Agent-based model

The new decision-making model, presented in this manuscript, is built on the agent-based model published by Katapodis, Zhang [15], which modeled the impact of accessibility on residents’ produce intake (i.e., dietary intake of fruit and vegetable) for one rural community in Northwestern Texas. The decision-making model considers multiple available locations (i.e., empty spaces in commercial buildings) in the community as potential locations to open new FV markets. In addition, the model accounts for the service capacity of the available locations (i.e., quantity of produce available for purchase) and budget constraints (i.e., financial resources needed to open new FV markets). Given those input factors, the model generates the recommended number and placement for new FV markets and the impacts of those decisions on the local population’s access to FV.

Decision-making model for number and placement of New FV markets

The lead author (E.P.) created a new decision-making model using Microsoft® Excel and the add-in OpenSolver, which is an open-source tool for linear and non-linear optimizations (https://opensolver.org). The decision-making model was a resource allocation model, specifically an integer programing model. The model optimizes location for new FV markets and measures the impacts of improved access for a rural community. In other words, the model decides how many and where to place new FV markets that will guarantee access within a specified driving distance for most of the population.

To create the base model, sets, parameters, and decision variables were specified. The base optimization model included several constraints that varied depending on the intervention scenario to be modeled. The following equations were included in the base model. Equation 1 that maximized access to FV markets in a rural community. Equation 2 that modeled the constraint of a community being within a specified distance of an existing or new FV market. Equation 3 that limited the ratio of fast food outlets versus existing and new FV markets. Equations 4 and 5 were used to decide if a new FV market should be opened at a specified location. Equations 6 and 7 checked if a specific neighborhood was covered by either an existing or proposed new FV market. The base model was relevant for answering questions such as “What is the impact of considering different driving distances to define the residential food environment when selecting the optimal locations for new FV markets?” However, additional constraints were required to determine the impact of considering varied service capacity levels in the placement of new FV markets. Three equations were added; Equations 8–10 considered market factors like demand of FV and availability of FV within a community. Finally, Equation 11 was added to consider financial resource limitations of establishing a new FV market at an eligible location. Details about the decision-making model are discussed next.

Let denote the set of neighborhoods in the city indexed and let set denote the current markets in the community that sell fruit and vegetables, indexed . Set represent empty commercial spaces in buildings available to rent or purchase, which can be a potential location for a FV market. Set denotes the current fast food outlet in the community, indexed . The following three sets are coverage sets that identify locations for which the driving distance ( is within a predetermined driving distance from a destination location. Set represents the current FV markets located within a predetermined driving distance from neighborhood represents the current empty commercial buildings ) available for rent and located within a predetermined driving distance from neighborhood , represents the current fast food outlets in the community located within a predetermined driving distance from neighborhood

The following parameters model important characteristics of the proposed model. Parameters , , and are binary in value and equal 1 when , and , respectively. If parameter then neighborhood has access to the new FV market located in . If parameter then neighborhood has access to an existing FV market located in . If parameter then neighborhood has access to an existing fast food restaurant located in . Parameter models the monthly budget available to fund new FV markets and parameter represents the average operating cost per month of a FV market. Parameter represent the demand of FV per month for neighborhood . Finally, parameters and represent the expected service capacity per month for existing and eligible new FV markets, respectively.

The decisions to be made by the model are represented by five binary decision variables: , , is binary and equals one if a new FV market is located . Decision variable equals one if community has a FV market located withing the predetermined driving distance . Decision variable equals one if community is located withing the predetermined driving distance of a new FV market . Decision variable equals one if community is located withing the predetermined driving distance of an existing FV market . Finally, decision variable equals one if community is located within the predetermined driving distance of a fast food outlet .

The optimization model can now be stated using the provided definitions for the sets, parameters, and decision variables. The number of constraints varies according to the research questions to be answered, however, five equations are always present in the model. The objective function (Equation 1), , maximizes access to FV markets in a rural community. Equation 2, is within distance of an existing or new FV market. Equation 3, is the second constraint and limits the ratio of fast food outlets versus existing and new FV markets. The ratio is captured by parameter . Equation 4, equation 5, . Equation 6, equation 7, is covered by either an existing or proposed new FV market.

Equations 1–7 represent the “Base Model.” The “Base Model” is useful to answer many public health questions such as, what is the impact of considering different driving distances to define the residential food environment when selecting the optimal locations for new FV markets?. However, additional constraints must be added to the model to study the impact of considering different service capacity for FV markets when selecting the optimal locations for new FV markets. To study service capacity, three additional constraints were added to the “Base Model”. Equation 8, equation 9, Equation 10, .

To examine the impact of financial resources limitations, the model includes equation 11, . A binary decision variable determines if a new FV market is sited at node and establishes the cost of establishing a new FV market in eligible market location . The right-hand side of the inequality () establishes the maximum budget availability to open new FV markets in the community.

The decision-making model is designed to be adaptable to various communities and can incorporate updated demographic and economic inputs. Parameters such as financial resources and the cost of establishing new FV markets can be adjusted to reflect current market conditions and funding availability. Similarly, the expected service capacity for existing and eligible new FV markets can be modified based on recent per capita dietary intake data and local population sizes. The model also utilizes population data and market distance data as inputs, allowing for updates to reflect current demographic and geographic information of a specific community.

Intervention factors

The model considered how three different intervention factors, or constraints, affected intervention outcomes related to FV accessibility. The three intervention factors were: 1) recommended driving distance to nearest FV market; 2) financial resources required to open new FV markets; and 3) service capacity of the existing and new FV markets. Each intervention factor had three levels (i.e., low, normal, high). S1 Table provides more information on defining levels of intervention factors. The levels for recommended driving distance to nearest FV market was based distances of 1, 2.5, and 5 miles [16,17], where 5 miles represent the benchmark for rural residents. For financial resources, the benchmark was $20,000 per month, which was based on the USDA Farmers Market Promotion Program that provides up to $250,000 per year [18]. The model considered two additional levels ± $5,000 per month. The levels of low, normal, and high corresponded to monthly funding of $15,000, $20,000, and $25,000. The benchmark for service capacity of new FV markets was based on per capita dietary intake of FV [19] and local population size [20]. The model considered three market service capacity at low, normal, and high levels that provided 20,000, 40,000, and 80,000 servings of fruits and vegetables per month, respectively. Because there were interventions based on three different driving distances, each with three levels of financial resources, and three levels of service capacity, the study modeled a total of 27 intervention scenarios.

Intervention outcomes

The model estimated effects for three different intervention outcomes: 1) population coverage; 2) number of new FV markets; and 3) ratio of fast food outlets to FV markets. The population coverage provides an estimate of the percentage (%) of the population that would have access to FV if the recommended number of new FV markets were established in the community. The number of new FV markets provides an estimate of the number of new FV markets to satisfy the community needs. The ratio of fast food outlets to FV markets provides an estimate of the number of fast food outlets per FV market in each neighborhood after implementation of the new FV markets. This study used multiple outcomes based on the heterogeneity in the literature [3,21,22], and prior research has shown that areas with limited access to supermarkets often had a higher concentration of fast food and convenience food outlets food [23,24]. S1 Table provides information about selecting ratio of fast food outlet to FV markets as an outcome.

The study does not involve the use of information about living humans through interaction or intervention or obtaining identifiable private information. As such, the study does not constitute human subjects research and does not require institutional review board approval at the institutions involved in the study.

Policy implications

This study developed a new decision-making model for a local population in a rural community in Texas and explored how different food environment interventions might maximize a local population’s access to fruits and vegetables (FV). First, the simulated interventions produced quite large impacts. Regarding the estimated increase in access to FV, the smallest increase was 19%, that is population coverage increased from 46.4% with the benchmark to 55.1%. The 19% gain was based on a recommended driving distance of 1 mile, low financial resource availability of $15,000 per month, and a low service capacity of new FV markets and achieved by adding one new FV market. Other intervention approaches increased the proportion of the local population with access to FV to 100%. In real terms, a 19% increase in access to FV at the population level could be significant for public health. Second, the most impactful intervention approaches appeared to be the less intensive options, that is with relatively less financial resources or based on greater distances. For example, the most limited approach (i.e., with a $15,000 per month investment at the lowest level of financial resources, lowest service capacity, with recommended driving distance of 2.5 or 5 miles) produced a 27% increase (almost, from 46.4% to 73.5%) in population coverage. There was greater improvement in access to FV associated with increasing financial resources from $15,000 to $20,000 (20% to 29%), compared to higher levels or increasing from $20,000 to $25,000 (29% to 37%). With more financial resources or a greater service capacity, the model predicted that the entire community or 100% would have access, which represented a relative increase of nearly 55% in population coverage. The model that produced the greatest impact, relative to the control (or the do-nothing approach), was when the driving distance was 2.5 miles and with $15,000 of available funding. Third, interventions focused on improving access to FV may be more effective compared to interventions aiming to change the ratio of fast food (FF) to FV outlets. For example, this study demonstrated that the better-funded approaches at $25,000 per month with higher service capacities decreased in the ratio of FF outlets to FV markets (from a ratio of 8 to a ratio of about 5), but the largest decrease in the ratio used an optimal driving distance of one mile, which may not be practical for rural communities.

Related research related to improving food access has been efficiency-driven and used decision models to address well-defined technical problems [25–27]. For instance, Lien, Iravani [25] proposed an optimization model to solve the sequential resource allocation problem faced by a not-for-profit facility distributing donated food. Unfortunately, most of the published studies have drawn conclusions based on single attributes of the community food environment, such as proximity to the nearest supermarket or the density of FF outlets [26,27]. Since shopping and purchasing decisions are likely to be made based upon the market of food outlets that are available within a particular distance of travel, single attribute studies appear to be suboptimal [28–32]. Ratios of healthy to unhealthy food outlets and other multi-attribute approaches [33,34] to capture resident exposure are comparatively rare in the literature and warrant further investigation. This study makes an important contribution. Specifically, this study was unique in developing and testing a multi-attribute model to optimize the number and placement of new FV markets for a rural community in Texas. It is crucial to emphasize that the model is formulated as a general optimization model, designed for broad applications. The case study presented here, using data from a specific rural Texas community, serves primarily to illustrate the potential and capabilities of this model in informing food environment interventions. The model was created in Microsoft® Excel and an open-source add-in Open Solver, rather than a specialized software package. The model is available by request from the corresponding author. Given the accessibility of necessary local data, similar analyses can be performed in other communities. Decision makers, especially those with limited budgets, can use this model to tailor potential community food environment interventions to their communities and generate context-specific evidence for policy change.

Previously, review papers have summarized evidence for interventions that established new food retailers (i.e., farmers’ markets and mobile FV markets) and examined intervention effects on FV intake, but with mixed results [35–37]. For example, the Veggie Van in North Carolina was a mobile FV market that sold more affordable fruits and vegetables to residents living in socioeconomically disadvantaged communities of North Carolina [38]. Findings showed improvements in dietary intake of FV but limited success in changing access. However, this type of community-engaged intervention is resource-intensive. Further, there have been very few PSE change interventions with FV markets for rural communities. Additional research is needed to develop evidence-based recommendations for how to change community food environments in rural communities.

This study had several limitations. While decision-making models are advantageous for informing policy, systems, and environmental (PSE) change interventions for the community food environment [39], they cannot yet consider factors related to the consumer food environment. Prior research has shown the importance of in-store features, like preferred brands or products, prices, placement, and promotions on food purchasing [40]. Interventions aiming to positively change food environments, and support purchase of healthful foods like FV, must consider the factors, beyond accessibility, like affordability, acceptability, and accommodation [3,41,42], that are meaningful to potential consumers in rural communities, those living locally and those who travel to the food retail places from longer distances.

There are a few other limitations of this study. First, the decision-making model assumed that residents shopped within their neighborhood or local area, defined by a driving distance of up to 5 miles, but prior research has challenged that assumption [43,44]. Though this model considered some aspects of consumer choice by testing varied driving distances, this model is unable to consider food retail outlets beyond that area. Future research is warranted to integrate consumer behavioral factors into agent-based models. Second, this model was based on findings from an existing agent-based model, which was created using data from 2007 [28] and may not be as relevant for food purchasing in 2021. Third, this decision-based model was developed based on one rural community in Texas and, thus may have limited generalizability to other rural communities in Texas or other states in the U.S. However, given the complexity in developing agent-based models, this study still offers insights into the potential impacts of interventions to modify the community food environment.