Optimizing food pantry stocking through client preferences: a novel elicitation and classification process Open Access

According to the United States Department of Agriculture, over 38 million people in America are food insecure (Agriculture, 2022). That means one out of ten Americans is unsure of having or unable to get enough food to meet their needs. Several methods exist for providing hunger relief, including food pantries, food banks, soup kitchens, vouchers, and gardens (Bazerghi et al., 2016; Mukoya et al., 2017). Operating primarily in the USA, food pantries provide free groceries and food items to individuals and families in need. This approach allows recipients to bring food home and prepare meals themselves, contrasting with soup kitchens that serve hot meals directly (An et al., 2019; Mukoya et al., 2017) and enabling pantry users to exercise greater autonomy over their dietary selections. With nearly 60,000 food pantries operating in the USA, distributing millions of pounds of food per year (Feeding America, 2020), most of these pantries are traditional, providing preselected sustenance to their clients. However, client-choice pantries are becoming more popular, featuring something comparable to a grocery store shopping experience.

Despite the attractiveness of the client-choice model, managers of traditional pantries may resist transitioning, due to concerns about potential increases in food waste, space requirements, volunteer needs, and distribution hours (McCormick, 2019). The dearth of literature examining food pantry and food bank operations only compounds the problem. This deficiency and the absence of research looking into the tactical challenges of food pantries leave pantry managers with little in terms of decision support to aid them in transitioning from traditional to client-choice food distribution.

In addition to the lack of a decision support system for pantry managers, another reason for our work is Feeding America’s initiative to provide more culturally appropriate and nutritious food (Thompson, 2021). Allowing clients to choose their foods not only offers a more dignified experience but also addresses feelings of shame and embarrassment that often accompany the need for food assistance. Such empowerment helps mitigate the dehumanization that can occur in traditional food aid settings(Caraher et al., 2014; Chung-Yi et al., 2016; Martin et al., 2013). Moreover, awareness of client food choices may also help reduce food waste. Traditional pantries are often inundated with shelf-friendly items donated by a variety of sources (Feeding America, 2020; Remley et al., 2013). Viewing donated food as either supplemental or urgent relief, donors give whatever they can spare, irrespective of the client’s culture, religion, diet, or actual need (Tarasuk and Eakin, 2003). Although pantries sometimes request specific items during a food drive, they seldom tailor these collections to actual client preferences. Instead, clients are given a box or bag of preselected food items. As a result, the client may receive unwanted or unusable food (Cooksey-Stowers et al., 2019b; Pritt et al., 2018; Wilson, 2016; Wilson et al., 2017). Even worse, the client may deal with food allergies or dietary restrictions, making the consumption of some foods life-threatening.

Understanding client preferences in food selection is crucial, particularly as these preferences can vary significantly across different demographics. Contrary to the notion that pantry users will accept any food provided to them, our research suggests that client preferences are not homogeneous across all food insecure demographics. We cannot assume the food chosen by the guests of one pantry will be preferred by the guests of another, even if the pantries are geographically close. Each pantry is autonomous and must be treated as such for planning and operation.

Presenting a framework pantry managers can implement to draw insights and inform decision-making, this research therefore aims to understand client food preferences and how pantry offerings can be classified by those preferences. We specifically seek to answer the following research questions:

To answer these research questions and develop our framework, we explore three food pantries within the Second Harvest Food Bank of Northwestern North Carolina (SHFBNWNC) network. Annually distributing over 7.5 million pounds to clients in 18 counties, SHFBNWNC operates through its main warehouse in Winston-Salem and a satellite in Greensboro. This structure allows for a wide array of donations, ranging from corporate donors to individuals, and promotes the efficient distribution of food to various partner agencies, such as food pantries and soup kitchens (refer to Figure 1 for the supply chain diagram of SHFBNWNC). In this study, we adopt the term ‘client’ to describe those who use these services, consistent with the terminology used by our partner food bank. In social science literature, ‘client’ typically indicates a reciprocal relationship between service providers and those they support (Cahill et al., 2019; Campbell et al., 2011; Cooksey-Stowers et al., 2019a; Long et al., 2022). We believe this term more accurately reflects the participative nature of food aid than alternatives such as ‘beneficiary’ ( Byrne and Just, 2021; Gomez-Pantoja et al., 2021; Sahinyazan et al., 2021) and ‘food insecure population’ (Sucharitha and Lee, 2021) used in other studies. Our choice emphasizes both the logistical and human elements integral to understanding and improving hunger relief networks (Bazerghi et al., 2016).

To collect data, we develop and administer customized surveys. Analyzing preferences through the use of survey-based data is the mainstay of statistical methods such as conjoint analysis (Green et al., 2001). Introduced in 1964, conjoint analysis, in the most general sense, alludes to any approach that seeks to estimate the make-up of a consumer’s preferences based on the consumer’s valuations of a set of alternatives (Green and Srinivasan, 1978, 1990). We use survey data similarly to explore client food preferences amid competing alternatives and to determine what demographic factors are associated with those choices. Another advantage of administering a questionnaire is that it avoids the logistical challenges and increased time of supervising a somewhat transient sample of pantry clients. Furthermore, pantry guests are not coming to a food pantry to get the same foods every day. Instead, they come as allowed to get whatever food is available. Hence, a survey administered to a sufficient sample size is better suited for gathering data, given these dynamics.

Using the survey data, we apply a nonparametric analysis of variance (ANOVA) to classify responses by client preferences. This approach tests the hypothesis that preferences for all foods in the initial food classification are the same. Having the same preference for all foods within a food classification shows interchangeability of those foods and has implications for the pantry’s stocking strategy. We then use binary logistic regression (BLR) to identify statistically significant (p < 0.05) demographic predictors of client food preferences.

The results of our BLR serve as inputs to a multidimensional bounded multiple knapsack (MBMKP) formulation that yields an optimal stocking strategy for the pantry. Our MBMKP is unique because it incorporates the pantry client’s food preferences and the pantry’s specified item limits and limits on poundage. In practice, pantry managers may place item limits on food to ensure fair distribution. For the same reason, the pantry may also indiscriminately limit the pounds of food distributed. For instance, the pantry may have a policy of limiting the total pounds of food distributed per client as well as the total pounds of certain categories of foods (e.g. a limit on the pounds of fresh food). A model encapsulating all of these dynamics at once has yet to be explored in the literature. Our MBMKP model not only improves operational efficiency but also furthers the ethical distribution goals of food pantries.

The results of our study show that food pantry clients prefer fresh and frozen foods over shelf-friendly canned foods and dry goods. This finding is consistent across two food pantries serving the general public and a college food pantry. These results also indicate that the primary demographic factors impacting food preferences are gender and age for the two pantries serving the general public and gender and religion for the university pantry. While the demographic factors affecting preferences for the pantries serving the general public are the same, the types of food are not. This finding further supports our contention that a one-size-fits-all approach is not appropriate when determining preferences. Our findings also demonstrate how a MBMKP formulation based on client preferences can inform an optimal stocking strategy for the food pantry. From this formulation, we develop a heuristic (Heuristic 1 in the e-companion) to help decision-makers apply this strategy. Our stocking strategy also has implications for food waste. Demographic factors impact client food preferences, and client food preferences are directly associated with potential food waste, so stocking the pantry’s shelves based on the client’s preferences can yield less food waste. Hence, applying the knapsack problem, we develop an optimal stocking strategy for the pantry that incorporates the client’s preferences and the pantry’s food storage constraints or item limits.

The remaining part of this paper proceeds as follows: A brief review of the related literature is provided in Section 2. In Section 3, we outline the methods involved in data collection and analysis. This section includes the survey instrument, its administration and the methods used for subsequent statistical analysis. Sections 4 and 5 report and discuss the results. Section 6 presents the conclusion.

Our study is related to three research areas critical to the development of a decision support system for pantry managers:

• preference elicitation of pantry guests;

• decision support models in food aid literature; and

• application of the knapsack problem in food aid efforts.

A growing body of literature addresses the elicitation of the food preferences of pantry guests. Qualitative and mixed-method studies use interviews with food pantry guests and partner agency managers to obtain this data (Kihlstrom et al., 2019; Cahill et al., 2019; Long et al., 2022). For example, a study in the Tampa Bay area questioned focus groups comprised of pantry clients to elicit their preferences (Kihlstrom et al., 2019). To obtain preferences for types of foods preferred by pantry goers in Arkansas, researchers interviewed 50 clients from six different pantries using a semistructured interview guide (Long et al., 2022). Cahill et al. (2019) use in-depth interviews with pantry directors in Atlanta to understand client food choices.

On the other hand, quantitative studies rely on questionnaires (Campbell et al., 2011; Cooksey-Stowers et al., 2019a; Caspi et al., 2021; Jones and Maclin, 2017; Bomberg et al., 2019). For instance, one study used a questionnaire where pantry clients ranked 16 food items from most preferred to least preferred (Campbell et al., 2011). This approach is similar to Cooksey-Stowers et al. (2019a) who asked clients to select 5 of 16 available food categories they would like to see more of in their pantry. Clients at food pantries in Minnesota and Indiana also used a survey to indicate which foods were most important for them (Caspi et al., 2021; Jones and Maclin, 2017). Another recent study used a questionnaire to elicit preferences at the categorical level of fruits, vegetables, dairy and protein (Bomberg et al., 2019). Taken together, these studies indicate that no standardized method exists to elicit client food preferences.

It is beneficial to consider preference elicitation in the broader setting of economic subsidiarity. In the context of hunger relief, economic subsidiarity refers to the idea that a secondary support system is required when people are unable to afford food due to economic constraints (Drew and Grant, 2017; Lamy, 2007). Ideally, this support should be “seated” as close to the need as possible. Compared to other forms of economic subsidiarity such as community markets (Nayak and Hartwell, 2023), cash grants and food vouchers (Orkin et al., 2022), food banks, food pantries and soup kitchens are sometimes viewed as being less sustainable and impactful on nutritional outcomes. Hence, in building upon the concept of preference elicitation within the framework of economic subsidiarity, it also becomes important to consider the nutritional outcomes of these efforts, as the quality of food provided directly influences the effectiveness in alleviating food insecurity (Simmet et al., 2017; Long et al., 2020).

There is a relatively small body of literature concerned with decision support models in food pantries and food banks. Statistical, simulation and optimization models comprise the available scholarship. Optimization models address decision-making at the strategic, tactical and operational levels of the food aid network. Strategic-level decision support models include facility location problems and the optimal location of food delivery points. Tactical level models aid in the optimization of resource allocation (food aid). In a typical food aid network, food is allocated from donors to the food banks and from the food banks to partner agencies. Partner agencies ultimately distribute to pantry clients. There are also operational level decision models, such as vehicle routing problems. We refer the reader to Mahmoudi et al. (2022) for a systematic review of decision support models for managing food aid supply chains and to Rivera et al. (2023) for a review exclusive to food banks with more focus on optimization models.

In addition to the studies outlined in the above reviews, several additional works offer decision support in the form of operational challenges faced by food banks during disaster relief (Pérez et al., 2023; Esteban et al., 2022), nutritional and economic considerations (Mandal et al., 2021; Castañón, 2020; Sahinyazan et al., 2021) and the equitable distribution of food resources (Orgut et al., 2018). However, food preferences are considered a part of the decision-making process in only one study. That analysis uses an optimization model to choose food aid modalities and indirectly considers beneficiary preferences (Sahinyazan et al., 2021). Specifically, they consider beneficiary preferences in terms of three types of food options (basic food, tasty food temptation food) and the preferences are incorporated using household specific utility functions (which is determined arbitrarily during the numerical study). In our model, we elicit food preferences from the actual food aid recipients, model the relationship between food preferences and demographic factors, statistically, and develop a pantry level inventory stocking plan based on the preferences.

Since Martello and Toth’s seminal work, the knapsack problem has been studied and applied extensively. The classic binary knapsack problem begins with a set of items of various values and weights. The problem then involves choosing a subset of items such that the total value is maximized without exceeding a total weight constraint. Over the years, the knapsack problem has been extended in terms of the number of constraints, the number of knapsacks, and the problem structure itself (Kellerer et al., 2004). However, it has seen limited application in the humanitarian food aid arena.

Researchers have used the knapsack problem to aid in more efficient and effective resource allocation during humanitarian relief efforts. For instance, Ertem et al. (2010) applied a multidimensional knapsack problem to procurement auctions during the bid evaluation phase to maximize bid quantities and the associated asset values. Their model is later extended to favor suppliers with the best access to disaster locations (Ertem and Buyurgan, 2011, 2013). Gomez-Pantoja et al. (2021) offer an optimization model for the food bank resource allocation problem that simplifies under certain conditions to a multiple knapsack problem with assignment restrictions. In an extension of the traditional vehicle routing problem, Nair et al. (2017) introduce three objective functions, one of which maximizes the total utility of the agencies (utilitarian). A fractional knapsack problem is used for the utilitarian food recovery allocation problem. Rivera-Royero et al. (2020) present a rolling horizon methodology for distributing relief supplies after a natural disaster, solving large instances of the problem, using a binary knapsack formulation. To help make optimal stocking decisions for various materials before and after a disaster while considering budget constraints, Acar and Kaya (2022) use a two-stage approach. They start with a newsvendor model that becomes a classical knapsack problem after the uncertainty wanes. Collectively, these studies outline a growing role for the knapsack problem in humanitarian relief resource allocation.

Researchers have also used the knapsack problem in other applications. For example, the binary knapsack problem is used in a route-allocation problem that optimizes the number and locations of depots and the allocation of routes to open depots. Here, the researchers minimize an objective function that includes location and delivery costs (Zhang et al., 2015). The knapsack problem has also seen usage in reducing food waste. Researchers at the University of Pittsburgh applied the results of a 0–1 knapsack problem to manage leftover food, producing an application that selects a subgroup of the student population to invite to certain events to consume the leftovers (Silvis et al., 2018). In another intriguing study, researchers used a multidimensional bounded knapsack problem to help Harvest House Food Bank of South Carolina come up with an optimal mix of promotional events to increase the total number of annual meals provided from donations (Ahire and Pekgün, 2018).

Our study contributes to existing scholarship in several ways. We offer an innovative approach to eliciting client food preferences that differs substantially from prevailing studies. Instead of considering preferences at the food type or categorical level (Bomberg et al., 2019; Sahinyazan et al., 2021), we elicit preferences for specific foods such as broccoli, green beans or frozen fish. Also, instead of ranking food items (Campbell et al., 2011), we ask respondents to rate or score each food item on a scale from one to five. In addition, our research provides insights for tactical decision making in food pantries, a context that has been underexplored.

While our study parallels Campbell et al. (2011) in exploring the food preferences of pantry guests and the use of surveys for data collection, notable differences exist. The studies differ significantly in their respective survey methodologies. The previous study asks participants to rank 16 food items from (1 = most prefer to receive; 16 = least prefer to receive). On the other hand, we assess preference levels for 64 unique food items offered across three food pantries using a Likert scale from (1 = strongly dislike; 5 = like a lot). Our survey also assesses dietary and allergy restrictions, further expanding the scope of our work.

Dissimilarities also exist for the demographic focus of each exploration. Although the former analysis contrasts the preferences of rural versus urban guests, our research constructs demographic profiles of the most likely pantry visitors, including such predictors as age, gender, race, self-description, household size, household members, number of children, zip code, marital status, education, employment status, and household income. We correlate these profiles with food preferences to suggest an optimal stocking strategy for the pantry. In terms of implications, the earlier work highlights the importance of considering nutrition and taste, while our work places more emphasis on the role demographic factors play in shaping and responding to food preferences. Our research provides a new perspective on the food preferences of pantry visitors, shifting the focus from assessment to optimization.

Among the limited number of studies that seek to optimize food-related processes in the hunger relief setting, our work holds a distinct position as it specifically focuses on food pantry-level optimization, in contrast to a broader food aid agency-level approach (Sahinyazan et al., 2021). Our study goes beyond the three classifications (basic food, tasty food, and temptation food) used in the earlier work and investigates individuals’ preferences for 64 distinct food products, which were informed by the pantry managers. This granular approach facilitates a better understanding of the nuanced food preferences of pantry visitors, resulting in more customized and effective food aid interventions. The earlier study used a utility function to assess preferences for basic, tasty, and temptation foods among beneficiaries of the World Food Programme’s aid operations in Garissa County of Kenya. On the other hand, our study gathers preference data directly from pantry clients through surveys. This method enables us to capture variations in food preferences at the individual level. As opposed to the previous study, which profiles beneficiaries by the gender of the head of the household, our work uses survey data to construct demographic profiles. This holistic procedure enhances our understanding of the community we cater to, including variations in age, gender, ethnicity and income levels. The present study proposes a MBMKP to determine an optimal food stocking strategy for food pantries based on client preferences and pantry limitations. By contrast, the former work aims to identify the most effective and efficient food aid modality, including cash, vouchers and in-kind donations.

This research also furthers tactical decision-making, informing resource allocation from various sources to the food pantry. To the best of our knowledge, no study has looked specifically at an optimal stocking strategy for the food pantry. We posit an optimization model that accomplishes this feat and also simplifies to a heuristic which pantry managers can easily apply. Our research also adds to the use of statistical models in pantry research by applying nonparametric ANOVA and BLR to determine what demographic factors are significant predictors of client food choices. This research contributes to the emerging body of research applying the knapsack problem to food aid efforts. Unlike existing models, our formulation involves stocking decisions at the food pantry instead of the food bank. Furthermore, to the best of our knowledge, our MBMKP is the first in the literature to incorporate the pantry client’s food preferences and the pantry’s specified item limits and limits on poundage. Furthermore, because our model is built on client food preferences, it has implications for reduced food waste.

Figure 2 presents an overview of our research methodology. To meet our objectives, we collect primary client data through the development and administration of customized surveys at three different food pantries. Using statistical analyses, we determine if the preferences for foods within a category (e.g. canned, dry goods, etc.) are homogeneous or heterogeneous. Then, we use binary logistic regression to identify the key predictors of client choices. Finally, we formulate a multidimensional bounded multiple knapsack model that determines an optimal food stocking strategy. Our model, the first of its kind to incorporate client food preferences, also includes the pantry’s specified limits on food items and poundage.

All data was collected in Greensboro, NC, during the summers of 2019 and 2020. We collected data from three primary sources and two secondary sources: one traditional food pantry (Pantry A), two client-choice food pantries (Pantries B and C), a local food bank and a local university. Table 1 summarizes the various data sources. To collect data from the three food pantries, we administered on-site and on-line surveys. The participants in this study comprised a convenience sample from each of the three pantries. Data from the food bank and the university enabled us to determine if our convenience samples represented the larger client populations. Respondents answered a combination of multiple-choice, text entry and Likert-scale questions. The multiple-choice and text entry questions were designed to elicit client demographic and food security information.

We opted to use a survey because it is a reliable instrument to collect data on client food preferences (Feldmann and Hamm, 2015) and a validated food preferences questionnaire was not available to obtain the primary data we needed on the subject population. To begin the survey development process, we met with the food pantry’s director and key staff to discuss the goals of the research project and elicit their cooperation. We obtained additional insights from periodic reviews with a research peer group. The survey underwent several refinements because of feedback from the food pantry and the peer group. Prior to administering the survey, we obtained ethical clearance from the university’s Institutional Review Board. Table 2 presents the initial food groupings for Pantries A (Traditional), B (Client-choice) and C (Client-choice), as informed by our meetings with the pantry organizers. It should be noted that the groupings are similar to how food banks classify their food items and typically represent the type of foods donated to pantries. As shown, Pantries A and B do not offer beverages and condiments, and Pantry C does not offer frozen foods. Furthermore, Pantries A and B do not provide specific details about the types of snacks offered to their clients, whereas Pantry C offers only whole fruit in the fresh foods category without specifying any particular items. This may not be indicative of all food pantries; however, the proposed groupings are transferable to any pantry.

We used a five-level Likert scale (as shown in Figure 3) to capture food preferences, with available ratings ranging from strongly dislike to like a lot. Demographic variables included age, gender, race, self-description, household size, household members, number of children, zip code, marital status, education, employment status and household income. Questions related to food insecurity included participation in the Supplemental Nutrition Assistance Program, pantry participation, primary source of food, missed meals, and food shortages.

We first administer the survey at a traditional food pantry (Pantry A) over a two-week period in the summer of 2019. Our goal was to have a convenience sample of at least 378 food pantry clients complete a paper and pencil survey on-site. See Supplementary data in the e-companion for sample size calculations. A food pantry client is defined as anyone who shows up at the food pantry and completes an application for food assistance during the two weeks of survey administration. In total, 401 participants completed the questionnaire while they awaited service, receiving a small gift for their participation. Respondents answered 27 questions. We administered a second, nearly identical survey, at a local client-choice food pantry (Pantry B) in the Spring of 2020 using the same procedure we used for Pantry A. A third survey was administered during the summer of 2020 at another client-choice food pantry (Pantry C), located on the campus of a leading HBCU in Greensboro. This survey, consisting of 25 questions, was administered completely on-line. There were 78 respondents for Pantry B and 341 respondents for Pantry C. To motivate student response, we offered respondents the opportunity to enter a raffle to win one of three $50 gift cards.

We use demographic data of the client population served by each partner agency to validate that our survey sample represents the larger population served by the agency. SHFBNWNC provided data about the client populations of Pantries A and B and the university’s pantry director provided demographic data about the client population of Pantry C. We conduct χ² tests to see if our sample data is representative of the client populations of each pantry. The null hypothesis is that there is not enough evidence to conclude that the observed frequencies are significantly different than the expected frequencies for the population. Section 4.1 details the results of these tests.

What follows is a brief description of our data analysis. Tableau Prep (Tableau, 2020), Python (Kluyver et al., 2016) and JMP (SAS Institute, 2018) are used to clean, analyze and visualize the data. In this study, we collect data from three pantries: Pantry A, which had 401 respondents, Pantry B, which had 78 respondents, and Pantry C, which had 341 respondents. The average rate of missing responses in Pantry A’s preference data is 17%, whereas the average rate of missing responses in its demographic data is 7%. The rates of missing data in Pantry B range from 4% to 28%, with an average of 11% for demographic data and 22% for preference data. Notably, Pantry C displays the lowest rate of missing data, ranging from 1% to 7%, with an average of 2% for demographic data and 4% for preference data. As approximately 75% of the survey is devoted to eliciting preferences, the higher incidence of missing preference data may be attributable to respondent fatigue. Because our data is primarily categorical, we impute the mode response for any missing data (Fowler, 2013; Heeringa et al., 2017).

Figure 4 presents an overview of the ANOVA. This process is repeated for Pantries A, B and C. The independent variable is the food item (e.g. canned green beans and canned tuna), and the dependent variable is the food preference (a Likert score ranging from 1 to 5). ANOVA is often used when trying to test the means of two or more populations to see if at least two of the samples represent populations with different mean values (Sheskin, 2011). The standard way of thinking about parametric model adequacy has it that normality, independence and equality of variance must all be established (Mircioiu and Atkinson, 2017; Montgomery, 2013; Sheskin, 2011). Our Likert-scale responses violated the homogeneity of variance condition. Therefore, we analyzed our data using the Kruskal–Wallis one-way ANOVA (nonparametric ANOVA).

Unlike parametric ANOVA, which tests if the means of the samples are equal, the Kruskal–Wallis test uses the relative rank of each of the observations to arrive at a test statistic, H. Subsequently, this test statistic is compared to the value χ² that corresponds to the appropriate significance level and degrees of freedom. Table 3 describes the terms of our Kruskal–Wallis model, and equation (1) presents the formula for calculating H. For ties, the mean rank is assigned to each observation in the tie. The variance of the ranks, S², is calculated using equation (2). If there are no ties in the rankings, equation (1) simplifies to equation (3) (Montgomery, 2013).

After calculating the appropriate statistic H, we test the following hypothesis:

1. Hypothesis:

   • Hypothesis H0: Preferences for all foods in the initial food classification are the same.

   • Hypothesis H1: The preference for at least one of the foods in the initial food classification is different than the others.

2. Significance level: α = 0.05

3. Test statistic: H

4. p-value: $P(χα,k−12>H)$

5. Decision: If p-value < 0.05, we reject H0; else fail to reject.

6. Conclusion

The null hypothesis states that the population medians for the food groups k are all equal. The alternative hypothesis indicates that there is a difference between at least two of the population medians. If the probability is less than α, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis. If the results are significant, we further classify the foods into most preferred and least preferred categories, using the Steel–Dwass method (Douglas and Michael, 1991).

Whenever analyzing nonparametric data, one option is to transform the data to stabilize the variance and proceed with parametric analysis. However, a generalized linear model is another approach that can be used (Montgomery, 2013). BLR is one such model. As the name implies, BLR requires a dichotomous dependent variable (Fowler, 2013), which we obtained by binarizing the responses to our Likert-scale questions. Using a threshold of three, we reduced multiple response classes (food preferences) to just two classes that are represented by zero and one (Brownlee, 2016). Three was chosen as the threshold because it is the neutral response of the five-point Likert scale and we interpret such a score as a negative response. There are two resulting classes: “not preferred,” denoted by zero, and “preferred,” denoted by one. Several assumptions must be satisfied before applying logistic regression, including independence, the absence of multicollinearity and no zero frequency classes among categorical predictors (Hosmer et al., 2013; Kim, 2018).

When y is a binary outcome variable, then E(y|x) = π(x), where π(x) is the probability that y = 1 is conditioned on predictors x. The probability that a client prefers a food is estimated using equation (4) with constant β₀, coefficients β_j and predictors x_j for k predictors (j = 1, …, k). The linear regression of equation (4) is the logit or log of the odds equation and is given in equation (5). However, 1 − π(x) is the probability that y = 0, the client does not prefer a food, conditioned on the same predictors, x. Hence, the probability of a client not preferring a food is given in equation (6) (Hosmer et al., 2013; Tabachnick et al., 2013).

To arrive at an optimal pantry stocking strategy, based on client demographics, we develop a MBMKP (Kellerer et al., 2004) using the preference ratings captured during the survey process. The knapsack problem provides a way to estimate what clients may choose based on their preferences. In this sense, we use it as a prediction method. Knowing what a user may select can inform the optimal sourcing strategy for the pantry, which in turn informs the sourcing for the food bank.

Table 4 summarizes the notation of our MBMKP. Following the steps outlined in Algorithm 1 (see Supplementary data of the e-companion), we generate demographic profiles for the most likely pantry guests from a probability tree (Genewein et al., 2020). The values of the predictors for the BLR are taken from these profiles. The results of our BLR become the preference scores (v_ij) for our knapsack problem. For foods lacking statistically significant predictors, we let (v_ij) equal the ratio of respondents who prefer a food to the total number of respondents. This approach enables the pantry to customize food offerings based on the demographics of pantry visitors. Our objective function (7) seeks a subset of food items that maximizes preference scores (v_ij) without exceeding the weight constraint of any food category (8) or the total weight constraint of the knapsack (10). Constraint (9) guarantees fair allocation of each food item, by limiting the total quantity, (Q_i), of a food item allowed per pantry guest. Finally, we constrain the food items selected (x_ij) to non-negative integers (11). The next section describes the results of our research.

Table 5 presents the results of χ² tests to see if the samples represented the client populations. As shown, at a significance level of 0.05, there is not enough evidence to conclude that the samples for Pantry A and C represent the client populations. To address this issue, our framework can be revisited by pantry managers to gather more data as it is easily replicable. In fact, this should be an evolving process as the population of pantry users evolves over time. Stratified random sampling and multipantry collaboration may also be considered. These methods would produce samples that are more diverse and representative. However, the concentration of African American clients in our study area enhances data representation for that demographic. On the other hand, there is enough evidence to conclude that the sample for Pantry B represents the client population with respect to age, gender, ethnicity and education.

A summary of demographics for the sample clients of each pantry is presented in Table EC.1. Some of the key differences between the sample population are as follows: Pantry B has a higher senior population, and Pantry C has the youngest population, which is expected given it is on a university campus. All samples contain more female participants than male participants, and this is consistent with current literature in relation to pantry users. Moreover, there are far more black respondents than any other ethnic group. This is not surprising since all three pantries are located in areas heavily populated by African Americans. Only a small percentage of the respondents are married, and most of the respondents report an annual income of less than $10,000. Most of the respondents from Pantries A and B (community pantries) are unemployed or unable to work. In terms of education, most of the respondents from community pantries report having a high school diploma or less education, and more than half of them come from households of two or less.

Figure 5 summarizes binarized food preferences for Pantry A, B and C in terms of percentages. We applied the methodology described in Subsection 3.2.2 to condense the five response classes (food preferences) from our survey results into two distinct classes, “not preferred” (denoted by zero) and “preferred” (denoted by one). What stands out are the distinctions that show up in the not preferred category. Pantry goers prefer fresh foods, frozen foods and snacks over canned foods and dry goods. These results are consistent with Campbell et al. (2011) findings, which showed shelf-friendly foods are the least preferred among foods distributed by food pantries. College students prefer shelf-friendly foods the least [Figure 5(c)], followed by traditional pantry clients [Figure 5(a)] and client-choice pantry clients [Figure 5(b)]. Although the campus pantry only offers whole fruit, fresh foods and snacks appear to be very popular among its clients. We provide the details behind this summary in the e-companion to this paper.

The Kruskal–Wallis (nonparametric ANOVA) test results are presented in Figure 6. Due to the absence of specific snack details provided by Pantries A and B, the food categories tested for homogeneity do not include snacks. Consequently, the original groupings are reduced from five to four. Furthermore, Pantry C exclusively offers whole fruit in the fresh foods category, resulting in a reduction of the original six groupings for Pantry C to five. The most interesting outcome is that client preferences are not homogeneous across initial food classifications. For instance, at a 0.05 significance level, Pantry A, B and C’s clients do not prefer all canned foods equally. Frozen foods are equally preferred by the clients of Pantries A and B, while the preference for dry goods is homogeneous among the clients of Pantry B. As previously noted, when the preference for food items within a category is homogeneous, those food items are equally substitutable. Hence, there is enough evidence to support further classification of all initial food groups, except frozen foods. Although the Kruskal–Wallis test indicates differences between client preferences for foods, it does not show how much difference there is or where those differences lie (Brownlee, 2015; Douglas and Michael, 1991). Therefore, we used the Steel-Dwass post hoc test to further classify foods as “less preferred” or “more preferred.”

The results of this post hoc test revealed significant (α < 0.05) pairwise differences between the foods within an initial food classification. For example, the preference for canned applesauce was shown to be significantly different from the preference for canned mixed beans, canned meat, canned chicken, canned soup and canned green beans (Figure 7). Therefore, we classified canned applesauce as a less preferred canned food. Using this same approach for each of the foods in the initial classifications yielded two subgroups of foods: less preferred and more preferred. Figure 8 presents the results obtained from the Steel–Dwass method. Closer inspection of the table shows only minor differences between the food preferences of Pantry A’s clients and Pantry B’s clients. For example, instead of tomatoes, Pantry B’s less preferred canned foods include soup. Pantry B’s clients prefer all dry goods, while Pantry A’s clients prefer beans, oatmeal and Macaroni and Cheese (Mac N Cheese) less than other dry goods. The least preferred fresh foods in Pantry A include corn, cucumbers, and tomatoes. But these foods are preferred by Pantry B’s clients. The food offerings of Pantry C differ substantially from the offerings of the other two pantries. But the Steel–Dwass test found significant differences in median food preferences for all food classifications.

Using BLR, we now explore the association between client demographics and their preferences. Figure 9 summarizes the frequency of statistically significant (α = 0.05) demographic predictors resulting from the BLR. The details supporting this summary are available in Supplementary data of the e-companion. Overall, our BLR model establishes an acceptable fit for over half of Pantry A’s food offerings (Table EC.2). However, our model shows an acceptable fit for less than half of the foods offered by Pantries B (Table EC.3) and C (Table EC.4). For Pantry A, gender is the most prevalent predictor of not preferred foods, showing up as a significant predictor in 10 foods. Age is the second most prevalent predictor, appearing as a key determinant in nine foods. Income and marital status are also important predictors of food preference for Pantry A’s clientele. The results are not as interesting for Pantries B and C. Our model is not significant for 36 of the 40 foods offered by Pantry B, with education and the number of children in the household being the only significant predictors. Performing better for Pantry C, our model showed significance for 14 of its 37 foods. Gender was the most common predictor, appearing as a predictor in seven different instances. Religion was the second most significant predictor, with four occurrences.

Equation (12) presents the predictive formula for the probability that a client will not like canned green beans. Using this formula, which was derived from the generalized form [equation (6)], we calculate the probability that a client will not like canned green beans, based on gender and income level. We used this approach for each food in which our model exhibits significant demographic predictors.

Using AMPL (AMPL Optimization Inc., 2019), we solve our MBMKP for the client profiles depicted in Table 6. Figure 10 depicts part of the probability tree we used to develop these profiles. We start by finding the terminal leaf with the highest probability (in this case, p = 0.0366). To build the profile, we traverse the branch, from the terminal leaf to the root node, noting the value of each leaf. Using this approach, the most probable client is a single (M = 1), black (E = 3), male (G = 1), between the ages of 50 and 59 (A = 5), who has a reported annual income less than $10,000 (I = 1) and uses food stamps (F = 1). Extending this approach to include additional demographics, we profile the most probable female and male pantry guests. Client 1 (the most probable female client) is a single, unemployed, black, female, between the ages of 40 and 49, who makes less than $10K per year, uses food stamps, travels from 1 to 5 miles to the pantry and has a high school diploma or equivalent. Client 2 (the most probable male client) is a single, unemployed, black, male, between the ages of 50 and 59, who also makes less than $10K per year, uses food stamps, travels from 1 to 5 miles to the pantry, and has a high school diploma or equivalent. We list additional client profiles from our probability tree results in the e-companion to this paper.

The results of the MBMKP for Clients 1 and 2 are shown in Table 7. Aggregating across Clients 1 and 2, this pantry would stock 3.1 lb of tuna, 4.8 lb of canned soup, 4.8 lb of canned sweet peas and so on. The pantry can continue this procedure, amassing across additional client profiles. Heuristic 1 (see the e-companion to this paper) provides practical guidance to the pantry in selecting foods based on demographics of the clients that will reduce food waste. As shown in Table EC.6, applying Heuristic 1 to Client 1 yields the same results as our MBMKP.

While the knapsack problem itself does not explicitly depict pantry or client indices, it remains intrinsically linked to the demographics and preferences of each pantry’s clientele. This interrelation is represented in Figure 11, where the process of transforming the survey-derived demographics and preference data to an optimized pantry stocking strategy is outlined. As shown, the survey yields essential demographic and preference data. Leveraging this data, we construct a probability tree from which we obtain distinct client profiles. The model then uses binary logistic regression equations derived from equation (6) to predict client food preferences for the most likely client profiles. Application of the binary logistic regression model results in the food preference scores, v_ij, corresponding to pantry clients based on their demographic characteristics (profiles) and preferences. By combining the insights gained from the survey data and the binary logistic regression analysis, the knapsack problem framework offers a means to optimize pantry stocking strategies.

We can make two observations regarding the outcomes depicted in Table 7. First, as expected, our results show that demographics affect the food preferences of pantry guests. Client 1 prefers canned soup and mixed beans instead of sweet peas and canned meat and rice instead of dried beans and crackers. There are also differences in the preferences of these two clients for fresh food. Second, by having this framework, we can consider food inventory at a pantry level by aggregating across the preferences of the most probable clients. The section that follows presents this consideration.

Table 8 shows the results of an optimized pantry stocking strategy based on varying food items and their corresponding quantities per client type for the 14 most likely client profiles. The top row indicates the distinct client profiles. The second row depicts the anticipated number of different client types per day. To estimate the expected number of pantry visitors for each client profile, we use an approach considering a daily average of 140 clients. The detailed methodology, including the probability distribution and normalized probabilities for each profile, can be found in the e-companion of this article. Each subsequent row corresponds to a specific food item, indicating its weight per item, the distribution among different client types (1 through 14), the weight per day and the percentage of the total weight. This table provides an overview of the optimized distribution, highlighting the preferences and quantities of different food items preferred by the pantry’s most likely visitors. In addition, the “Total” row summarizes the total weight distributed across all food items, offering a holistic view of the overall stocking strategy. The results illustrate the dynamic relationship between client profiles and an optimized pantry stocking strategy, thereby revealing the nuanced preferences and needs of diverse clientele. In particular, the findings underscore the imperative for a versatile and adaptable strategy in pantry management to proficiently accommodate the diverse clientele. Overall, this analysis demonstrates the potential of customized stocking strategies in aligning food distribution with the complexities of client diversity, thereby making a valuable contribution to the optimization of food assistance programs.

Upon examination of Table 8, it seems counterintuitive that canned foods are as prevalent as fresh and frozen foods. These results seemingly contradict our survey results, which suggest that clients exhibit a preference for fresh and frozen commodities. It is crucial to remember that the data presented in Table 8 has been subject to the pantry’s weight limitations across food categories, as well as quantity restrictions imposed on specific items. For a more precise and direct comparison of food category usage, we refer the reader to Figure EC.4 in the e-companion of this document. Figure EC.4 uses a standardized metric, free from pantry’s weight limitations. The next section discusses these results and their broader significance.

This study demonstrates a systematic approach to classifying pantry foods according to client preferences and identifying the demographic factors that affect those choices. Our findings indicate that food pantry clients prefer fresh and frozen foods over shelf friendly canned foods and dry goods. This conclusion is consistent across two food pantries serving the public and a college food pantry. The results also indicate a correlation between demographic data from the client and food preferences. The primary demographic factors affecting food preferences are gender and age for the two pantries serving the public and gender and religion for the university pantry. This research exploits that correlation to profile the pantry’s most likely guests and uses those profiles to develop a heuristic which can be applied to better match inventory with the needs of the clients served by the pantry. This has important implications on food waste as pantries move to provide more culturally relevant food (Thompson, 2021).

The role of food pantries has evolved from emergency relief to long-term provision (Kicinski, 2012; Martin et al., 2013; Robaina and Martin, 2013). This change means that it is important for food pantries to put more emphasis on meeting the nutritional and dietary needs of their clients (An et al., 2019; Bazerghi et al., 2016; Eicher-Miller, 2020). A customized food preferences survey such as the one used in this research can help food pantries gather and analyze data to better understand and meet these needs.

However, in undertaking this task, it is important to understand the context, specifically regarding the perception and designation of the recipients of food aid distribution. The decision to use the term “client” instead of “beneficiary” reflects our commitment to a service offering approach that is more dynamic and mutually beneficial. This decision is particularly relevant, considering regional disparities, such as in Latin America, where the term “beneficiary” generally conveys a sense of passive reception of assistance.

Moreover, this study recognizes the role of economic subsidiarity in the context of alleviating hunger. The concept of economic subsidiarity, which entails the provision of secondary support systems for people who are unable to afford necessities, forms the foundation for the establishment of food pantries and other such services. As previously noted, these services are no longer temporary solutions but are essential components of a broader economic and social structure that tackles inequalities in the allocation of resources. It is important to acknowledge that food pantries, although necessary, may not always effectively meet the underlying nutritional needs as well as alternative interventions such as cash grants or community markets. This observation highlights the significance of not only supplying food, but also ensuring that the food supplied adheres to nutritional criteria.

This analysis supports our hypothesis that client food preferences vary significantly within typical food groupings (canned foods, dry goods, frozen foods and fresh foods) found in most food pantries. This result is important in at least two main respects. It incentivizes pantries to identify and go after “more preferred” foods, thereby reducing food waste and improving the pantry’s efficiency, and it supports the case for client-choice food pantries (Martin et al., 2013; Second Harvest, 2014).

One of the most important findings was that pantry clients prefer fresh and frozen foods over their shelf-friendly counterparts. This finding, while consistent with previous research (Campbell et al., 2011), is concerning because traditional pantries usually distribute more of the latter. Prior research has noted that traditional food pantries often lack adequate refrigerator and freezer capacity to store fresh and frozen foods (Long et al., 2020). Another challenge for traditional pantries in providing fresh food to their clients is the lack of a systematic approach to ensuring timely and quality food donations (Campbell et al., 2011).

One of the implications of these results is an increased burden on food pantry data collection efforts. In the past, food pantries have been able to serve communities without identifying their clients’ food preferences. However, as pantries make the shift from emergency food relief to long-term providers, it is increasingly important for pantry organizers to collect and maintain data on their clients’ food preferences and what drives those preferences. This can be easily done in a non-evasive way by including a food preference survey in the application process. To further automate data collection efforts, pantries may resort to an online survey, which can be administered via a tablet or smartphone. Another approach is for food pantries to develop an app similar to the apps that have been developed for online grocery shopping. Clients who are waiting for service can use the app to indicate their food preferences and dietary restrictions.

Not surprisingly, the results of this research suggest that college students’ food preferences may be centered on convenience. This would help explain the popularity of whole fruit and snacks among college students. This research also indicated that college students dislike canned foods almost twice as much as the general public. A plausible explanation is that most canned foods may not be as convenient as food available to them from the university cafeteria or other sources.

The results of this study suggest that there is an association between demographics and food preferences of pantry guests. This finding is consistent with that of Boek et al. (2012) who found that demographics play an important role in the predictors of food preferences of college students. The current study suggests that gender and age are the primary factors affecting food choices in the community pantry, whereas gender and religion are the most important determinants of food preferences among college students. Hence, these pantries may benefit from adapting their food offerings to the predominant demographic. It is surprising that ethnicity is not one of the key drivers of client food choices, showing up as a significant predictor in only two instances. An explanation for this might be that all three pantries are in an area predominated by African Americans.

To understand the applicability and value of our model, it is necessary to discuss the selection flexibility of pantry managers. Prior research indicates that in-kind donations are not merely supplementary to monetary ones (Orgut et al., 2016; Campbell et al., 2013). We asked the food pantries that participated in our study the following questions to determine how much discretion they have in deciding what foods to stock.

Two of the three participating food pantries have provided feedback. Five to ten percent of the food at Pantry A is purchased, with the remainder coming from in-kind donations. Notably, Pantry A has recently adopted a client-choice model, allowing them to tailor their food selection to the preferences and requirements of those who visit them. They allocate funds strategically to acquire fresh items and adapt food drives to their clientele’s preferences, ensuring a diverse and individualized food selection that meets their clients’ needs.

Pantry C, on the other hand, estimates that approximately 70% of their food is purchased from local grocery stores, farmers, and the regional food bank. This combination allows for some stock balancing, but it makes it difficult to maintain the consistent availability of specific products. To combat this, Pantry C actively communicates their needs to donors and makes targeted purchases or requests for products that are in high demand. Despite these restrictions, Pantry C visitors value the variety of food options available.

Overall, these responses suggest that food pantries may have considerable autonomy over the types of food they stock, challenging the notion that monetary donations are merely supplemental to in-kind contributions. These pantries can better combat food insecurity and contribute to more equitable, effective, and efficient food bank operations by adopting innovative strategies and forming collaborative partnerships.

While these results are not generalizable to other pantries, the methods we use can be applied in any food pantry to systematically collect and analyze client preference data and inform an optimal stocking strategy. In fact, the participating food bank has decided to administer an ongoing food preference survey to its partner agencies. This data presents unprecedented research opportunities to minimize food waste and improve pantry and food bank operations. From the food bank’s perspective, future researchers can use these data to inform the food bank’s purchasing decisions and to help route donations to locations where the food is least likely to be wasted. Future researchers may also wish to extend our knapsack formulation to include additional constraints, such as nutrition.

The primary goal of the current study was to develop a framework for eliciting client preferences, classifying pantry food offerings by those choices and using the results to suggest an optimal stocking strategy for the food pantry. We accomplished this objective through the use of a customized client preferences survey and the application of appropriate statistical and optimization models.

To collect data to conduct this analysis, the customized client preferences survey that we developed proved to be an effective tool. While stratified sampling may have resulted in a more representative sample than convenience sampling, we decided that the reduction in data collection time associated with the latter outweighed the benefits of the former. We learned that online surveys are easier to administer and analyze than the paper-and-pencil edition but require more incentives to spur responses. Similarly, nonparametric ANOVA proved useful in classifying pantry foods according to preferences. Because the Kruskal–Wallis test relies on rankings for categorical data, this is an excellent choice of analysis. However, future researchers may wish to explore any of a number of machine learning models available for classification. This also applies to the use of BLR in identifying the most significant predictors. Our focus in this study was the development of the overall decision support model. Our MBMKP successfully produces an optimal pantry stocking strategy. Furthermore, it reduces to a heuristic that pantry managers can easily apply to help reduce food waste. Future researchers may wish to introduce uncertainty in various formulation elements to make the model more realistic.

These conclusions suggest several courses of action. First, practitioners should consider taking the necessary steps to offer more fresh and frozen foods to their clients. This is especially true for pantries that serve the public. This may mean investing in additional refrigerator and freezer capacity and developing a system to secure quality and timely food donations. Second, pantry and food bank managers may wish to invest in client preference elicitation and data collection. In the for-profit sector, identifying customer preferences translates into more profits. However, in the nonprofit sector, identifying the client’s preferences translates into greater efficiency. Efficiency is just as important to the stakeholders of a nonprofit as profits are to the stakeholders of a for-profit business. Finally, pantry managers should consider implementing our framework.

One of the most important takeaways from this research is a procedure pantry managers can apply to stock their shelves according to the pantry’s most likely guests. The process includes the following steps:

• Collect the data.

• Classify the food offerings according to client preferences.

• Fit the data to a predictive model, correlating demographics to food choices and obtaining preference scores.

• Profile the pantry’s most likely clients.

• Use the client profiles to see how they will select food items.

• Aggregate across client profiles to determine what the pantry should stock.

Practitioners can use the results of this research to target the most preferred foods and tailor food offerings to the predominant demographic. Furthermore, pantry organizers can use these findings to facilitate a transition to the client-choice food distribution model and thereby reduce food waste. Together, these findings suggest an important role for classifying pantry foods according to client food preferences in positioning the pantry to better meet the needs of their clients and reduce food waste.

The possibility of sampling bias limited this study. Some segments of the population may have been underrepresented because these were convenience samples taken from specific locations. For this reason, caution should be exercised in generalizing the results to pantries in different locations. Moreover, respondents who receive aid based on specific criteria may have been inclined to provide answers that ensure the continuance of that assistance or to give answers that portray them more positively. To combat sampling bias, we administered an anonymous survey that included a preamble to assure respondents that their answers would not affect them negatively. Another limitation was missing data; some respondents failed to answer all the survey questions. We imputed the mode response for missing categorical data to overcome this limitation.

Notwithstanding these constraints, the study has revealed significant insights and opportunities for further investigation. Our research underscores the vital role of terminology in influencing the dynamics of food aid, particularly in diverse cultural settings such as Latin America. We emphasize the differentiation between the terms “client” and “beneficiary.” This finding indicates the need for reverence and proactive involvement in humanitarian logistics, suggesting an area for future research to look into these dynamics more deeply.

Furthermore, by acknowledging the roles of economic subsidiarity and nutritional value, our study gains a more comprehensive perspective on the challenges and objectives involved in addressing hunger, even though these aspects are not explicitly included in our model. These factors emphasize the importance of not only supplying food, but also ensuring that the assistance is both economically sustainable and nutritionally adequate. Future research on food aid in the field of humanitarian logistics and supply chain management could be enhanced by integrating these components. By adopting a multidimensional approach that takes into account both logistical and socio-economic issues, food aid programs can improve their effectiveness and influence, making them more closely aligned with wider health and societal goals.

This work was supported by the NSF National Research Traineeship Project Improving Strategies for Hunger Relief and Food Security Using Computational Data Science (Award No. DGE-1735258). The authors also thank the staff, volunteers, and clients of Greensboro Urban Ministries, One Step Further, and Aggie Source of Greensboro, North Carolina for their contributions, along with Nikki McCormick of Second Harvest Food Bank of Northwest North Carolina.

The supplementary material for this article can be found online.