the land-use demand of the basic industries; the spatial interaction of each district; the land-use demand for service industry activities per person; the labour participation rate; the population density and service industry economies of scale in each district; and the vulnerability of each district.

2.4. Constraints

Two restriction conditions are added to the developed model. First, each district has an upper limit of population density because government policy stipulates an upper limit of population density in each district to control quality of life and achieve growth management. Second, the number of people assigned to the service industries in each district must reach the lower limit of an economy of scale, and urban development must conform to the principle of efficiency.

2.5. Model

The allocation must consider the influence of the accessibility and vulnerability indicators of the service industry. The spatial distance and vulnerability parameters are assumed to be equal to 1. The accessibility index is negatively proportional to the spatial distance and positively proportional to the residential population and the employment opportunities of adjacent districts. The number of people employed in the service industries and the number of residents allocated to each district must be positively proportional to the accessibility index and negatively proportional to the vulnerability index of each district. The land-use model, the ROLTM, used in this study considers the predicted value as the total quantity of population and allocates this quantity to each district according to the resilience distribution ratio.

3. Results

This study used 12 vulnerability indicators from the 2015 and 2016 Taoyuan City Statistical Census Report as the population and environmental risk factors [32,33], including 「Under 5 [20,22]」, 「Elderly [20,22]」, 「Illiterate [22]」, 「Garbage [22]」, 「Native [20,22]」, 「Arable land [14,15]」, 「No tap water [14,15]」, 「Move out [14,15]」, 「Low power [14,15]」, 「Low income [20,22]」, 「Disability [20,22]」, and 「Non-urban [14,15]」(

Table 2. Descriptive Statistics of the Vulnerability and Accessibility Indicators of Taoyuan City in 2015 and 2016.

Variable (Unit of Measurement) [Description]	Mean	Standard Deviation	Minimum	Maximum
Under 5 (number of people)   [population under 5 years old]	8034	5862	775	20,328
Elderly (number of people)   [population over 65 years old]	15,664	10,834	1233	38,953
Illiterate (number of people)   [illiterate population]	1537	701	107	2908
Garbage (ton)   [amount of garbage]	51,921.69	41,766.91	3007.55	148,846.40
Non-urban (hectare)   [non-urban land area]	8590.927	7501.996	1271.024	33,038.760
Native (number of people)   [Aboriginal population]	5211	2333	691	8151
Arable land (hectare)   [long-term leisure land area of cultivated land]	226.755	413.501	0.390	1630.210
No tap water (number of people)   [population without tap water supply]	7540	4490	1676	17,440
Move out (number of people)   [emigrated population]	6221	4490	586	16,049
Low power (house)   [number of houses with low electricity consumption]	6887.923	5542.254	489.000	18,621.000
Low income (number of households)   [number of low-income households]	533	363	182	1457
Disability (number of people)   [number of people with disabilities]	6082	3935	719	14,437
Vulnerability (-)   [comprehensive vulnerability index]	5.306	2.155	2.392	10.150
Accessibility (number of people per minute)   [accessibility index]	31,735.14	11,111.16	12,529.47	51,529.63

Source: Taoyuan City Statistical Census Report, 2015–2016, Department of Budget, Accounting and Statistics, Taoyuan City Government. 「-」: indicates no measurement unit.

). Table 2 indicates that the comprehensive vulnerability index $V_{ij}$ is calculated through the normalization of all vulnerability variables. The comprehensive vulnerability index of district i is calculated by $\widetilde{V_i}={\sum }_j{V}_{ij}/\left(\underset{i}{\max }{V}_{ij}\right)$, where $V_{ij}$ is the vulnerability variable j in district i and $\widetilde{V_i}$ is the sum of the index of normalized values of the 12 vulnerability indicators.

Table 3. Employment in the Basic Industries and the Land Area and Undeveloped Land Area of Taoyuan City in 2015 and 2016.

	Basic Industry Population (Number of People)	Land Area (Square Kilometers)	Undeveloped Land Area (Square Kilometers)	Basic Industry Land Area (Square Kilometers)
Taoyuan	52,664	34.8046	1.6716	2.6243
Zhongli	79,205	76.5200	30.8560	6.6883
Daxi	16,675	105.1206	80.0705	1.0645
Yangmei	43,547	89.1229	65.0582	4.8304
Luzhu	72,852	75.5025	25.4572	8.4544
Dayuan	34,526	87.3925	72.6176	2.8395
Guishan	85,911	72.0177	14.8383	9.7755
Bade	29,785	33.7111	23.0410	0.8121
Longtan	36,119	75.2341	62.0370	2.3860
Pingzhen	35,351	47.7532	19.3472	1.9802
Xinwu	6530	85.0166	79.6498	0.8438
Guanyin	41,813	87.9807	76.9562	8.3342
Fuxing	690	350.7775	310.3014	0.0085

Source: (1) Taoyuan City Agriculture, Forestry, Fishery and Animal Husbandry Census Report, 2015, Department of Budget, Accounting and Statistics, Taoyuan City Government. (2) Taoyuan City Industry and Service Census Report, 2016, Department of Budget, Accounting and Statistics, Taoyuan City Government. (3) Territorial Planning Geographic Information System, 2020, Urban and Rural Development Branch, Construction and Planning Agency, Ministry of the Interior, Taiwan.

indicates that, in 2016, the Guishan District and the Zhongli District had the two highest numbers of people employed in the basic industries in Taoyuan City. These areas mainly provide employment opportunities in the electronics, metal, machinery, equipment, and high-tech industries. The top three areas in descending order with the highest land-use area for the basic industries are the Guishan District, the Luzhu District, and the Guanyin District.

Table 4. Taoyuan City Interdistrict Travel Time in 2016 (minutes).

	Taoyuan	Zhongli	Daxi	Yangmei	Luzhu	Dayuan	Guishan	Bade	Longtan	Pingzhen	Xinwu	Guanyin	Fuxing
Taoyuan	6.00	14.25	22.20	36.00	10.95	23.10	6.75	12.90	40.80	16.35	41.70	50.40	46.50
Zhongli	14.25	5.00	22.20	18.90	19.80	18.90	19.20	12.00	18.90	4.65	24.75	33.30	46.50
Daxi	22.20	22.20	9.00	33.45	45.15	54.60	32.40	10.50	14.25	22.95	38.85	47.55	24.90
Yangmei	36.00	18.90	33.45	10.00	37.80	47.70	52.20	31.05	26.25	18.60	12.30	22.65	56.70
Luzhu	10.95	19.80	45.15	37.80	13.00	22.05	13.20	25.95	47.70	22.95	40.95	49.65	66.30
Dayuan	23.10	18.90	54.60	47.70	22.05	15.00	36.90	33.30	55.05	22.20	24.60	19.50	73.65
Guishan	6.75	19.20	32.40	52.20	13.20	36.90	11.00	15.75	33.75	22.05	55.50	64.20	52.35
Bade	12.90	12.00	10.50	31.05	25.95	33.30	15.75	11.00	16.80	12.60	36.45	45.15	34.80
Longtan	40.80	18.90	14.25	26.25	47.70	55.05	33.75	16.80	13.00	14.70	31.35	40.05	42.30
Pingzhen	16.35	4.65	22.95	18.60	22.95	22.20	22.05	12.60	14.70	6.00	22.50	31.05	46.95
Xinwu	41.70	24.75	38.85	12.30	40.95	24.60	55.50	36.45	31.35	22.50	10.00	10.80	62.10
Guanyin	50.40	33.30	47.55	22.65	49.65	19.50	64.20	45.15	40.05	31.05	10.80	10.00	70.80
Fuxing	46.50	46.50	24.90	56.70	66.30	73.65	52.35	34.80	42.30	46.95	62.10	70.80	22.00

Source: Google Maps is used to calculate the travel time between each district office at a speed of 40 km/h.

indicates that the travel time from the Fuxing District to each of the other districts is the longest. It takes 73.65 and 70.8 minutes to go from the Fuxing District to the Dayuan District and the Guanyin District, respectively. The Fuxing District covers a large area in the southeast of Taoyuan City and is located far from the downtown area.

Table 5. Service Industry Types, Economies of Scale, and Demand Parameters of Taoyuan City in 2015.

Parameter	Service Industry Type
(Unit of Measurement for Variables)	Neighborhood	City	Metropolitan
Economies of scale in the service industries (number of people)	500	1000	2500
Number of service industry employment per household (number of employed persons in the service industries/person)	0.080	0.160	0.096
Land area required by each service industry employed person (square kilometer/employed person in the service industries)	0.00003	0.00004	0.00005
Resident population weight	0.9	0.7	0.5
Employed population weight	0.1	0.3	0.5
Number of people supported by each employed person (supported persons/employed person)	2.1	2.1	2.1
Maximum residential density (population/square kilometer)	10,000	10,000	10,000

Source: Calculated for this study.

indicates that the economies of scale within the employed population of the neighborhood, city, and metropolitan sectors are 500, 1000, and 2500 employed persons, respectively. In addition, three types of service sector parameters must be set when implementing land-use allocation. The numbers of people from each household working in the neighborhood, city, and metropolitan sectors are 0.08, 0.16, and 0.096, respectively. Based upon previous information, the demand for land-use area for each employed person in the neighborhood, city, and metropolitan sectors is 3 × 10⁻⁵, 4 × 10⁻⁵, and 5 × 10⁻⁵ km², respectively, and each employed person supports 2.1 persons. The upper limit of population density is 10,000 people/km².

Table 6. Accessibility and Vulnerability Indicators of Taoyuan City in 2015.

District	Accessibility	Vulnerability
		Under 5	Elderly	Illiterate	Native	Garbage	No Tap Water	Non-Urban	Arable Land	Low Power	Low Income	Disability	Move Out
Taoyuan	46,576.31	20,328	38,428	2746	7069	125,457.20	9903	1271.024	88.75	18,440	1457	13,777	16,049
Zhongli	25,296.62	19,512	38,953	2908	8151	148,846.40	2365	3387.752	76.30	18,621	1124	14,437	14,259
Daxi	51,529.63	4123	11,063	1320	7084	33,180.50	11,594	9769.161	28.52	4349	230	3339	3319
Yangmei	26,281.79	8207	15,258	1422	3898	43,508.88	17,440	8921.636	75.10	7116	425	4824	5315
Luzhu	31,174.40	8834	11,843	1541	4289	47,534.22	1676	7277.991	216.39	4678	557	5674	6117
Dayuan	24,636.68	4370	8520	1980	3372	21,949.12	9691	8436.193	21.23	3521	698	7621	3337
Guishan	35,104.66	7784	13,936	1288	6831	58,804.55	4537	7072.498	159.07	5172	385	4887	7285
Bade	35,437.94	9229	17,863	1794	6833	52,280.91	1902	3321.610	32.83	9232	553	6021	7640
Longtan	24,615.45	5356	12,366	834	3740	37,270.17	10,501	7341.759	1630.21	5869	547	8028	4193
Pingzhen	49,704.30	11,075	19,413	1265	6412	78,792.05	7229	4350.234	287.90	8492	245	4514	8909
Xinwu	26,864.63	1759	7397	1336	691	12,589.27	2929	8311.061	133.06	1367	182	2454	1545
Guanyin	22,804.89	3090	7357	1442	1577	11,761.14	9546	9182.365	0.39	2197	239	2767	2320
Fuxing	12,529.47	775	1233	107	7801	3007.55	8702	33,038.760	198.06	489	285	719	586

indicates that the Daxi District, the Pingzhen District, and the Taoyuan District are the ones with the top three highest accessibility indices, respectively. These districts are the most geographically advantageous districts. In terms of vulnerabilities, the Taoyuan District is the one with the most migrants, the most children under five years old, at the highest number of low-income households, as well as the highest comprehensive vulnerability index. The Yangmei District is the one with the highest number of people without tap water supply, the Longtan District is the one with the largest area of cultivated land for long-term leisure use, and the Fuxing District is the one with the largest area of nonurban land.

In the original Lowry model, urban land is allocated with accessibility only. However, this mechanism often results in one of two types of allocation displacement: the displacement of assigning excess population and land use to high-risk areas with a high accessibility index or of assigning insufficient population and land to high-capacity areas with a low accessibility index.

Table 7. Distribution of the Employed Population and Residential Land Area in Taoyuan City in 2015 During the First Round of Using the ROLTM.

District and Variable	Employed Population in Basic Industries (People)	Residential Land Area a (Square Kilometer)
Taoyuan	49,070	30.5087
Zhongli	85,197	38.9757
Daxi	24,053	23.9856
Yangmei	53,818	19.2343
Luzhu	79,808	41.5909
Dayuan	45,009	11.9354
Guishan	86,870	47.4039
Bade	30,921	9.8580
Longtan	40,588	10.8111
Pingzhen	39,491	26.4258
Xinwu	30,750	4.5230
Guanyin	52,012	2.6903
Fuxing	7339	40.4676
Total	62,4926
Total Population (people)	1,312,345
Total Employment in the Service Industries (people)	0

Note: ^a Equal to the land area of the district minus the sum of the undeveloped land area, the land area for basic industry use, and the land area for service industry use. The land area of the service industries is considered to be 0 at the time of the first distribution.

reveals that the number of employees in the service industry assigned in the first round is zero, and the demand for land use is zero.

Table 8. Comprehensive Vulnerability, Resilience Index, and Assigned Population for the Districts of Taoyuan City in 2015.

District	Comprehensive Vulnerability	Resilience Index	Probability of Distributed Population	Population Allocated for Resilience a
Taoyuan	9.2462	5037.324	0.052927	69,459.08
Zhongli	8.9047	5786.775	0.060802	79,793.17
Daxi	3.8402	6587.251	0.069213	90,830.84
Yangmei	4.7102	5579.736	0.058627	76,938.34
Luzhu	3.9709	7850.773	0.0825	108,253.40
Dayuan	3.9037	6311.054	0.0663	87,022.39
Guishan	4.3229	8120.555	0.0853	111,973.40
Bade	4.7172	7512.485	0.0789	103,588.80
Longtan	4.9093	5014.098	0.0527	69,138.81
Pingzhen	5.0090	9923.089	0.1043	136,828.30
Xinwu	1.8709	14,359.210	0.1509	197,997.40
Guanyin	2.5530	8932.570	0.0939	123,170.20
Fuxing	3.0125	4159.181	0.0437	57,350.46

Source: Calculated for this study ^a: The assigned population of each district is lower than the upper limit of the population obtained by multiplying the maximum population density by the land area.

illustrates that the districts with the two highest comprehensive vulnerabilities are the Taoyuan District and the Zhongli District, respectively, even though these two districts are highly urbanized with complete public facilities and infrastructure. However, the buildings in these two districts are old and dangerous, and the proportion of houses of more than 30 years old is also very high. The comprehensive vulnerability indices of the Xinwu District and the Guanyin District are 1.8709 and 2.5530, respectively. These two districts are less developed than the other districts. However, the social and economic vulnerabilities of these districts are not as serious as those of the other districts. The future development prospects of these two districts are favourable. The resilience indicators of the Xinwu District, the Pingzhen District, the Guan-yin District, and the Guishan District exceed those of the other districts. Therefore, they are allocated a high proportion of population and land area.

The calculation process in the first round is described in the following text. The total population of 1,312,345 people is multiplied by the employed population demand parameters of 0.08, 0.16, and 0.096 for the service industries. The employed populations in the neighborhood, city, and metropolitan service sectors are 104,988, 209,975, and 125,985 people, respectively.

The total employed population of 1,065,874 people is multiplied by the dependency ratio of 2.1 to obtain the total population (i.e., 2,238,335;

Table 9. Final Allocation of Land Area for Service Industry and Residential Use by the ROLTM for Taoyuan City in 2015.

District	Total Population (People)	Service Industry Land Area (Square Kilometer)	Residential Land Area (Square Kilometer)
	2,238,335
Taoyuan		$1.6197$	28.889
Zhongli		$2.1042$	36.871
Daxi		$0.8864$	23.099
Yangmei		$1.0097$	18.225
Luzhu		$1.3401$	40.251
Dayuan		$0.8895$	11.046
Guishan		$1.5974$	45.807
Bade		$1.2465$	8.611
Longtan		$0.9782$	9.833
Pingzhen		$1.6788$	24.747
Xinwu		$0.7146$	3.808
Guanyin		0.8707	1.820
Fuxing		$0.2586$	40.209

). Table 9 indicates that the land area of the service sector can be obtained by multiplying the number of people employed in the three service industries in each district by the area of land required for each employed person. The service sector land areas of the Zhongli District and the Pingzhen District are 2.1042 and 1.6788 km², respectively, which are higher than those of the other districts. The Fuxing District, the Xinwu District, and the Guanyin District are the areas with the three lowest service industry land areas. The final distribution results indicate that the Guishan District, the Luzhu District, and the Fuxing District are the areas with the three highest residential land areas of 45.807, 40.251, and 40.209 km², respectively. The Guanyin District and the Xinwu District are the areas with two lowest residential land areas of 1.820 and 3.808 km², respectively.

Table 10. Final Allocations of Land Area for Service Industry Use by the Lowry Model and the ROLTM for Taoyuan City in 2015.

District	Service Industry
	LM		ROLTM		Difference (ROLTM-LM)
	Land Use Area	%	Land Use Area	%	Area	%
Taoyuan	1.52684	4.3867	1.6197	4.6537	0.0929	0.2669
Zhongli	2.05886	2.6906	2.1042	2.7499	0.0454	0.0593
Daxi	0.9034	0.8594	0.8864	0.8432	−0.0170	−0.0162
Yangmei	1.0403	1.16724	1.0097	1.1329	−0.0306	−0.0343
Luzhu	1.33174	1.7638	1.3401	1.7749	0.0084	0.0111
Dayuan	0.9271	1.0608	0.8895	1.0178	−0.0376	−0.0430
Guishan	1.5350	2.1315	1.5974	2.2180	0.0624	0.0866
Bade	1.2038	3.5711	1.2465	3.6976	0.0427	0.1266
Longtan	0.9692	1.2882	0.9782	1.3002	0.0090	0.0120
Pingzhen	1.6404	3.4351	1.6788	3.5155	0.0384	0.0804
Xinwu	0.8595	1.0110	0.7146	0.8405	−0.1449	−0.1705
Guanyin	0.9063	1.0301	0.8707	0.9896	−0.0356	−0.0405
Fuxing	0.2731	0.0779	0.2586	0.0737	−0.0145	−0.0041
Total	1220.9540		1220.9540

LM: Lowry model.

displays the difference between the ROLTM and original Lowry model in the service sector land-use allocation. Compared to the original Lowry model, the ROLTM allocates a 0.171% (0.1449 km²) and 0.0405% (0.0356 km²) lower land area to the Xinwu District and the Guanyin District, respectively. The areas allocated to the Taoyuan District, the Zhongli District, the Luzhu District, the Guishan District, the Bade District, the Longtan District, and the Pingzhen District are higher when using the ROLTM than when using the original Lowry model. The areas allocated to the Daxi District, the Yanmei District, the Dayuan District, the Xinwu District, the Guanyin District, and the Fuxing District are lower (0.0041% to 0.1705% lower) when using the ROLTM than when using the original Lowry model. The differences between the residential use allocation results obtained with the ROLTM and the original Lowry model are presented in

Table 11. Final Allocations of Land Area for Residential Use by the Lowry Model and the ROLTM for Taoyuan City in 2015.

District	Residential Use
	LM		ROLTM		Difference (ROLTM-LM)
	Land Use Area	%	Land Use Area	%	Area	%
Taoyuan	28.982	83.270	28.889	83.003	−0.0930	−0.2670
Zhongli	36.917	48.245	36.871	48.185	−0.0460	−0.0600
Daxi	23.082	21.958	23.099	21.974	0.0170	0.0160
Yangmei	18.194	20.415	18.225	20.449	0.0310	0.0340
Luzhu	40.259	53.322	40.251	53.311	−0.0080	−0.0110
Dayuan	11.008	12.596	11.046	12.639	0.0380	0.0430
Guishan	45.869	63.691	45.807	63.605	−0.0620	−0.0860
Bade	8.654	25.672	8.611	25.545	−0.0430	−0.1270
Longtan	9.842	13.082	9.833	13.070	−0.0090	−0.0120
Pingzhen	24.785	51.903	24.747	51.823	−0.0380	−0.0800
Xinwu	3.663	4.309	3.808	4.480	0.1450	0.1710
Guanyin	1.784	2.028	1.820	2.068	0.0360	0.0400
Fuxing	40.195	11.459	40.209	11.463	0.0140	0.0040
Total	1220.954		1220.9540

LM: Lowry model.

. The resilience factors added into the Lowry model result in an increase of up to 0.1450 and 0.0360 km² (an increase of 0.1710% and 0.0400%, respectively) in the residential area allocated to the Xinwu District and the Guanyin District, respectively. Similar trends are observed for the Daxi District, the Dayuan District, the Yangmei District, and the Fuxing District. The resilience factors added into the original Lowry model result in a decrease of up to 0.0080 and 0.0930 km² in the residential areas allocated to the Luzhu District and the Taoyuan District, respectively. Similar trends (0.0380% to 0.0620% decreases) are also observed for the Zhongli District, the Guishan District, the Bade District, the Longtan District, and the Pingzhen District.

4. Conclusions

Traditional comprehensive planning lays out the long-term vision for cities by considering economic development, transportation planning, and improvement of quality of life. Connecting city with land-use coordination to allocate employment and land area in the context of vulnerability and resilience, besides accessibility, is significant for the sustainability and health of future cities under climate change. The empirical research of Taoyuan City in this article finds that land-use planning incorporated with resilience can help allocate employment and land area to districts with less vulnerable features and more accessible characteristics. The Lowry-type model in this article indicates allocation by means of objective probabilistic assignment technique and normative planning justice.

How cities operate has always been followed up how they are planned. However, the central role of urban planning in decarbonization has only recently been appreciated. The latest two chapters of the 2022 IPCC (Intergovernmental Panel on Climate Change; IPCC) are introduced to highlight the role of land-use planning and urban system in the reduction of carbon emissions and to provide guidelines for different cities. Land-use planning is the key tool for allocating city capital and managing urban environment and is central to the integration of climate change mitigation and adaptation plans into cities.

The current urban planning has resulted in high carbon emission and has trapped our communities in urban lifestyles dominated by cars. It has also failed to alleviate the damage to biodiversity and slow down habitat loss, increased resource scarcity, and ignored planning justice.

If Taoyuan City’s land-use plannings continue to serve rapid urban development and expansive industrial growth, which even trump all other efforts in rethinking urban planning, including decarbonization and resilience strategies, then the ethical prospects for urban health and sustainability are hard to realize.

In this study, the concept of resilience allocation is used in the operation of the ROLTM to adjust the land-use allocation of Taoyuan City. In the developed model, vulnerability is an exogenous variable of resilience to indicate the location risks being faced. Economies of scale and density control should be implemented to strengthen the efficiency criteria and quality maintenance of employment and population distribution. Finally, the government should confirm whether the allocation results satisfy the system equilibrium convergence constraint for accurate population distribution, which is the basis for land-use allocation.