Exploring Trade-Offs between Potential Economic, Social and Environmental Outcomes of Urban Agriculture in Adelaide, Australia and the Kathmandu Valley, Nepal

Abstract

Urban Agriculture (UA) is widely presented as a feature of sustainable cities, with various claims around economic, social, and/or environmental benefits. However, the extent to which these different benefits may reinforce or compete with one another is not clear. This paper presents an integrated modelling framework using proxy measures for economic benefit (the net margin, NM), social benefit (the full-time farmer employment equivalent (FTE) per consumer) and environmental benefit (reduction in carbon dioxide emissions, CO₂). The model is applied in two divergent development scenarios, including Adelaide, Australia, and the Kathmandu Valley, Nepal, to study the characteristic features of UA in different settings. Two-stage optimisation is used to explore trade-offs and synergies when pursuing different objectives (NM, FTE and CO₂). The model seeks the optimal farming area and selects from three levels of mechanisation (non-mechanised, garden tiller and garden cultivator), two purposes (gardening and commercial), two crop value categories (mixed and mid- to high-value vegetables) and two market mechanisms (wholesale vs. retail). The results of the optimisation provide insights into the key features of a UA system depending on the objective(s) being pursued, which we believe is a novel approach to justify UA research. For instance, the model favours a commercial UA form (in which both land and labour are costed) with a larger area when pursuing an economic objective, whereas it favours a gardening form of UA when aiming to maximise participation in the food system, with the preferred area depending on the extent to which either the economic or environmental objective is also being pursued. In Adelaide, the model favours commercial UA for the best-case profit and carbon emissions, and gardening for FTE maximisation. In the Kathmandu Valley, the model chooses the gardening UA within the given model assumptions.

1. Introduction

Factors like rapid urbanisation, concerns around the impacts of climate change on conventional agriculture systems and food insecurity, the need for healthy and diversified foods, and innovative lifestyles have encouraged growing foods in or near cities in the form of urban farming [1,2]. Urban Agriculture (UA) has been succinctly defined as “simply growing crops in cities” [3]. Diverse in its mission, scale, means, and forms [4], UA can provide some portions of fresh and safe food with shorter and simpler supply chains than the conventional food system, with other claimed social, economic and environmental benefits [5]. A typical characteristic of UA is the combination of small and dispersed production units creating a supply system mainly within the proximity of consumption [6].

The literature characterises UA based on factors such as the farming environment (controlled/uncontrolled), growing method (vertical/horizontal), type of crop (monoculture to mixed and integrated) and purpose (economic/social/environmental). UA typically has social and economic food production motives [7]. UA can include vegetable and fruit production, raising small livestock, beekeeping, aquaculture and hydroponics, and exists in many forms and at different sites using private and public land [8]. UA has been defined as a concept with multiple dimensions that deals with community building, green space and high property values based on the location of UA within cities [9]. Similarly, Van Tuijl et al. [10] defined UA based on a strategic focus referring to its purpose, market and product.

The purposes of UA differ depending on the development context; in developing countries, UA is intended to help feed rapidly growing populations [11]. In developed countries, UA is typically undertaken to improve lifestyle, health, community development, and innovation [2]. Globally, UA has evolved in response to several drivers, including war [12] or poor economic conditions and growing environmental concerns in urban areas [13]. Increasing food prices, environmental concerns, and a growing interest in achieving self-sufficiency during the 1960s and 1970s were factors driving UA growth [14]. After the 1980s, developed countries like Australia, New Zealand, the USA, the UK, Canada, and European countries like France, the Netherlands, and Germany promoted UA for social and mental wellbeing rather than food production [15]. However, in a developing country, UA is still a major source of livelihood [16]. As such, UA can be broadly classified as either being performed for community recreation (gardening form) or as a source of livelihood (commercial form).

The most common UA types in practice are community gardens, home gardens, individual gardens, commercial farms, institutional gardens, guerilla gardens, controlled environmental farms, and urban parks [17]. According to Soomro [18], there are ten types of urban agriculture: tactical gardens, backyard gardens, forest gardening, greenhouses, green walls, animal husbandry, street landscaping, vertical farms, beekeeping and aquaponics. The common uncontrolled environmental UA practices cover farming in the community, allotments, farms, gardens on housing areas and rooftops, organisational gardens, market-driven vegetable production, and growing food in public parks [19], while hi-tech farming, including indoor and vertical farms, is a less common controlled environment UA practice, promoted for social, economic and environmental motives [20] or simply food production motives [7]. Hodgson et al. [21] categorised UA as a widespread food production practice in a city area using non-commercial, commercial and hybrid production technologies. He has reported eight non-commercial forms (gardening activities), four commercial forms (market-oriented production), and one hybrid form of UA (integrated farming) in different parts of the world. The variations in UA are mainly governed by the types of economic activity, location and tenancy, crop types, scale and technology, destination markets and types of people involved [22]. The choice of production methods depends on community conditions and preferences [23].

2. Literature Review

Some past researchers have contended that the benefits of UA have been grossly underestimated [24]. UA can reduce food miles and economic pressure, with estimates that some 100–200 million urban farmers worldwide already provide fresh horticultural products directly to city markets [25]. However, the high price of land, limited space for production expansion and high living costs, combined with the potentially low availability of input resources and lack of efficiency at small production scales, represent significant challenges for profitable UA in most cities [26]. Previous work by Kafle et al. [27] showed the importance of economic viability, and within that consideration, labour costs in high-income countries and land costs in both high- and low-income countries are potentially significant factors preventing the economic viability of UA. Kafle et al. [27] proposed various measures such as free access to land (gardening style UA), or commercial UA along with subsidised labour. Appropriate labour-saving technology, such as mechanisation, was also proposed to deliver a more feasible economic solution [27]. Raising labour productivity is important to lowering food prices [28].

Kafle et al. [29] recommended further exploratory research on the social, economic and environmental nexus to quantify the growth potential of UA for its sustainability, viability and replicability. As a more localised and diverse food production system, UA can bring production closer to the consumer, provide access to cheap and nutrient-rich food, and is therefore theorised to help in mitigating the adverse effects associated with the long-distance global food supply chain [30]. However, Kafle et al. [31] noted that the emissions associated with freight inefficiency when using small-scale distribution with cars may undermine the potential emissions reduction benefit gained from localised food production. There is considerable scope for improving the current distribution system for UA produce via more localised/decentralised markets, ultimately reducing larger emissions, as identified by Kafle et al. [31] during UA produce distribution.

A key social benefit of UA is the increased participation within the food system, reducing the separation between producers and consumers of food. To this end, Kafle et al. [31] used ‘full-time equivalent’ (FTE) as a proxy measure for people’s time (labour) spent actively within the food system, both in production and distribution. The FTE is a measure of how many people may be employed per consumer in UA under various scales and production assumptions [31]. This is directly related to labour efficiency and the total economic output. A low FTE model would generally show higher economic efficiency (i.e., greater labour productivity), while a high FTE corresponds to greater inclusion/participation (but decreased economic viability). UA is claimed to offer urban employment prospects [32,33], but previous studies have questioned its economic viability based on labour costs [27]; therefore, there is a need to better understand the potential trade-off between economic and social outcomes. Moreover, Kafle et al. [31] showed that UA’s economic, social and environmental outcomes are all intrinsically connected via parameters like labour use, scale of operation, level of mechanisation, crop type, and distribution distance. These connections allow us to develop a theory for optimal UA systems to understand the maximum possible benefit or outcome when pursuing different—and potentially competing—objectives (economic, social and environmental).

Simulation and optimisation techniques are tools and approaches that can be applied in order to seek sustainable solutions for urban environments [34]. Optimisation techniques are applied to select the best elements among a set of available alternatives that would help to achieve the best possible result under a specified goal, which is typically to minimise costs or maximise benefits [35]. The three main categories of parameters in mathematical optimisation are decision variables, constraints and objective functions. The model then aims to find a unique combination of values for decision variables and generates an optimal value for one objective function while fulfilling a set of equalities or inequalities called constraints [36]. A range of optimisation techniques are available for optimising agriculture production, but comparatively little work has been performed applying optimization to UA activities. Optimisation has been applied in UA with regard to the crops and livestock raised for household and community gardens in order to improve urban food security by increasing self-reliance and/or decreasing costs [37], increasing household resilience via self-food production [38], understanding the net value of UA, specifically in relation to water use and water costs [39], and modelling potential productivity via yield evaluation [40].

This study aims to apply optimisation to the problem of UA design, specifically to explore the key elements governing best-case UA practices under the divergent development contexts of Adelaide, Australia, and the Kathmandu Valley, Nepal, and to demonstrate a comprehensive quantification technique for the combined economic, social and environmental benefits. An optimisation model will be developed, allowing separate (potentially competing) objectives in economic, social and environmental domains. The results of optimisation against these different objectives will allow the identification of potential synergies and/or trade-offs between economic, social and environmental benefits or outcomes. The potential applications of the study will be to develop strategies and policies based on optimisation outcomes for economically viable, socially acceptable and environmentally sustainable UA practices to meet needs based on the developmental context.

3. Materials and Methods

3.1. Conceptual Model

UA has evolved as an alternate form of farming to cope with food prices, reduce environmental impacts and create a self-sufficient economy [14] with more orientation towards social and environmental motives in developed countries [15]; however, UA is still a major source of income and employment in developing countries [16]. In the past, UA research has been performed in isolation, with some focused on economic aspects, some on mental health and wellbeing, including its employment capacity, and others on environmental impacts, but the research has lacked a comprehensive assessment approach based on its economic, social and environmental potentiality for wider replicability depending upon the need and interest.

In this regard, a model has been constructed based on the recommendation of Kafle et al. [29] to quantify the growth potential of UA for broader sustainability, viability and replicability based on the exploratory research on the social, economic and environmental nexus. The NM, FTE and CO₂ emissions reduction potentiality were taken as proxy measures for UA’s economic, social and environmental potential. While other potential benefits have been claimed by other researchers, with or without a firm foundation, in this paper, we have considered these three indicators as tangible and calculable measures representing broader economic, social and environmental benefits. For brevity and clarity, the NM analysis was performed based on the income from vegetable production under mixed and mid to high-value scenarios in a specified area and the costs associated with accessing land, labour (production, marketing and distribution), machinery and distribution. Likewise, we considered the labour days, number of people feeding vegetables and effective working days in a year for analysing the FTE. Finally, the per-kilogram carbon dioxide emissions analysis was performed based on the petrol emissions produced by a machine during production and the distribution emissions produced by a small vehicle, like a car. The decision variables, i.e., area, crop value, level of mechanisation and market mechanism, were considered for an optimisable UA model based on the major input parameters (income, costs, labour, number of people consuming vegetables, working days, emissions generated during production and distribution) related to the economic, social and environmental objectives. Constraints (i.e., upper and lower bounds) have been applied to the decision variables and objectives during the single and multi-objective optimisation process to limit them within a specific range. A schematic representation of the conceptual model of the study is presented in Figure 1.

3.2. Description of the Optimisation Process

Based on the broad layout of the conceptual framework for the model with three proxy measures for economic, social and environmental objectives (i.e., NM, FTE and CO₂ emissions reduction), two-stage optimisation was used to pursue potentially conflicting and competing objectives, with input parameters describing the divergent development scenarios in Adelaide, Australia, and the Kathmandu Valley, Nepal. The optimisation approach is illustrated conceptually using the triangular prism shown in Figure 2. The first stage of the optimisation was to find the best case for each of the three independent objectives as a single-objective optimisation. This provides one dimension for each of the points on the triangle in Figure 2. Then, the second stage was to run the multi-objective optimisation using objectives and constraints to modify the lower and upper bounds for each domain (social, environmental and economic); this was performed in order to identify whether there were trade-offs, thereby constraining the other two dimensions of the points of the triangle. The edges of the triangle then effectively illustrate the trade-offs (if any) between each pair of objectives. The values of the upper and lower bounds used in this multi-objective optimisation are found in Appendix A (

Table A2. The decision variables were implemented with the constraints applied, as follows:

S.N.	Description	Lower Bounds	Upper Bounds
1	Adelaide
1.1	NM	−10,000	−1808.61
1.2	FTE	0.002	0.088
1.3	Etot.	0.00725	3
2	Kathmandu
2.1	NM	517.19	3683.40
2.2	FTE	0.0358	0.09238
2.3	Etot.	0.00725	0.0755

).

The objective is a dependent variable, and the model seeks to either maximise (in the case of NM, FTE) or minimise (in the case of CO₂ emissions) the variables by changing the values of the decision variables by satisfying all conditions of the constraints. It is not possible to optimise all of the above objectives simultaneously. Therefore, the strategy of optimising one objective and progressively constraining another to an appropriate range, as adopted by Ward et al. [37], has been adopted.

Likewise, optimisation involves minimising or maximising an objective under a range of constraints: the variables less than, greater than or equal to a specific value. In this model, constraints aim to ensure that optimised UA remains within a specified range of available land areas, level of mechanisation, purpose of farming, market mechanism, crop value, net margin, FTE and carbon footprint. The constraints help to identify and explore trade-offs between the economic, social and environmental domains without dropping performance below a pre-defined threshold.

Most of the parameters investigated will depend on the area available, crops grown, the yield of crops, per capita demand, the distance of production and mode of supply, typical market price, and costs of inputs, including land. The objectives and constraints adopted in this study are presented in Appendix A.

3.3. Detailed Description of the Model

The model being used in this study is an extension of the model developed by Kafle et al. [27] to explore economic viability, and by Kafle et al. [31] to investigate the social, economic and environmental benefits of UA. Based on this past research and current need, we assumed that the optimal solution is widely governed by the decision variables (mechanisation, purpose, crop types, area and market mechanism) under a given set of constraints (upper and lower bound limits). The inputs are key to determining the single objective optimal solution (i.e., the maximum possible economic benefit, social benefit or minimal environmental cost).

The mathematical expression of the model is presented in Appendix A. The input (data) needed to run the model was collected via past research on UA and available information in the literature. In the Kathmandu Valley case, the Nepalese currency was converted to an Australian dollar value for ease of comparison based on the case study findings (NPR 87 is equivalent to AUD 1 based on the typical rate observed in 2023). The following steps have been applied to develop the UA model:

3.3.1. Area and Distance Line Selection Based on the Purpose

In our model, the area chosen (as a decision variable) for cultivation dictates how far from the city centre a farm may be located. This is because the population density typically decreases with distance [41] and, therefore, larger parcels of land are likely to be more accessible for cultivation further from the city centre. The derivation of the area–distance relationship is recognised as a significant simplifying step that could be refined in future research. However, it is used to rapidly establish a plausible link between the size of an UA plot (which influences the economy of scale) and an indicative location at a minimum distance from the Central Business District(CBD), which influences access to consumers. As such, to avoid limiting the analysis to land parcels currently on the market, an approach was taken whereby a fraction of land area per person (dictated by population density) was deemed potentially available for UA. The area–distance relationship used in the model is an empirical formula derived from mapping real estate data on the location of real land parcels currently (or recently) on the market [42], retrieved 1 January 2023 and [43] retrieved 1 January 2023, against census data on the population density of their location in Adelaide [44] and Kathmandu [45].

The model assumes that the fraction of gross land available for UA will vary depending on its purpose, with more land available when the land can be paid for (i.e., commercial) and less land available for free access (i.e., gardening).

3.3.2. Production Sites to Market Distance Determination

The market distance is widely governed by the purpose, which is ultimately related to area availability. If a larger fraction of the area is available, people prefer commercial UA, which typically needs long-distance transport (to sell produce at a wholesale market), and if a smaller area is available, produce is consumed within a short distance depending upon the population density distribution and nature of products demanded. For this purpose, 30 distinct location data related to population density and area availability (per capita) were extracted from Adelaide, Australia [44], and the Kathmandu Valley, Nepal [45], and the distance (in km) was determined by extracting the information on the graphs plotted in Appendix B1 and B2. We assumed that there was a 10% per-person gross area availability for gardening and a 20% area availability for commercial UA, which were used for deriving mathematical relationships. The area-based distance from CBD, D (Km) was determined using Equations (1) and (2).

For Adelaide, Australia:

$$\mathrm{D}=\left\{\begin{array}{c}13.587\times \mathrm{l}\mathrm{n}\left(\mathrm{A}\right)-42.677,\hspace{1em}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}\\ 13.587\times \mathrm{l}\mathrm{n}\left(\mathrm{A}\right)-52.095,\hspace{1em}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\end{array}\right.$$

(1)

For the Kathmandu Valley, Nepal:

$$\mathrm{D}=\left\{\begin{array}{c}2.3411\times \mathrm{l}\mathrm{n}\left(\mathrm{A}\right)+5.5311,\hspace{1em}\mathrm{g}\mathrm{a}\mathrm{r}\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}\\ 2.3411\times \mathrm{l}\mathrm{n}\left(\mathrm{A}\right)+3.9082,\hspace{1em}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{l}\end{array}\right.$$

(2)

where the constant values are calibrated using property data (see Appendix B Figure A1 and Figure A2)

3.3.3. Population Density Determination

The two driving distance lines up to 10 km and greater than 10 km from the CBD were used to analyse the population density distribution in order to understand the characteristic features of UA classified as inner city and suburban by Kafle et al. [27]. The population density information was extracted from ABS [44] and City Population [45] to develop a mathematical relationship between distance and the population density based on the population density graph presented in Appendix B. The population density (PD) in people/km² was determined based on Equations (3)–(6).

For Adelaide:

$$\mathrm{For} \mathrm{D}\le 10 \mathrm{km},\mathrm{PD} =2326$$

(3)

$$\mathrm{For} \mathrm{D}>10 \mathrm{km},\mathrm{PD} =\max (50, 2800-47.43\times \mathrm{D})$$

(4)

For the Kathmandu Valley:

$$\mathrm{For} \mathrm{D}\le 10 \mathrm{km},\mathrm{PD} =20000$$

(5)

$$\mathrm{For} \mathrm{D}>10 \mathrm{km},\mathrm{PD} =\max (25, 10401-389.73\times \mathrm{D})$$

(6)

where the constant values are calibrated using population data (see Appendix B Figure A3 and Figure A4).

3.3.4. Yield and Total Production Determination Based on the Purpose

The UA vegetable yield based on the purpose (either gardening or commercial UA) was considered in this study due to the relatively low yield compared to the global average yield of UA crops in both contexts. A gardening base yield (Y_bas.) of 2.21 kg/m² was assumed for Adelaide [46], and 1.95 kg/m² was assumed for the Kathmandu Valley [47]. For commercial UA, a base (Y_bas.) yield of 2.56 kg/m² was adopted for both development contexts based on data from Satzewich and Christensen [48] for the combination of vegetables presented in

Table 1. List of vegetables included in the analysis.

S.N.	Crop Value	List of Vegetables
1	Mixed vegetables	Carrot, radish, turnip, tomato, brinjal, capsicum, beans, lettuce, spinach, celery, cabbage, cauliflower, broccoli, cucumber, zucchini
2	Mid- to high-value vegetables	Tomato, capsicum, beans, lettuce, spinach, celery, broccoli

. The income associated with the crop categories of ‘mid to high value’ and ‘mixed’ was considered based on the present market value of vegetables.

The total production Y_veg., (kg/year) was calculated based on the yield of vegetables produced under gardening and commercial UA and the area under cultivation, as follows:

$${\mathrm{Y}}_{\mathrm{v}\mathrm{e}\mathrm{g}.}={\mathrm{Y}}_{\mathrm{b}\mathrm{a}\mathrm{s}.}\times \mathrm{A}$$

(7)

where Y_bas. is the base productivity of vegetables under gardening and commercial UA.

3.3.5. Per Capita Demand and Population Served

As part of the model assumptions, we need to understand the number of consumers served and how they access produce from the garden or farm. This depends on the type of crops grown, as people consume larger quantities of mixed vegetables and smaller quantities of high-value vegetables based on the recommended standard serve. The per capita demand is calculated based on the recommended standard serving of five cups of mixed vegetables per day for an adult (

Table 2. Per capita vegetable demand.

Symbol and Unit	Vegetable Types	Adelaide	Kathmandu	Source
Dem. (kg/person/year)	Mixed	136.87		[49]
	Mid to high value	54.75

). The number of people served is calculated by dividing the total production by the per capita demand, as per Equation (8).

Population served, Pop. (number of people):

$$\mathrm{P}\mathrm{o}\mathrm{p}=\frac{{\mathrm{Y}}_{\mathrm{v}\mathrm{e}\mathrm{g}.}}{\mathrm{D}\mathrm{e}\mathrm{m}.}$$

(8)

where Dem. is the per capita vegetable demand (kg/year).

3.3.6. Catchment Area Determination

The population density (which tells us how large an area may potentially be served by the garden or farm), and the market mechanism (which tells us whether we are distributing produce in batches over a long distance, or if consumers are visiting the farm themselves to access the produce locally) are the key to the catchment area. Two modes of distribution, i.e., wholesaling for commercial UA and retailing (direct distribution from the farm gate) for gardening, were assumed. This analysis assumed that a fraction (f, assumed to be 20%) of the immediate local population may plausibly access farm-gate sales. Finally, the catchment area, CA, (Km²) was determined based on the population served, the proportion of produce sold as direct consumables and the population density based on Equation (9).

$$\mathrm{C}\mathrm{A}=\frac{\mathrm{P}\mathrm{o}\mathrm{p}.}{\mathrm{P}\mathrm{D}\times \mathrm{f}}$$

(9)

where f is an assumed fraction of the population served by the UA operation.

3.3.7. Distribution Radius Determination

It is important to know the distribution radius in order to decide the marketing strategy (wholesaling and retailing), which is largely governed by the population density and amount of vegetables available for consumption. The distribution radius from the potential UA production zone, r (km,), was calculated using an assumed circular catchment area centred on the farm location, as in Equation (10).

$$\mathrm{r}=\sqrt{\frac{\mathrm{C}\mathrm{A}}{\mathsf{\pi }}}$$

(10)

3.3.8. Distribution Distance Determination

The market mechanism (wholesaling and retailing) is key to determining the produce distribution distance. The distribution distance is a key component of CO₂ emissions in UA, so properly determining the carbon emissions produced by vehicle use is important. To be more practical, the distribution distance required to access retail markets (i.e., direct distribution from the farm) was calculated based on the number of people served from the farm, the distribution radius and a multiplication factor of 2 (for two-way transport). Likewise, the wholesale distribution distance was determined based on the market distance from the farm (i.e., CBD) and a factor of 2. The distribution distance, R (km), was determined based on Equation (11).

$$\mathrm{R}=\left\{\begin{array}{c}2\times \mathrm{P}\mathrm{o}\mathrm{p}\times \mathrm{r},\hspace{1em}\mathrm{r}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{l}\\ 2\times \mathrm{D},\hspace{1em}\mathrm{w}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\end{array}\right.$$

(11)

3.3.9. Labour Requirement Calculations

As noted previously, the model adopts labour, measured as the FTE per consumer, as a ‘proxy’ for ‘participation in the food system’ (being one of the proposed social benefits of UA). Participation in the food system is not limited to production but also distribution and marketing, hence why we are calculating the labour in production, sales and distribution.

First, the production labour (L_prod.) is derived based on the labour required per square meter area, total area and workload information, all derived from Kafle et al. [31]. The yearly labour per square meter (L_sqm.) is calculated based on the operating and non-tilling labour hours based on the UA type (i.e., gardening or farming). The operating labour hour is calculated based on the labour required to operate a machine for tilling and bed preparation. Data on the non-tilling labour hours (planting, weeding, and harvesting labour hours) for gardening and commercial UA were derived from past UA research on SPIN farming and Edible Gardens [46,48]. The labour required for production, L_prod. (days/year), was determined using Equation (12).

$${\mathrm{L}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}.}=\frac{{\mathrm{L}}_{\mathrm{s}\mathrm{q}\mathrm{m}.}\times \mathrm{A}}{8}$$

(12)

The per square meter labour, L_sqm. (per year), was calculated using the following formula:

$${\mathrm{L}}_{\mathrm{s}\mathrm{q}\mathrm{m}.}={\mathrm{H}}_{\mathrm{o}\mathrm{p}\mathrm{e}.}+{\mathrm{L}\mathrm{H}}_{\mathrm{n}\mathrm{c}.}$$

(13)

where H_ope. represents the operating labour hour and LH_nc. is is the non-tilling labour hours.

H_ope. is calculated as follows:

$${\mathrm{H}}_{\mathrm{o}\mathrm{p}\mathrm{e}.}=\frac{1}{{\mathrm{A}}_{\mathrm{t}\mathrm{i}\mathrm{l}.}}\times 4+\frac{1}{{\mathrm{A}}_{\mathrm{b}\mathrm{e}\mathrm{d}.}}\times 2$$

(14)

where A_til. represents the area covered during tillage (m²/h), and A_bed. is the area covered during bed preparation (m²/h).

A_til. is calculated as follows:

$${\mathrm{A}}_{\mathrm{t}\mathrm{i}\mathrm{l}.}={\mathrm{V}}_{\mathrm{t}\mathrm{i}\mathrm{l}.}\times {\mathrm{W}}_{\mathrm{w}\mathrm{i}\mathrm{d}.}\times 1000$$

(15)

where V_til. represents the assumed velocity for tillage activity (km/h), and W_wid. is the working width (m).

Likewise, A_bed. is calculated as follows:

$${\mathrm{A}}_{\mathrm{b}\mathrm{e}\mathrm{d}.}={\mathrm{V}}_{\mathrm{b}\mathrm{e}\mathrm{d}.}\times {\mathrm{W}}_{\mathrm{w}\mathrm{i}\mathrm{d}.}\times 1000$$

(16)

where V_bed. is the assumed velocity of the bed preparation activity (km/h). A description of the parameters used in the equations is given in

Table 3. Description of parameters used in Equations (12)–(16).

Symbol and Unit	Description	Adelaide	Kathmandu	Source
LHnc (h/m2/year)	Non-tilling labour hours:
	- Gardening	2.310	2.310	[46]
	- Commercial UA	0.146	0.146	[48]
Vtil. and Vbed (km/h)	Assumed velocity:
	- Manual	0.26	0.26	[31]
	- Garden tiller and cultivator	1.32	1.32
Wwid (meter)	Working width:
	- Manual	0.1	0.1	[31]
	- Garden tiller	0.28	0.28
	- Garden cultivator	0.48	0.48

.

Then, the distribution labour (L_dist.) is determined based on the marketing mechanism (retailing or and or wholesaling). Where the produce is distributed via the wholesale market, the distribution labour is derived based on the distribution distance, the number of trips (T_num.) and the assumed work hours per day. The number of trips is taken as the maximum of either 52 (i.e., one trip per week, assumed to be the minimum frequency to bring products to consumers) or the value calculated by dividing the production quantity by the vehicle capacity (i.e., more than one trip per week). The distribution process was simplified to the straightforward activities of driving, dropping and returning from the point of production. As such, the distribution labour, L_dist. (days/year) was derived by assuming a travel speed of 60 km/h and labour for 8 h/day using the relationships in Equation (17):

$${\mathrm{L}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.}=\left\{\begin{array}{c}0, \mathrm{retail}\\ \frac{\mathrm{R} {\times \mathrm{T}}_{\mathrm{n}\mathrm{u}\mathrm{m}.}}{60 \times 8},\hspace{1em} \mathrm{wholesale}\end{array}\right.$$

(17)

where T_num. the number of trips, is calculated as follows:

$${\mathrm{T}}_{\mathrm{n}\mathrm{u}\mathrm{m}.}=\max \left(52,\mathrm{ROUNDUP}\left(\frac{{\mathrm{Y}}_{\mathrm{v}\mathrm{e}\mathrm{g}.}}{\mathrm{F},0}\right)\right)$$

(18)

where ROUNDUP implies rounding up to the nearest integer value, and F is the maximum freight capacity (kg/trip). The maximum freight capacity was assumed to be 200 kg/trip. The labour for sales (L_sales) are determined based on whether UA involves direct distribution from the farm to the consumer (i.e., retailing) or produce distributed to the wholesale market. The L_sales for retailing is calculated assuming that the average retailing and packaging time (t) is 10 min/per week/consumer, while the value of zero is considered for wholesale, as there is no involvement of labour for sales in wholesaling based on our model assumptions. Finally, the retail sales labour is calculated based on the per-customer time spent, the number of people served weekly, and workload. L_sales (days/year) is determined using Equation (19):

$${\mathrm{L}}_{\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}}=\left\{\begin{array}{cc}\frac{\mathrm{t} \times \mathrm{P}\mathrm{o}\mathrm{p}. \times 52}{60 \times 8},& \mathrm{r}\mathrm{e}\mathrm{t}\mathrm{a}\mathrm{i}\mathrm{l}\\ 0,& \mathrm{w}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{e}\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\end{array}\right.$$

(19)

where t is the time (minutes/week) spent per customer. The constant value of 52 implies the number of weeks in a year used for distributing produce.

3.3.10. Calculating the Cost

The cost of land, production (including labour, equipment and machinery), packaging materials and distribution are considered in this modelling based on the previous study reported by Kafle et al. [31]. Land cost is incorporated using the approach of Kafle et al. [27], including the characterisation of available inner city and suburban land parcels, hence the two different equations provided in Annex 2.

Land price as a function of distance, LC_D (AU$/m²), is determined based on the UA type; if it is gardening, then the land is assumed to be free (but as per the earlier definition of the land–distance relationship, it is also more scarce). For commercial UA, we assume that land must be purchased; compared with gardening, it is easier to access parcels of land closer to the city, but at a higher price (see Appendix B Figure A5 and Figure A6). It could also be noted that whilst commercial UA inherently brings land costs, under our model’s assumptions, this form of UA also brings a significant labour productivity advantage.

Land cost as a function of distance is approximated by evaluating 30 distinct parcels of land for sale in Adelaide [42], Australia, and the Kathmandu Valley, Nepal [43], in Equation (20) and Kathmandu, Nepal, in Equation (21).

$$\begin{gathered} \mathrm{For} \mathrm{D} \le 10 \mathrm{km}: {\mathrm{L}\mathrm{C}}_{\mathrm{D}}=-7.0961\times \mathrm{D}+123.6 \\ \mathrm{For} \mathrm{D} > 10 \mathrm{km}: {\mathrm{L}\mathrm{C}}_{\mathrm{D}}=-1.0116\times \mathrm{D}+69.038 \end{gathered}$$

(20)

$$\begin{gathered} \mathrm{For} \mathrm{D} \le 10 \mathrm{km}: {\mathrm{L}\mathrm{C}}_{\mathrm{D}}=-1.1449\times \mathrm{D}+128.54 \\ \mathrm{For} \mathrm{D} > 10 \mathrm{km}: {\mathrm{L}\mathrm{C}}_{\mathrm{D}}=-3.6301\times \mathrm{D}+104.06 \end{gathered}$$

(21)

where the constant values are calibrated using land price data (see Appendix B Figure A5 and Figure A6). The total price, P_land (AU$/year), is calculated as follows:

$${\mathrm{P}}_{\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{d}}={\mathrm{L}\mathrm{C}}_{\mathrm{D}}\times \mathrm{A}$$

(22)

The annualised land cost, C_lan.,(AU$/year), and mortgage repayments are calculated using a constant interest rate of 3% over a 30-year period, as shown in Equation (23).

$${\mathrm{C}}_{\mathrm{l}\mathrm{a}\mathrm{n}.}={\mathrm{P}}_{\mathrm{l}\mathrm{a}\mathrm{n}\mathrm{d}}\frac{\left(\mathrm{r}{\left(1+\mathrm{r}\right)}^{\mathrm{n}}\right)}{\left({\left(1+\mathrm{r}\right)}^{\mathrm{n}}-1\right)}$$

(23)

where P_land is the land price (AU$), r is the interest rate (% per year) and n is the payment period (years).

The production cost per square meter area (C_prod.) is calculated by including major cost items (equipment and machine, operating cost, operating and non-cultivating labour cost). The annualised equipment and machinery cost calculation is based on the depreciation value of three levels of mechanisation (non-mechanised hand tools, garden tiller and garden cultivator). The model chooses the mechanisation level based on the purpose, i.e., gardening and farming. The production cost per square meter (C_prod.) is calculated using the following formula:

$${\mathrm{C}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}.}=\frac{({\mathrm{C}}_{\mathrm{e}\mathrm{q}\mathrm{p}.}\times \mathrm{m}\mathrm{a}\mathrm{x}\left(\frac{1}{{\mathrm{L}\mathrm{S}}_{\mathrm{a}\mathrm{s}\mathrm{s}.}},\frac{{\mathrm{H}}_{\mathrm{o}\mathrm{p}\mathrm{e}.}\times \mathrm{A}}{{\mathrm{R}}_{\mathrm{h}\mathrm{r}\mathrm{s}}}\right)+{\mathrm{H}}_{\mathrm{o}\mathrm{p}\mathrm{e}}\times \mathrm{A}\times \left({\mathrm{C}}_{\mathrm{l}\mathrm{a}\mathrm{b}.}+{\mathrm{C}}_{\mathrm{f}\mathrm{u}\mathrm{e}.}\times {\mathrm{F}}_{\mathrm{h}\mathrm{r}\mathrm{s}}.\right)+{\mathrm{L}\mathrm{H}}_{\mathrm{n}\mathrm{c}.}\times {\mathrm{C}}_{\mathrm{l}\mathrm{a}\mathrm{b}.}\times \mathrm{A})}{\mathrm{A}}$$

(24)

where C_eqp. is the equipment cost (AU$), LS_ass. is the asset life span (years), R_hrs. is the replacement hours (hours), C_lab. is the labour rate (AU$/h), C_fue. is the fuel cost (AU$/litre), and F_hrs. is the fuel consumption (litre/h). The list of parameters used in Equation (24) is presented in

Table 4. List of parameters for production cost calculations (C_prod.).

Symbol and Unit	Description	Adelaide	Kathmandu	Source
Ceqp. (AU$/year)	Equipment and machinery cost			[31]
	Manual digging equipment	20	10
	Garden tiller with bed maker	1000	800
	Garden cultivator with bed maker	2000	1600
Hope. (h/m2)	Operating hours			[31]
	Non mechanised	0.023
	Garden tiller	0.016
	Garden cultivator	0.009
LSass. (years)	Asset life span			[31]
	Manual	1	1
	Garden tiller and cultivator	5	5
Rhrs. (hours)	Replacement hours	2000	2000	[31]
Clab. (AU$/h)	Hourly labour rate	25.88	0.875	[50,51]
Cfuel (AU$/L)	Fuel cost	1.75	2.0	[52]
Fhrs. (litre/h)	Fuel consumption			[31]
	Non mechanised farming	0	0
	Garden tiller	0.54	0.54
	Cultivator	1.98	1.98

.

Finally, the per square meter cost is multiplied by the area to calculate the total production cost CPROD_tot. (AU$/year) using the following formula:

$${\mathrm{C}\mathrm{P}\mathrm{R}\mathrm{O}\mathrm{D}}_{\mathrm{t}\mathrm{o}\mathrm{t}.}={\mathrm{C}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}.}\times \mathrm{A}$$

(25)

The packaging material cost, C_pak. (AU$/year), is assumed as a function of the total yield of vegetables (Y_veg.) multiplied by the cost of material, C_mat. (AU$/kg). The packaging materials costs (AU$/kg) for Adelaide and the Kathmandu Valley were considered as 0.1 and 0.02 based on the previous study conducted by Kafle et al. [27], and are calculated using Equation (26):

$${\mathrm{C}}_{\mathrm{p}\mathrm{a}\mathrm{k}.}={\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{t}}\times {\mathrm{Y}}_{\mathrm{v}\mathrm{e}\mathrm{g}.}$$

(26)

In this study, the distribution cost, C_dist. (AU$/year), includes the fuel and labour required for distribution. The model assumes different distribution costs based on the wholesaling and retailing of produce. If wholesaling is performed, then the distribution cost is calculated based on the distribution distance, R (km), fuel cost incurred, C_fuel (AU$/L), fuel consumption, F_con. (L/km), and labour cost in the distribution (L_dist. and C_lab.). The model assumes zero cost for retailing activity (i.e., direct farm distribution). The fuel consumption, F_con (L/km) is considered as 0.111 for Adelaide [53] and 0.074 for the Kathmandu Valley [54]. The relationship is shown in Equation (27):

$${\mathrm{C}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.}=\left\{\begin{array}{cc}0,& \mathrm{retail}\hfill \\ \mathrm{R}\times {\mathrm{F}}_{\mathrm{c}\mathrm{o}\mathrm{n}.}\times {\mathrm{C}}_{\mathrm{f}\mathrm{u}\mathrm{e}\mathrm{l}}+ {\mathrm{L}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.}\times {\mathrm{C}}_{\mathrm{l}\mathrm{a}\mathrm{b}.},& \mathrm{wholesale}\hfill \end{array}\right.$$

(27)

The sales cost, C_sales (AU$/year), is determined for the cost of directly distributing produce from the UA site. C_sales is derived based on the time spent distributing the produce and hourly cost information, as per Equation (28):

$${\mathrm{C}}_{\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}}={\mathrm{C}}_{\mathrm{l}\mathrm{a}\mathrm{b}.}\times {\mathrm{L}}_{\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}.}$$

(28)

3.3.11. Emission Calculations

The potential carbon dioxide emissions generated per kilogram of produce during the production and distribution activities were considered in this modelling. The total amount of carbon dioxide emitted per kg of production, E_tot. (CO₂ equivalent per kg of production), was determined using Equation (29):

$${\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}.}=\frac{{(\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}.}+{\mathrm{E}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.})}{{\mathrm{Y}}_{\mathrm{v}\mathrm{e}\mathrm{g}.}}$$

(29)

where E_pro. is the emissions generated from fuel during production activities (CO₂ equivalent/kg production) and E_dist. is the emissions generated during distribution activities (CO₂ equivalent/kg production).

The UA mechanisation using small-scale machinery has previously been identified as a key strategy for improving the economic scale of UA for economic benefit [31], so the production emissions calculation in this modelling is based on the CO₂ emissions during tilling and bed preparation activities under three types of mechanisation—non-mechanised/hand-operated tools, garden tiller and garden cultivator. In this model, we assume that the production emissions are largely governed by area, type of mechanisation, frequency of tilling and bed preparation activities before planting crops, and the emission factors per litre of fuel used.

The total amount of emissions generated by mechanised and non-mechanised UA during production, Epro. (CO₂ equivalent per kg production), is calculated using Equation (30):

$${\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}.}={\mathrm{E}}_{\mathrm{t}\mathrm{i}\mathrm{l}.}+{\mathrm{E}}_{\mathrm{b}\mathrm{e}\mathrm{d}.}$$

(30)

where E_til. is the CO₂ emissions generated during primary tillage and E_bed. is the CO₂ emissions generated during bed preparation. The emissions generated by machine use during primary tillage (E_til.) using a petrol engine are calculated using Equation (31):

$${\mathrm{E}}_{\mathrm{t}\mathrm{i}\mathrm{l}.}=\frac{4\times \mathrm{A}\times {\mathrm{F}}_{\mathrm{h}\mathrm{r}\mathrm{s}.}\times {{\mathrm{E}}_{\mathrm{f}\mathrm{a}\mathrm{c}.}\times \mathrm{H}}_{\mathrm{o}\mathrm{p}\mathrm{e}.}}{1000}$$

(31)

where E_fac. is the CO₂ emission factor (grams CO₂/litre of petrol used). A constant value of 4 is adopted by assuming that there are 4 tillage operations per year. The emissions factor (gram/litre) for petrol-operated vehicles is 2392 [55]. The emissions generated by machine use during bed preparation (E_bed.) using a petrol engine are calculated using Equation (32):

$${\mathrm{E}}_{\mathrm{b}\mathrm{e}\mathrm{d}.}=\frac{2\times \mathrm{A}\times {\mathrm{F}}_{\mathrm{h}\mathrm{r}\mathrm{s}.}\times {{\mathrm{E}}_{\mathrm{f}\mathrm{a}\mathrm{c}.}\times \mathrm{H}}_{\mathrm{o}\mathrm{p}\mathrm{e}.}}{1000}$$

(32)

A constant value of 2 is applied by assuming that there are 2 tillage operations per year for planting vegetables.

The CO₂ emissions produced during distribution are largely governed by the trip frequency and distribution distance. The number of trips (based on trip frequency) in this model is calculated based on the maximum number of trips and load capacity of the vehicle. It is worth investigating the distribution emissions using a small vehicle like a car, which is common in UA produce distribution; despite their low contribution to the cost, car-based distribution emissions have the potential to add a significant amount of carbon emissions [31]. Like vehicles, the marketing mechanism also influences the amount of emissions. It is important to note that when consumers come to the farm, their emissions (from vehicle transport to and from the farm) are considered in this modelling. The distribution emissions are calculated based on the trip information, catchment area, emission factors and car petrol consumption per kilometre.

The amount of emissions produced during distribution E_dist. by non-mechanised UA is calculated using the following formula:

$${\mathrm{E}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.}=\frac{{{\mathrm{E}}_{\mathrm{f}\mathrm{a}\mathrm{c}.}\times \mathrm{F}}_{\mathrm{c}\mathrm{o}\mathrm{n}.}\times \mathrm{R}\times {\mathrm{T}}_{\mathrm{n}\mathrm{u}\mathrm{m}.}}{1000}$$

(33)

3.3.12. Calculating the Net Margin, FTE, and Carbon Dioxide Emissions

The net margin from UA vegetables under gardening and farming, NM (AU$/kg), is calculated based on the total production, market price, and cost information. The wholesale and retail market price information for the selected list of vegetables is used to calculate profit. Finally, the land, production, packaging distribution and sales costs are subtracted to determine the NM (S/kg), as per Equation (34):

$$\mathrm{N}\mathrm{M}={\mathrm{Y}}_{\mathrm{v}\mathrm{e}\mathrm{g}}\times \mathrm{P}-{\mathrm{C}}_{\mathrm{l}\mathrm{a}\mathrm{n}}-{\mathrm{C}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}.}-{\mathrm{C}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.}-{\mathrm{C}}_{\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}}{-\mathrm{C}}_{\mathrm{p}\mathrm{a}\mathrm{k}.}$$

(34)

where P is the retail or wholesale price depending on the market mechanism. The wholesale price (AU$/kg) of vegetables was used in this analysis based on the annual price information available for the selected list of vegetables for Adelaide and the Kathmandu Valley. In Adelaide, the average wholesale prices for the mixed and mid- to high-value vegetables were 7.5 and 12.5 AU$/kg, respectively [56], while in Kathmandu, the prices were 1.69 and 2.32 AU$/kg, respectively [57]. An additional 20% price was considered for retail price approximation.

The FTE per consumer is calculated by summing up all the labour requirements in UA divided by the number of people consuming vegetables and the effective yearly workdays required to produce vegetables.

The labour, as the FTE (full-time farmers per consumer), is calculated as follows:

$$\mathrm{F}\mathrm{T}\mathrm{E}=\frac{{({\mathrm{L}}_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{d}.}+\mathrm{L}}_{\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}.}+{\mathrm{L}}_{\mathrm{s}\mathrm{a}\mathrm{l}\mathrm{e}\mathrm{s}})}{\mathrm{P}\mathrm{o}\mathrm{p}. \times 260}$$

(35)

where 260 is an assumed constant value for the number of effective working days in a year by considering 5 days of effective work per week with an average 8 h per day workload.

The total carbon emissions reduction potential (E_red.) is calculated by summing the carbon emissions generated during production and distribution, dividing them by the total production, and comparing the reduction potential with conventional food systems by subtracting the optimisation outcomes using a global average (E_glob.). In a global-scale vegetable carbon emissions study conducted by Poore and Nemecek [58], vegetables, including tomatoes, root vegetables, brassicas and other vegetables, were found to emit 0.814 kg equivalent of CO₂ per kg produced by land use change, the farm level, processing, transport, retail, packaging and losses. Therefore, we considered 0.814 kg equivalent of CO₂ to determine the difference in emissions relative to the carbon footprint of conventional food production, and a larger value implies a benefit (greater reduction). The total emissions reduction, E_red. (kg of CO₂ per kg of production), is calculated using Equation (36).

$${\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{d}.}={\mathrm{E}}_{\mathrm{t}\mathrm{o}\mathrm{t}.}-{\mathrm{E}}_{\mathrm{g}\mathrm{l}\mathrm{o}\mathrm{b}.}$$

(36)

Adelaide, Australia, and the Kathmandu Valley, Nepal, have very expensive land, making it difficult to identify economically viable options for UA without access to free land, and the large difference in labour costs between the two places led to more economically viable options being identified in Kathmandu than in Adelaide [27]. This makes the two cases interesting to study in an optimisation context when we are interested in the trade-offs between economic viability and maximising participation in the food system. Finally, we studied the trade-off between the best-case profit (margin), the best-case FTE and the best-case CO₂ emissions reduction using optimisation via solver in order to understand the magnitude, scale and characteristics of the trade-off for an optimisable UA.

4. Results

The results are presented based on the optimisation outcomes under the scenarios for Adelaide, Australia, and the Kathmandu Valley, Nepal. UA is optimised under both scenarios to explore the characteristics of UA in a high-income and low-income setting. The model focuses on three distinct objectives: the best-case net margin, the FTE and carbon emissions reduction potential (reduction potential compared to the conventional food system).

4.1. UA Optimisation in Adelaide

The results of the optimisation (i.e., the three optimised objectives and the decision variables leading to each solution) in Adelaide are presented in

Table 5. Summary of the UA optimisation in Adelaide, Australia.

S.N.	Steps	Units	Best-Case Net Margin	Best-Case FTE	Best-Case Carbon Emissions
1	Inputs
1.1	Farm distance	km	41	20	10
1.2	Population density	People/km2	851	1856	2303
1.3	Yield	kg/m2	2.56	2.21	2.56
1.4	Total production	kg	2435	221	256
1.5	Per capita demand	kg/year	54.75	136.875	136.875
1.6	Population served	people	44	2	2
1.7	Serving area	km	0.261	0.0043	0.0040
1.8	Distribution radius (retail only)	km	0.288	0.037	0.035
1.9	Distance of distribution	km	82	40	0.134
1.10	Labour	days/year	28.20	36.07	6.74
1.11	Land cost	AU$/year	25,947	0	5838
1.12	Production labour cost	AU$/year	4209	6595	995
1.13	Packaging material cost	AU$/year	243	22	25
1.14	Distribution plus sales cost	AU$/year	1858	900	419
1.15	Distribution trips	trips/year	52	52	52
1.16	Distribution emissions	kg of carbon equivalent emissions/year	1134.47	549.32	1.857
1.17	Production emissions	Kg of carbon equivalent emissions/year	33.60	0	0
2	Outputs
2.1	Maximum margin (AU$/kg)	year	−0.74	−26.51	−19.43
2.2	Maximum FTE	producer per consumer	0.00244	0.0859	0.0138
2.3	Minimum carbon dioxide	kg CO2/kg of production	0.479	2.48	0.00725
2.3.1	Carbon dioxide reduction difference (compared to conventional farming)	kg CO2/kg of production	0.335 (41.1%)	−1.66 (204.66%)	0.80 (99.1%)
	Decision variables
1	Area	m2	951.44	100	100
2	Mechanisation		Garden cultivator	Non-mechanised	Non-mechanised
3	Market mechanism		Wholesale	Wholesale	Retail
4	Purpose		Commercial	Gardening	Commercial
5	Crop value		Mid to high	Mixed	Mixed

. When pursuing an economic objective (maximum net margin), the model in Adelaide chooses land located furthest from the CBD to access cheaper, larger parcels of land. It also chooses the highest possible mechanisation in order to maximise the efficiency of labour use and production for high-yield and mid- to high-value crops selling to a wholesale market.

When pursuing a social objective, the model chooses approximately half the distance of the economic case, opting for a gardening style of UA that focuses on mixed crops in order to engage more producers per consumer, and moves to one-tenth of the area using labour-intensive (non-mechanised) farming practices to maximise the FTE.

Finally, when optimising for a reduction in the carbon emissions, the model chooses a farm distance that is even closer to the CBD, along with a smaller distribution radius and retailing mechanism (i.e., direct distribution via the farm within a small radius); this is rather than the transport of produce to a market. Interestingly, the model chooses relatively smaller land areas with commercial (albeit non-mechanised) UA practices and retailing market mechanisms. This is because the smaller farm area leads to fewer consumers and a smaller distribution distance.

The small size of the population served under the best-case FTE and carbon emissions (i.e., two persons) implies a ‘self-sufficiency’ scenario.

4.2. UA Optimisation in the Kathmandu Valley

The results of the economic, social and environmental objectives in the Kathmandu Valley are presented in

Table 6. Summary of the UA optimisation in the Kathmandu Valley, Nepal.

S.N.	Steps	Units	Best-Case Net Margin	Best-Case FTE	Best-Case Carbon Emissions
1	Inputs
1.1	Farm distance	km	22	22	19
1.2	Population density	people/km2	2010	1945	2825
1.3	Yield	kg/m2	1.95	1.95	1.95
1.4	Total production	kg/area	1810	1944	740
1.5	Per capita demand	kg/year	54.75	136.875	136.875
1.6	Population served	people	33	14	5
1.7	Serving area	km	0.082	0.0365	0.00957
1.8	Distribution radius (retail only)	km	0.161	0.107	0.0552
1.9	Distance of distribution	km	11	3	0.597
1.10	Labour	Days/year	330.71	332.11	126.51
1.11	Land cost	AU$/year	0	0	0
1.12	Production labour cost	AU$/year	2074	227	854
1.13	Packaging material cost	AU$/year	36	39	15
1.14	Distribution and sales cost	AU$/year	251	108	41
1.15	Distribution trips	trips/year	52	52	52
1.16	Distribution emissions	kg of carbon equivalent emissions/year	98.50	28.197	5.50
1.17	Production emissions	kg of carbon equivalent emissions/year	0	0	0
2	Outputs
2.1	Maximum margin (AU$/kg)	year	2.0	0.77	0.82
2.2	Maximum FTE	producer per consumer	0.0384	0.0899	0.0899
2.3	Minimum carbon dioxide	kg of CO2/kg of production	0.0544	0.0145	0.0074
2.3.1	Carbon dioxide reduction difference (compared to conventional farming)	kg of CO2/kg of production	0.759 (93.3%)	0.799 (98.2%)	0.80 (99%)
	Decision variables
1	Area	m2	928.49	997.23	379.87
2	Mechanisation		Non mechanised	Non-mechanised	Non-mechanised
3	Market mechanism		Retail	Retail	Retail
4	Purpose		Gardening	Gardening	Gardening
5	Crop value		Mid to high	Mixed	Mixed

. All three objectives (economic, social and environmental) choose gardening over commercial UA, and retail (local direct distribution) over wholesale.

The economic optimum (maximum net margin) in the Kathmandu Valley chooses the furthest farming distance from the CBD, the largest piece of land and medium mechanisation (garden tiller), medium yield, and mid- to high-value crops.

Interestingly, the social objective chooses almost exactly the same distance from the CBD as the economic objective, focusing on mixed crops in order to employ more producers per consumer and using labour-intensive farming practices (non-mechanised) to maximise the FTE.

For the best-case reduction in carbon emissions, the model chooses a slightly shorter distance from the CBD, along with a close distribution radius, a 2.5 times smaller land area and retail (direct distribution via the garden within a small radius); this is due to the assumption that there are significant emissions produced by a petrol-operated small vehicle during distribution.

The difference between the distribution distance in the case of the margin with the FTE and carbon emissions is primarily due to the difference in the population served and the distribution radius, thus adding up in the consumer trip to visit the farm, depending upon the scale of operation.

5. Discussion

5.1. Features of the Optimised UA in Adelaide, Australia

The characteristic features of UA under the best-case margin, FTE and reduction in carbon emissions based on our model assumption in Adelaide, Australia, are presented in Figure 3. The model reflects the trade-offs between the economic, social and environmental objectives. Interestingly, there is an intense trade-off between the FTE and carbon emissions in the FTE model due to distribution; the best-case FTE (maximising participation) favours long-distance distribution with the associated time spent driving (a form of food system participation), while minimising carbon emissions favours the short-distance distribution of produce direct from the farm or garden to local consumers. In this optimised case, this would most likely lead to self-provisioning. This trade-off reflects some assumptions in the model but highlights the importance of studying the distribution and the market mechanism in UA; it is important to understand whether car-based transport is or is not included in the UA food system, as it can potentially contribute significantly to both labour/participation and carbon emissions. The study by Kafle et al. (2023) [31] also highlighted that the small petrol-operated vehicle (i.e., car-based produce distribution, which is most common) is inefficient in terms of a reduction in the carbon emissions. It is possible to envisage larger-scale operations with local retail distribution that requires greater participation, e.g., in sales, which the current model does not represent.

The most profitable UA (best-case net margin) is responsible for relatively high carbon emissions due to the mechanisation and area favouring products for long-distance transport, thus increasing production and distribution emissions when there is a low FTE due to the mechanisation effect. The economic model (representing the best-case net margin) favoured the largest possible area, with moderately mechanised commercial UA producing mid- to high-value crops for wholesale markets near the CBD. In this case, the best-case margin is still negative, implying the lowest loss or margin closest to the break even.

The social model (representing the best-case FTE) highlights the potential for participation in the food system via both the production and distribution of food, with the optimisation identifying a (perhaps unrealistic) solution involving a small garden-style UA system plus the transport of food over a long distance. This may be seen as akin to someone growing food at home and delivering it to a friend or family member across town. For the best-case FTE, a nearly ten-times-smaller area than the economic objective, with non-mechanised directly distributed mixed-value crops used for the gardening styles of UA, is identified as a characteristic feature via this optimisation study.

The environmental model (representing the difference in the carbon dioxide emissions when considering commercial farming) highlights the relevance of the production efficiency (more kg produced reduces the emissions per kg) and minimises the distribution distance, effectively opting for self-provisioning with negligible transport.

Due to the slightly higher UA productivity in Adelaide than in the Kathmandu Valley (2.21 kg/m² vs. 1.95 kg/m²), the proposed model chooses a less labour-efficient mode of production and distribution (the model chooses a high FTE within a small land area and an inefficient distribution mechanism). The need for a pragmatic approach owing to this artifact of the modelling was recognised due to the greater trade-off between carbon emissions and the FTE, as per the uncorrected FTE (Figure 3); however, as can be seen in Table 2, placing the farm being very far away in order to serve only two people seems an impractical solution, compared to the more feasible cases proposed for the Kathmandu Valley (i.e., a higher number of people served). Therefore, the same feasible solution as that of the Kathmandu Valley (considering same area, market mechanism and purpose) has been applied to test a more realistic scenario in Adelaide, rather than simply relying on the outputs generated based on the mathematical assumptions (Figure 4). The revised relationship between the FTE and carbon emissions is observed in this more practical FTE model, and there is a less intense trade-off between the FTE and margin (a slight improvement in the margin with the same intensity of the FTE trade-off as that of the uncorrected FTE).

5.2. Features of the Optimised UA in the Kathmandu Valley, Nepal

The features of UA under the competing economic, social and environmental objectives in the Kathmandu Valley, Nepal, are summarised in Figure 5. As was the case with Adelaide, the model reflects trade-offs between the three objectives. However, it is noteworthy that in the Kathmandu Valley, in the pursuit of each of the three distinct objectives, the optimal solution was economically viable (positive NM). This is largely due to the very cheap labour cost, as highlighted by Kafle et al. [27]. There is a moderate to low trade-off between the margin, carbon emissions and FTE due to the mechanisation effect; the best-case profit favours the non-mechanised cultivation of mid- to high-value vegetables targeting local consumers, while minimising the carbon emissions and/or maximising the FTE favours the non-mechanised short-distance direct distribution of produce from the farm or garden to local consumers (self-provisioning), helping to employ more people.

The economic objective (best-case net margin) favoured relatively low carbon emissions due to the non-mechanised cultivation and maximum possible area favouring products for short transport, with minimal production emissions and a relatively low FTE.

The social objective (represented by the best-case FTE) favours a garden-style UA with a relatively higher area and mixed-value crop distributed throughout the farm, favouring the maximum possible opportunity for employment.

The environmental objective (represented by the difference in the carbon dioxide emissions reduction) highlights the relevance of non-mechanised farming, with a smaller farm size (approximately one-third) than in the profit and FTE cases, and using a direct distribution mechanism with negligible transport.

A moderate trade-off between the margin and carbon emissions, a more intense trade-off between the margin and FTE, and a negligible trade-off between the carbon emissions and FTE were observed. No trade-off between the FTE and carbon emissions (best-case FTE in best-case carbon emissions) was observed due to our assumption in the model (reduction in carbon emissions employing more people via direct product distribution). The best-case margin favours moderate emissions and a low FTE due to the relatively large-scale area that focuses on mid- to high-value crops, which employ fewer people per consumer. Likewise, the best-case FTE favours low emissions and a low margin due to non-mechanised mixed-crop-based farming, and the best-case carbon emissions favoured a high FTE and a relatively better margin under non-mechanised gardening styles of UA.

In Adelaide, our model favours commercial UA for the best-case profit and best-case carbon emission reductions, while it chooses gardening-style UA for the FTE. In the Kathmandu Valley, the model chooses the gardening style of UA under all scenarios due to the colossal difference in land cost between Adelaide and Kathmandu (land cost is far higher in Kathmandu, relative to labour and food prices) and the comparatively high labour cost in Adelaide. These results reflect the findings of earlier research, in which land and labour costs have been identified as the major barriers to scalable, economically viable UA in Adelaide, Australia; meanwhile, land costs are the primary threat to the scalability of UA in the Kathmandu Valley, Nepal [27]. The apparent unrealistic solution to the trade-off between the FTE and carbon emissions in Adelaide has been observed due to the artifact of modelling, and the more practical solution has been investigated by applying the solution from Kathmandu as an alternative; this showed better efficiency in terms of a reduction in the carbon emissions and a lower trade-off with the FTE. In this study, downscaling production (i.e., land area) showed a higher environmental advantage with few economic advantages, as the positive effect of downscaling has been reported by Grosskopf [59]. The modelling presented here suggests the following key lessons based on the optimisation study in Adelaide, Australia, and the Kathmandu Valley, Nepal:

• Pursuit of the economic objective will tend towards larger scales in order to make use of mechanisation (labour-saving), irrespective of the development context. If this analysis had allowed the use of larger land areas and additional (heavier duty) mechanisation categories, it is likely that it would have pushed the production further away from the city in order to access larger plots of land and larger economies in terms of their scale; this would have ultimately replicated what we see in the conventional food system with large monoculture production systems that are located relatively far from the point of consumption.
• In high-labour-cost scenarios (e.g., Adelaide), commercial practices may be favoured due to increased labour efficiency, even if this means switching over to paying for land (commercial UA). In low-labour-cost/high-land-cost scenarios (e.g., the Kathmandu Valley), the economic objective favours forms of UA that allow access to free land (gardening UA), even if this is substantially less labour-efficient.
• The pursuit of higher participation in the food system (social objective of UA) requires reduced mechanisation and may favour more time spent in distribution (possibly including sales). In high-labour-cost scenarios, there is a trade-off between participation and economic viability.
• The potential to reduce carbon emissions (as a proxy for the environmental impact of the food system) depends critically on the marketing and distribution mechanism. If car-based transport is part of the distribution system, the impact of this (both in terms of the time spent and carbon emissions generated) needs to be considered when evaluating the environmental benefit of UA.
• Accessing consumers close to the point of production appears to be key to both the social and environmental outcomes. This modelling analysis reveals that there is scope to consider the marketing/sales component in more detail (and what this means for participation and emissions). Researchers like Burton et al., 2013 [30], have stated the importance of a short food supply chain in order to reduce adverse environmental impacts by bringing production closer to the consumers and mitigating the emissions generated by the long-distance supply chain. This study shows UA’s added social and environmental benefit via improvements in the distribution system, but stresses the importance of including the emissions generated by a vehicle such as a car, as identified by Kafle et al. 2023 [31].

5.3. Limitations of the Research

We have established a comprehensive modelling method to study different UA scenarios, which we have applied in a deliberately parsimonious way using a limited range of scenarios. The technique can be readily extended to different scenarios by introducing different combinations of parameters or by considering small parts of the model (like distribution distance) slightly differently. These changes could be readily implemented within the proposed overall framework that links together profitability, social participation and carbon emissions.

Such research could use the same modelling approach presented in this study to consider the potential trade-off between the higher capital cost of infrastructure and the gain in terms of yield (and hence income potential from smaller land parcels), as well as labour efficiency and the difference in the environmental impact had between outdoor and controlled environment production, as achieved via the two-step hydro-economic modelling performed by Moore et al. (2020) [60]. The insights and questions raised in the present analysis regarding distribution (in terms of labour/participation and emissions associated with transport) would remain relevant irrespective of the production method.

The example land parcels used to parameterise the model covered 30 different distance/area combinations for Adelaide and the Kathmandu Valley, and are not fully representative of the overall global scenario. Temporal and spatial variation in the land, labour and distribution costs may exist depending on the location and development contexts. We have also ignored the other potential costs, like borrowing money for land acquisition, paying for labour as production begins (and there is no product to sell), equipment, and other production input costs. Other costs associated with labour vary, such as leave loading or superannuation contributions. Other costs not included in the analysis include the insurance and administration costs associated with purchasing/selling, related accounting, and taxation. We assumed the availability of farmer-owned small vehicles like cars and therefore excluded purchase cost/payments, car rental or maintenance costs. If paying someone to act as a courier, they would normally have to provide a vehicle or pay a higher cost so that they could use their own car.

The model assumptions are based on idealised cases that broadly represent gardening and commercial production modes in UA. The potential productivity and labour used in each mode are derived from past UA research and are significantly influenced by additional factors such as the soil type, farming skill/knowledge, crop type and other factors that were beyond our consideration. These factors could be incorporated explicitly in a future iteration of the model, or simulated implicitly via modified parameters (such as yield, crop value and labour input) using the existing modelling framework.

Environmental impact was modelled using greenhouse gases as a proxy for the overall impact of the food production and distribution system, excluding emissions generated via water use, land management, pesticide and fertiliser use and other input use during production. The potential cost and carbon emissions generated by machine use during production are assumed to be limited to tilling and bed preparation activities, but may extend to seeding and harvesting if these processes are mechanised (this was not considered in this study due to the typically small scale of UA). Likewise, the marketing and distribution of the product are assumed to be wholesaling, where the excess product is disposed to the market via car-based transport and retailing in which the direct distribution of products from the production site takes place. There may be other potential alternative food distribution mechanisms via cooperative marketing, farmers’ markets and others, which may be more efficient in reducing transport, with or without additional labour requirements.

The term ‘mid- to high-value crops’ is context-specific, and the definition may vary with market price conditions under the development contexts. In the interests of generality, we included the common groups of vegetables focusing on Adelaide and Kathmandu, and the recommended serving is derived based on those categories. The inflation rate and other temporal and seasonal variations may influence the cost of the items presented here, and the nature of this broad crop category could therefore change in future calculations. In the cost analysis, we followed the approach used by Kafle et al. (2022) [27], which focuses on gross viability considering major cost items (land and labour). A more detailed economic analysis could be applied to confirm viability once the additional costs are included. The labour associated with the marketing and distribution of produce was applied in a deliberately simplified way, and the model could be extended to consider this in more detail by including activities such as quality control, advertising, business administration and so on.

6. Conclusions

Optimisation is widely used to understand the trade-offs and synergies between different objective functions under a given set of decision variables. In this analysis, UA has been simulated as a food production and distribution system with interrelated and quantifiable economic, social and environmental dimensions that can be formulated as three objective functions and then optimised. This optimisation has focused on two low-cost and common practices in UA (i.e., gardening and commercial) to explore the different optimal conditions in pursuit of the three objectives.

The optimisation model is formulated using three potentially contrasting and conflicting objectives in order to maximise the net margin (a proxy for economic benefit), the full-time equivalent (FTE) labour (a proxy for social benefit, representing participation in the food system) and reduction in carbon dioxide emissions (a proxy for environmental benefit). The decision variables were the area under cultivation, the purpose (gardening or commercial), the level of mechanisation, the marketing mechanism and the broad category of crop value. The model was evaluated using available secondary information for Adelaide, Australia (high land cost and high labour cost), and the Kathmandu Valley, Nepal (higher land cost but significantly lower labour cost), under the range of economic, social and environmental constraints.

This study has demonstrated a common optimisation method that can be extended under divergent development contexts to understand the characteristics of UA and actions for improvement based on the targeted objectives. In both development contexts, the optimisation demonstrates a clear trade-off between economic, social and environmental objectives, but the features of the optimised UA in Adelaide and the Kathmandu Valley are different. The specific trade-offs and synergies vary depending on the context, availability of resources and objective being pursued.

In this analysis, under the given set of assumptions, the economic objective is primarily influenced by the efficiency of work (mechanisation), crop value, input cost (land and labour), marketing mechanism and area under cultivation. Likewise, the social objective (a measure of the number of producers per consumer) is largely influenced by the mechanisation level, crop type, the market mechanism and area. In a high-labour-cost context (such as in Adelaide), there is a greater conflict between economic and social (participation) objectives. The distribution of produce is a potentially significant component of the overall labour and cost. Ultimately, the volume of carbon emissions per kg of production is significantly influenced by the distribution distance, mechanisation level, yield and how the produce is marketed (locally or via distant markets). In Adelaide, the model favours commercial UA when targeting the best-case profit and carbon emissions, and small-scale gardening UA when maximising the FTE. In the Kathmandu Valley, the model chooses gardening-style UA under all scenarios investigated.

Recommendations and Ways for Improvement

If UA is to be scaled up, there is a need to identify the elements that make it economically viable, socially acceptable and/or environmentally sustainable. The policy and approaches used for promoting UA depend upon the motives (economic, social and environmental) and an appropriate blend of the different elements required to fulfil the motives. The generic model presented here allows the following features of UA to be identified, with relevance to the concerned practitioners, planners and policymakers involved in the promotion of UA:

• Clear trade-offs between the social, economic and environmental objectives take place when optimising UA. It is important to study the characteristic features of UA (decision variables) based on the objectives that guide the intensity and direction of trade-offs. This ultimately helps to identify proper correction measures for the long-term sustainability and viability of UA practices. The styles of UA (i.e., gardening and commercial) are key to determining its economic viability, as the land and labour costs are the most potent threats to the economic viability. Therefore, appropriate policy measures, i.e., subsidised land or labour (or both) based on the development context, are needed for economic viability in UA.
• The social objective (i.e., the FTE) is largely influenced by the number of consumers per grower, which depends on the types of food grown and the level of mechanisation. The distribution and marketing of produce are also potentially significant in terms of labour, particularly for small-scale farming or gardening. In high-labour-cost scenarios (such as in Adelaide), the trade-off between social and economic objectives needs to be carefully evaluated for the upscaling of UA.
• The environmental objective function (carbon emission reduction) is very significantly influenced by the distribution distance if using the car-based transport of produce. To maximise the environmental benefit, it is important to support market mechanisms that allow UA produce to be directly distributed to local consumers very close to the point of production. The mechanisation of production using petrol-powered machines also contributes to carbon emissions, and the model shows a trade-off between the economic objective (which increases when the labour productivity is improved by mechanisation, particularly in high-labour-cost scenarios) versus the environmental objective, which favours non-mechanised production. The adoption of technologies, like making improvements to the machinery via electrification (battery-powered small machines like garden tillers and cultivators), may improve the environmental/economic trade-off, which should be further explored.
• The isolated UA system research performed by researchers focusing either on economic viability (margin analysis), social acceptability (whether employment or general participation) and environmental sustainability (carbon emissions reduction potential) can be substantially improved, leading towards sustainable practices via the identification of the features of UA presented in this study, along with a future course of action.