Use of Linear Programming to Develop Cost-Minimized Nutritionally Adequate Health Promoting Food Baskets

Developing a novel optimisation approach for keeping heterogeneous diets healthy and within planetary boundaries for climate change

BACKGROUND AND OBJECTIVES

Current dietary habits have substantial negative impacts on the health of people and the planet. This study aimed to develop a novel approach for achieving health-promoting and climate-friendly dietary recommendations for a broad range of consumers.

SUBJECTS AND METHODS

Hierarchical clustering analysis was combined with linear programming to design nutritionally adequate, health-promoting, climate-friendly and culturally acceptable diets using Swedish national dietary data (n = 1797). Diets were optimised for the average consumption of the total population as well as for the dietary clusters.

RESULTS

Three dietary clusters were identified. All optimised diets had lower shares of animal-source foods and contained higher amounts of plant-based foods. These dietary shifts reduced climate impacts by up to 53% while leaving much of the diet unchanged. The optimised diets of the three clusters differed from the optimised diet of the total population. All optimised diets differed considerably from the food-group pattern of the EAT-Lancet diet.

CONCLUSIONS

The novel cluster-based optimisation approach was able to generate alternatives that may be more acceptable and realistic for a sustainable diet across different groups in the population.

Nutrient density of Bangladeshi foods and its application in planning diet for pregnant women

Nutrient profiling is a method that classifies foods based on their nutrient content and identifies foods that are high in micronutrients both across and within food groups. This study aimed to identify foods that are rich sources of the seven micronutrients (iron, zinc, calcium, thiamine, riboflavin, vitamin A, and vitamin B12) of public health concern for the Bangladeshi population.. This study developed a metric termed "naturally nutrient-rich score 7 (NNR7)" specifically for third-trimester pregnant women to identify nutrient-dense foods. Further, it computed the nutrient adequacy score (NAS) of the top NNR7-scored foods for seven micronutrients to assess the extent (percent) to which foods can meet pregnant women's recommended dietary allowances (RDA). A linear programming technique was then used to construct a nutrient-adequate model diet for third-trimester pregnant women using the top ten NNR7-scored foods. According to the NNR7, food groups such as leafy vegetables, fish, meat, poultry and eggs, and vegetables are the richest sources of the problem micronutrients. Mutton liver (916.7%), soybean (39.3%), lamb liver (2160%) and duck liver (50.0%) were found to fulfill the highest percentage of the RDA of vitamin A, zinc, vitamin B12, and iron, respectively. In the formulated nutrient-adequate diets for pregnant women, rice, potato, brown wheat flour, and soya oil were universal to all three diets and Bengal gram, orange, Ganges River sprat, and duck liver were the most common ones. The study findings highlight the need for the consumption of foods such as leafy vegetables, fish, meat, poultry, eggs, pulses and vegetables to increase the intake of problematic micronutrients. Planning a nutrient-adequate diet for pregnant women using linear programming can be an alternative approach to optimize and shape food choices to meet their nutritional requirements.

A community focused approach toward making healthy and affordable daily diet recommendations

Introduction

Maintaining an affordable and nutritious diet can be challenging, especially for those living under the conditions of poverty. To fulfill a healthy diet, consumers must make difficult decisions within a complicated food landscape. Decisions must factor information on health and budget constraints, the food supply and pricing options at local grocery stores, and nutrition and portion guidelines provided by government services. Information to support food choice decisions is often inconsistent and challenging to find, making it difficult for consumers to make informed, optimal decisions. This is especially true for low-income and Supplemental Nutrition Assistance Program (SNAP) households which have additional time and cost constraints that impact their food purchases and ultimately leave them more susceptible to malnutrition and obesity. The goal of this paper is to demonstrate how the integration of data from local grocery stores and federal government databases can be used to assist specific communities in meeting their unique health and budget challenges.

Methods

We discuss many of the challenges of integrating multiple data sources, such as inconsistent data availability and misleading nutrition labels. We conduct a case study using linear programming to identify a healthy meal plan that stays within a limited SNAP budget and also adheres to the Dietary Guidelines for Americans. Finally, we explore the main drivers of cost of local food products with emphasis on the nutrients determined by the USDA as areas of focus: added sugars, saturated fat, and sodium.

Results and discussion

Our case study results suggest that such an optimization model can be used to facilitate food purchasing decisions within a given community. By focusing on the community level, our results will inform future work navigating the complex networks of food information to build global recommendation systems.

Climate-friendly, health-promoting, and culturally acceptable diets for German adult omnivores, pescatarians, vegetarians, and vegans - a linear programming approach

OBJECTIVES

A frequently suggested approach to reduce greenhouse gas emissions (GHGEs) caused by food production is to reduce the intake of animal products, which can create nutritional deficiencies. This study aimed to identify culturally acceptable nutritional solutions for German adults that are both climate friendly and health promoting.

METHODS

Linear programming was applied to optimize the food supply for omnivores, pescatarians, vegetarians, and vegans considering nutritional adequacy, health promotion, GHGEs, affordability, and cultural acceptability by approaching German national food consumption.

RESULTS

Implementing dietary reference values and omitting meat (products) reduced the GHGEs by ≤52%. The vegan diet was alone in staying below the Intergovernmental Panel on Climate Change (IPCC) threshold of 1.6 kg carbon dioxide equivalents per person per day. The optimized omnivorous diet constrained to meet this goal maintained ≥50% of each baseline food and, on average, deviated from baseline by 36% for women and 64% for men. Butter, milk, meat products, and cheese were reduced by half for both sexes, whereas bread, bakery goods, milk, and meat were reduced mainly for men. The intake of vegetables, cereals, pulses, mushrooms, and fish increased by between 63% and 260% for the omnivores, compared with baseline. Besides the vegan dietary pattern, all optimized diets cost less than the baseline diet.

CONCLUSIONS

A linear programming approach for optimizing the German habitual diet to be healthy, affordable, and meet the IPCC GHGE threshold was possible for several dietary patterns and appears to be a feasible way forward toward including climate goals into food-based dietary guidelines.

Assessing the Cost of Healthy and Unhealthy Diets: A Systematic Review of Methods

PURPOSE OF REVIEW

Poor diets are a leading risk factor for chronic disease globally. Research suggests healthy foods are often harder to access, more expensive, and of a lower quality in rural/remote or low-income/high minority areas. Food pricing studies are frequently undertaken to explore food affordability. We aimed to capture and summarise food environment costing methodologies used in both urban and rural settings.

RECENT FINDINGS

Our systematic review of high-income countries between 2006 and 2021 found 100 relevant food pricing studies. Most were conducted in the USA (n = 47) and Australia (n = 24), predominantly in urban areas (n = 74) and cross-sectional in design (n = 76). All described a data collection methodology, with just over half (n = 57) using a named instrument. The main purpose for studies was to monitor food pricing, predominantly using the 'food basket', followed by the Nutrition Environment Measures Survey for Stores (NEMS-S). Comparatively, the Healthy Diets Australian Standardised Affordability and Price (ASAP) instrument supplied data on relative affordability to household incomes. Future research would benefit from a universal instrument reflecting geographic and socio-cultural context and collecting longitudinal data to inform and evaluate initiatives targeting food affordability, availability, and accessibility.

Nationally representative estimates of the cost of adequate diets, nutrient level drivers, and policy options for households in rural Malawi

A growing literature uses least-cost diets to evaluate how effectively a food system supports access to nutritious foods. We identify the cost of meeting nutrient requirements for whole households in rural Malawi from and the nutrient-level drivers thereof. From 2013 to 2017, we can identify a household least-cost diet only 60% of the time with an average cost of $2.32/person/day (2011 US$ PPP). We illustrate that larger households have more diverse nutrient needs and face a higher cost for 1000 calories of a sufficiently nutrient dense diet. Shadow price analysis shows riboflavin to be the costliest nutrient in the market. We use policy scenarios to understand what drives the infeasibility and high cost. Simulating the impact of selenium soil biofortification of maize results in a feasible diet 94% of the time at half the cost ($1.22/person/day on average) and eliminates the shadow price of copper. This is explained by insufficient selenium from sources low in copper such that under baseline conditions it is impossible to get enough selenium without too much copper. Even when feasible, to avoid copper, more higher cost foods enter the diet than would be otherwise needed to meet remaining nutrient requirements. Other value chain scenarios to increase the availability and lower the cost of nutrient-dense foods did not meaningfully change the diet cost results. Of direct relevance to Malawi, this study demonstrates more broadly how least-cost diet methods can be used to assess barriers to accessing an adequate diet and the potential impacts of policy options.

Daily food planning for families under Covid-19: combining analytic hierarchy processes and linear optimisation

In many households, preparation of food in normal times proves to be problematic, particularly when parents endeavour to keep their children on a balanced diet. The COVID-19 pandemic has further exacerbated this problem imposing the requirement of social distancing, which led to disruptions in the food supply chain and multiplication of responsibilities faced by families with children. The present study revisits the standard "Diet Problem" to address these challenges and to develop a participatory approach to provide a diversified weekly meal plan that is easy and fun but simultaneously complies with the unique requirements of each participant. This is done by providing a novel framework, which combines linear optimisation with the Parsimonious Analytic Hierarchy Process, a method for individual choices. This novel approach to participatory modelling is tested within two young family settings in Brazil. The model produced through this contemporary framework provides a weekly menu that best meets expectations of the members of a young family in the context of the COVID-19 pandemic.

Food-Level Analysis to Identify Dietary Choices With the Highest Nutritional Quality and Lowest Greenhouse Gas Emissions and Price

Introduction

Food systems are challenged to provide healthy, sustainable and affordable foods. From a consumer perspective, identifying healthy, sustainable and affordable choices based on individual food products rather than diets could promote better shopping choices.

Objective

To identify foods and drinks with the highest nutritional quality and lowest greenhouse gas emissions (GHGE) and price. We also assessed how a combination of these indicators (e.g., nutritional quality, GHGE and price) for food categories aligned with current United Kingdom dietary recommendations.

Materials and Methods

We performed a secondary analysis of the National Diet and Nutrition Survey (NDNS) nutrient databank year 11 (2018/2019). Spearman correlation coefficients were used to assess the strength of relationships between nutritional quality, environmental impact and/or prices per 100 kcal. In addition, we developed an optimized nutritional quality, GHGE and price score for each food or drink item based on the overall medians for each of these indicators.

Results

Median nutritional value was highest for fruit and vegetables, whilst median GHGE and price was lower for starchy carbohydrates, fats and items of which consumption should be limited. The relative proportions of foods considered the most nutritious and with a low GHGE and price in each of the food categories, on a per 100 kcal basis, were comparable to the proportions in the Eatwell Guide, except for the proportion of fruits and vegetables being smaller and the proportion of potatoes, bread, rice, pasta, and other starchy carbohydrates being larger in our analysis.

Conclusion

Public health efforts should consider the impact of dietary choices not only in terms of nutritional quality but also in terms of environmental and economic impact. Our food-based analysis shows a large variation in nutritional quality, GHGE and price within and across food categories, which provides consumers with opportunities for "food swaps" that are more nutritious and have lower GHGE and price.

Replacing ultra-processed foods with fresh foods to meet the dietary recomendations: a matter of cost?

The study aimed to analyze the economic impact of the adoption of optimized and nutritionally balanced diets to Brazilian families, considering the Brazilian dietary guidelines and the economic disparities of the population. Data from the Brazilian Household Budget Survey from 2008-2009 (550 strata; 55,970 households) were used. About 1,700 foods and beverages purchased by the Brazilians were classified into 4 groups according to NOVA system. Linear programming models estimated isoenergetic diets preserving the current diet as baseline and optimizing healthier diets gradually based on the "golden rule" of the Brazilian dietary guidelines, respecting nutritional restrictions for macronutrients and micronutrients (based on international recommendations) and food acceptance limits (10th and 90th percentiles of the per capita calorie distribution from the population). The diet cost was defined based on the sum of the average cost of each food group, both in the current and optimized diets (BRL per 2,000Kcal/person/day). The economic impact of the Brazilian dietary guidelines to Brazilian household budget was analyzed by comparison the cost of the optimized diets to the cost of the current diet, calculated for the total population and by income level. Three healthier diets were optimized. Current diet cost was BRL 3.37, differed among low- and high-income strata (BRL 2.62 and BRL 4.17, respectively). Regardless of income, diet cost decreased when approaching the guidelines. However, low-income strata compromised their household budget more than two times the high-income strata (20.2% and 7.96%, respectively). Thus, the adoption of healthier eating practices can be performed with the same or lower budget.

Designing Nutritionally Adequate and Climate-Friendly Diets for Omnivorous, Pescatarian, Vegetarian and Vegan Adolescents in Sweden Using Linear Optimization

Low-carbon diets can counteract climate change and promote health if they are nutritionally adequate, affordable and culturally acceptable. This study aimed at developing sustainable diets and to compare these with the EAT-Lancet diet. The Swedish national dietary survey Riksmaten Adolescents 2016-2017 was used as the baseline. Diets were optimized using linear programming for four dietary patterns: omnivores, pescatarians, vegetarians and vegans. The deviation from the baseline Riksmaten diet was minimized for all optimized diets while fulfilling nutrient and climate footprint constraints. Constraining the diet-related carbon dioxide equivalents of omnivores to 1.57 kg/day resulted in a diet associated with a reduction of meat, dairy products, and processed foods and an increase in potatoes, pulses, eggs and seafood. Climate-friendly, nutritionally adequate diets for pescatarians, vegetarians and vegans contained fewer foods and included considerable amounts of fortified dairy and meat substitutes. The optimized diets did not align very well with the food-group pattern of the EAT-Lancet diet. These findings suggest how to design future diets that are climate-friendly, nutritionally adequate, affordable, and culturally acceptable for Swedish adolescents with different dietary patterns. The discrepancies with the EAT diet indicate that the cultural dietary context is likely to play an important role in characterizing sustainable diets for specific populations.

Cost and affordability of nutritious diets at retail prices: Evidence from 177 countries

Many policies and programs aim to bring nutritious diets within reach of the poor. This paper uses retail prices and nutrient composition for 671 foods and beverages to compute the daily cost of essential nutrients required for an active and healthy life in 177 countries around the world. We compare this minimum cost of nutrient adequacy with the subsistence cost of dietary energy and per-capita spending on all goods and services, to identify stylized facts about how diet cost and affordability relate to economic development and nutrition outcomes. On average, the most affordable nutrient adequate diet exceeds the cost of adequate energy by a factor of 2.66, costing US$1.35 per day to meet median requirements of healthy adult women in 2011. Affordability is lowest in Sub-Saharan Africa. The sensitivity of diet costs to each requirement reveals the high cost of staying within acceptable macronutrient ranges, particularly the upper limit for carbohydrates. Among micronutrients, total diet costs are most sensitive to requirements for calcium as well as vitamins A, C, E, B12, folate and riboflavin. On average, about 5% of dietary energy in the least-cost nutrient adequate diets is derived from animal source foods, with small quantities of meat and fish. Over 70% of all animal products in least-cost diets is eggs and dairy, but only in upper-middle and high-income countries. In lower income countries where egg and dairy prices are significantly higher, they are replaced by larger volumes of vegetal foods. When controlling for national income, diet costs are most significantly correlated with rural travel times and rural electrification. These data suggest opportunities for targeted policies and programs that reduce market prices and the cost of nutritious diets, while improving affordability through nutrition assistance, safety nets and higher earnings among low-income households.

Making a Sustainable Diet Acceptable: An Emerging Programming Model With Applications to Schools and Nursing Homes Menus

Background: Food consumption is one of the most important drivers of the relation between human well-being and Earth's ecosystems. The current production level is difficult to sustain without compromising environmental integrity or public health. This calls for a decisive change in food consumption patterns in order to improve nutrition quality while respecting biodiversity and ecosystems. This change will produce some effect only if it is also culturally acceptable, accessible, economically fair and affordable. The design of food plans is traditionally carried out using mathematical optimization models, such as linear programming. This method has proved to be successful in providing nutritionally adequate diets while minimizing their economic and environmental impact. Nevertheless, cultural habits as well as attractiveness and variety of meals is very difficult to deal with, and no fully satisfactory way to include these issues in linear programming has been found. Objective: The aim of this paper is to move from traditional linear programming to a new programming methodology in order to cope also with acceptability in the design of meal plans. Method: Binary integer linear programming is the new modeling paradigm. In the proposed model, meal plans consist of providing the sequence and composition of daily meals over a given period of time and each meal can be composed using dishes from a given set. Therefore, instead of defining just a level of consumption of food groups or food items, the proposed model provides a realistic menu. To cope with sustainability, the energy and nutritional content of each dish is calculated together with its price and environmental impact. Furthermore, acceptability can be explicitly taken into account in a very natural way, that is bounding the daily, weekly, or total repetitions of single dishes and of dishes in the same food groups. Results: The paper reviews three successful studies with increasing complexity considering lunch plans for schools and full-board menus for nursing homes. The case studies show a great reduction of the environmental impact of the meal plans while ensuring an adequate nutritional intake, affordable prices and most importantly the plans are varied and culturally acceptable.

Designing a healthy, low-cost and environmentally sustainable food basket: an optimisation study

OBJECTIVE

Sustainable diets are diets with low environmental impacts and high affordability which contribute to food and nutrition security. The present study aimed to develop a healthy, low-cost and environmental-friendly food basket for Iran based on current consumption.

DESIGN

The Households Income and Expenditure Survey data were used. Linear Programming was utilised to obtain the optimal diets, separately, for each goal of the sustainable food basket: (1) Diet with maximum Nutrient Rich Food (NRF) index, (2) Diet with minimum cost, (3) Diet with the minimum water footprint and (4) Diet with the minimum carbon footprint. Goal Programming techniques were used to optimise the sustainable food basket by considering all goals simultaneously.

SETTING

Iran.

PARTICIPANTS

Households (n 100 500) in urban and rural areas of Iran, nationally representative.

RESULTS

In the 'optimal model', compared with the usual consumption, the amount of the 'bread, cereal, rice, and pasta', 'meat, poultry, fish, eggs, legumes, and nuts' and 'fats, oils, sugars, and sweets' groups was decreased. Inside those food groups, cereals, poultry and vegetable oil subgroups were increased. Also, dairy, fruits and vegetable groups were increased. In this model, there was a 14 % reduction in the total water footprint, a 14 % decrease in the total carbon footprint, a 23 % decrease in the cost and a 7 % increase in NRF of diet compared with the usual consumption.

CONCLUSIONS

Increasing the consumption of dairy, fruits and vegetables and reducing the consumption of bread, rice, pasta, meat, fish, eggs, legumes, nuts, hydrogenated fats and sugars are required to achieve a sustainable food basket.

Culturally Optimised Nutritionally Adequate Food Baskets for Dietary Guidelines for Minimum Wage Estonian Families

Although low socioeconomic groups have the highest risk of noncommunicable diseases in Estonia, national dietary guidelines and nutrition recommendations do not consider affordability. This study aims to help develop nutritionally adequate, health-promoting, and culturally acceptable dietary guidelines at an affordable price. Three food baskets (FBs) were optimised using linear programming to meet recommended nutrient intakes (RNIs), or Estonian dietary guidelines, or both. In total, 6255 prices of 422 foods were collected. The Estonian National Dietary Survey (ENDS) provided a proxy for cultural acceptability. Food baskets for a family of four, earning minimum wage, contain between 73 and 96 foods and cost between 10.66 and 10.92 EUR per day. The nutritionally adequate FB that does not follow Estonian dietary guidelines deviates the least (26% on average) from ENDS but contains twice the sugar, sweets, and savoury snacks recommended. The health-promoting FB (40% deviation) contains a limited amount of sugar, sweets, and savoury snacks. However, values for vitamin D, iodine, iron, and folate are low compared with RNIs, as is calcium for women of reproductive age. When both the RNIs and dietary guidelines are enforced, the average deviation (73%) and cost (10.92 EUR) are highest. The composition of these FBs can help guide the development of dietary guidelines for low income families in Estonia.

Replacing the nutrients in dairy foods with non-dairy foods will increase cost, energy intake and require large amounts of food: National Health and Nutrition Examination Survey 2011-2014

Objective:

The US Dietary Guidelines for Americans recommends increased consumption of the dairy group to three daily servings for ages 9+ years to help achieve adequate intakes of prominent shortfall nutrients. Identifying affordable, consumer-acceptable foods to replace dairy’s shortfall nutrients is important especially for people who avoid dairy.

Design:

Linear programming identified food combinations to replace dairy’s protein and shortfall nutrients. We examined cost, energy and dietary implications of replacing dairy with food combinations optimised for lowest cost, fewest kJ or the smallest amount of food by weight.

Setting:

National Health and Nutrition Examination Survey (2011–2014).

Participants:

Nationally representative sample of US population; 2 years and older (n 15 830).

Results:

Phase 1 (only dairy foods excluded): when optimised for lowest cost or fewest kJ, all non-dairy food replacements required large amounts (2·5–10 cups) of bottled/tap water. Phase 2 (dairy and unreasonable non-dairy foods excluded (e.g. baby foods; tap/bottled water): when intake of non-dairy foods was constrained to <90th percentile of current intake, the lowest cost food combination replacements for dairy cost 0·5 times more and provide 5·7 times more energy; the lowest energy food combinations cost 5·9 times more, provide 2·5 times more energy and require twice the amount of food by weight; and food combinations providing the smallest amount of food by weight cost 3·5 times more and provide five times more energy than dairy.

Conclusions:

Identifying affordable, consumer-acceptable foods that can replace dairy’s shortfall nutrients at both current and recommended dairy intakes remains a challenge.

Sustainable and acceptable school meals through optimization analysis: an intervention study

Background

School meals hold considerable potential to shape children’s diets and reduce food-related greenhouse gas emissions (GHGE)—in the short and long term. This study applied linear optimization to develop a GHGE-reduced, nutritionally adequate, and affordable school lunch menu. The effects on food waste, consumption and pupils’ satisfaction with the meals were evaluated.

Methods

A pre-post design was employed to assess the effects of implementing an optimized lunch menu on daily food waste, consumption, and pupils’ school meal satisfaction in three schools (grades 0–9) from one Swedish municipality. A food list containing amounts, prices, nutrient content, and GHGE-values of all foods used for a previously served (baseline) four-week lunch menu was created. Using linear programming, this food list was optimized for minimum deviation and constrained to ensure nutritional adequacy and a reduced climate impact. The optimized food list was developed into a new (intervention) four-week lunch menu by a professional meal planner, following the baseline menu as closely as possible. The baseline and intervention menus were served for four weeks, respectively, with a two week break in between. Prepared, wasted and leftover food were weighed daily by the school kitchen staff during both periods. Interrupted time series analysis assessed mean and slope differences in daily food waste and consumption between the two periods. School lunch satisfaction was assessed with an online questionnaire at baseline and during the intervention.

Results

Optimization resulted in a food list that was 40% lower in GHGE, met all nutrient recommendations for school meals, and cost 11% less compared to baseline. The intervention menu was served as planned, with only minor changes required (for practical reasons). Plate waste, serving waste, consumption and school lunch satisfaction did not differ significantly from baseline, in any of the schools.

Conclusions

The findings demonstrate that school meals can successfully be improved regarding health and environmental sustainability using linear optimization, without negative effects on food waste, consumption or cost. This approach offers the necessary flexibility to tailor menus towards different priorities and could therefore be transferred to other types of meal services.

Trial registration

The trial is registered at clinicaltrials.gov (NCT04168632 Fostering Healthy and Sustainable Diets Through School Meals (OPTIMAT).

Nutritionally adequate food baskets optimised for cultural acceptability as basis for dietary guidelines for low-income Czech families

BACKGROUND

Czech nutrition recommendations prioritize health aspects without considering affordability. Low socio-economic groups have the highest risk of nutrition-related noncommunicable diseases and cost has been identified as an obstacle to achieve a healthy diet, making the implementation of affordability into dietary guidelines necessary. The aim of this study was to develop a food basket (FB) for a low income Czech family of four that is nutritionally adequate, health-promoting and culturally acceptable at an affordable price.

METHODS

Linear programming optimisation was used to ascertain that the FB covered the recommended nutrient intakes from the Czech Nutrition Society and from the World Health Organization (WHO). Cost of the FB was calculated on the basis of more than 3900 prices of 330 foods. Within a given cost constraint, all FBs were optimized for the highest possible similarity to the reported food group intake according to the most recent Czech National Food Consumption survey, which was used as a proxy for cultural acceptability.

RESULTS

The optimised FB affordable at a daily food budget for a Czech family on minimum wage (CZK 177, ~ € 6.8) contained 76 foods and had an average relative deviation of 10% per food category from reported intake. The main deviations were: 72% less sweets and confectionery; 66% less salt; 52% less meat; 50% less milk products; 8% less potatoes; and 484% more milk; 69% more oils and fats; 20% more cereals; and 6% more vegetables.

CONCLUSIONS

The optimised FB can help to guide the development of food-based dietary guidelines for low income households in Czech Republic.

Optimisation modelling to improve the diets of First Nations individuals

We examined the feasibility of linear programming (LP) to develop diets that were economical, included traditional (cultural, non-market) foods and met the dietary reference intakes (DRI) in a Canadian Indigenous population. Diet optimisation using LP is a mathematical technique that can develop food-based dietary guidelines for healthy eating in Indigenous populations where food insecurity, availability and cost are important considerations. It is a means of developing nutritionally optimal food combinations that are based on economical and culture-specific foods. Observed food consumption data were derived using 24-h food recalls from the First Nations Food, Nutrition and Environment Study. The LP models were constructed to develop diets meeting DRI, cost and food constraints. Achieving the recommended food intake was not feasible in a model meeting all nutrient requirements. Models that met most nutrient requirements at reduced cost were designed for men and women, separately. In women, it was necessary to increase energy intake to meet most nutrient requirements. Nutrient requirements could not be met for fibre, linoleic and linolenic acids, vitamin D, Ca and K in both sexes, P in women, and Mg and vitamin A in men. Using LP to develop optimal diets for First Nations people, we found simultaneous achievement of all DRI was difficult, suggesting that supplementation might be necessary which goes against recommendations for individuals to meet their nutrient needs through healthy eating patterns. Additionally, to make diets feasible, programmes to reduce market food costs and to support First Nations people in traditional food harvesting are recommended.

Cost-Minimized Nutritionally Adequate Food Baskets as Basis for Culturally Adapted Dietary Guidelines for Ethiopians

The high prevalence of undernutrition, especially stunting, in Ethiopia hampers the country's economic productivity and national development. One of the obstacles to overcome undernutrition is the relatively high cost of food for low economic groups. In this study, linear programming was used to (i) identify urban and rural nutritionally adequate food baskets (FBs) with the highest affordability for an Ethiopian family of five and (ii) create urban and rural FBs, optimized for cultural acceptability, which are affordable for a family with the lowest income. Nutritionally adequate rural and urban FBs with highest affordability cost as little as Ethiopian Birr (ETB) 31 and 38 (~USD 1.07 and 1.31), respectively, but have poor dietary diversity (16 and 19 foods). FBs that cost ETB 71.2 (~USD 2.45) contained 64 and 48 foods, respectively, and were much more similar to the food supply pattern reported by FAO (15% and 19% average relative deviation per food category). The composed FBs, which are affordable for the greater part of the Ethiopian population, may serve as a basis for the development of culturally acceptable food-based dietary guidelines. These guidelines would recommend a diet composed of approximately up to 60% cereals, up to 20% roots and tubers, 10% legumes, and 10% fruits and vegetables by weight, plus only a small share from animal foods.

Optimizing School Food Supply: Integrating Environmental, Health, Economic, and Cultural Dimensions of Diet Sustainability with Linear Programming

There is great potential for reducing greenhouse gas emissions (GHGE) from public-sector meals. This paper aimed to develop a strategy for reducing GHGE in the Swedish school food supply while ensuring nutritional adequacy, affordability, and cultural acceptability. Amounts, prices and GHGE-values for all foods and drinks supplied to three schools over one year were gathered. The amounts were optimized by linear programming. Four nutritionally adequate models were developed: Model 1 minimized GHGE while constraining the relative deviation (RD) from the observed food supply, Model 2 minimized total RD while imposing stepwise GHGE reductions, Model 3 additionally constrained RD for individual foods to an upper and lower limit, and Model 4 further controlled how pair-wise ratios of 15 food groups could deviate. Models 1 and 2 reduced GHGE by up to 95% but omitted entire food categories or increased the supply of some individual foods by more than 800% and were deemed unfeasible. Model 3 reduced GHGE by up to 60%, excluded no foods, avoided high RDs of individual foods, but resulted in large changes in food-group ratios. Model 4 limited the changes in food-group ratios but resulted in a higher number of foods deviating from the observed supply and limited the potential of reducing GHGE in one school to 20%. Cost was reduced in almost all solutions. An omnivorous, nutritionally adequate, and affordable school food supply with considerably lower GHGE is achievable with moderate changes to the observed food supply; i.e., with Models 3 and 4. Trade-offs will always have to be made between achieving GHGE reductions and preserving similarity to the current supply.

Planning dietary improvements without additional costs for low-income individuals in Brazil: linear programming optimization as a tool for public policy in nutrition and health

BACKGROUND

Meeting nutrient intake recommendations may demand substantial modifications in dietary patterns, and may increase diet cost. Incentives for modifying one's dietary intake that disregard prices are unlikely to be effective in the general population, especially among low-income strata, due to the high percentage of income committed to food purchases. The aim of this study is to evaluate how much the nutrient content can be increased through a modeled diet, without any cost increase, for low-income Brazilian households.

METHODS

Low-income households were selected from the Household Budget Survey (24,688 households) and National Dietary Survey (6,032 households, 16,962 individuals), from where we obtained food prices and consumption data. Food quantities were modeled using linear programming to find diets that meet nutritional recommendations in two sets of models: cost-constrained (the cost should not be higher than the observed diet cost) and cost-free. Minimum and maximum amounts of each food in the modelled diets were allowed at three levels of food acceptability: rigorous (least deviance from the current observed diets), moderate, and flexible (higher deviance from the current observed diets).

RESULTS

We found no feasible solution that would accommodate all the nutritional targets. The most frequent limiting nutrients were calcium; vitamins D, E, and A; zinc; fiber; sodium; and saturated and trans-fats. However, increases in nutrient contents were observed, especially for fiber, calcium, copper, magnesium, vitamin A, vitamin C, and vitamin E. In general, the best achievement was obtained with cost-free models. Fruits and beans increased in all models; large increase in whole cereals was observed only in the flexible models; large increase in vegetables was observed only in the cost-free models; and fish increased only in the cost-free models. Reductions were observed for rice, red and processed meats, sugar-sweetened beverages, and sweets. The mean observed cost was US$2.16 per person/day. The mean cost in the cost-free models was US$2.90 (moderate), US$2.70 (rigorous), and US$2.60 (flexible).

CONCLUSION

The complete nutritional adequacy is unattainable, although feasible changes would substantially improve diet quality by improving nutrient content without additional costs.

Mathematical Optimization to Explore Tomorrow's Sustainable Diets: A Narrative Review

A sustainable diet is, by definition, nutritionally adequate, economically affordable, culturally acceptable, and environmentally respectful. Designing such a diet has to integrate different dimensions of diet sustainability that may not be compatible with each other. Among multicriteria assessment methods, diet optimization is a whole-diet approach that simultaneously combines several metrics for dimensions of diet sustainability. This narrative review based on 67 published studies shows how mathematical diet optimization can help with understanding the relations between the different dimensions of diet sustainability and how it can be properly used to identify sustainable diets. Diet optimization aims to find the optimal combination of foods for a population, a subpopulation, or an individual that fulfills a set of constraints while minimizing or maximizing an objective function. In the studies reviewed, diet optimization was used to examine the links between dimensions of diet sustainability, identify the minimum cost or environmental impact of a nutritionally adequate diet, or identify food combinations able to combine ≥2 sustainability dimensions. If some constraints prove difficult to fulfill, this signals an incompatibility between nutrient recommendations, over-monotonous food-consumption patterns, an inadequate supply of nutrient-rich foods, or an incompatibility with other dimensions. If diet optimization proves successful, it can serve to design nutritionally adequate, culturally acceptable, economically affordable, and environmentally friendly diets. Diet optimization results can help define dietary recommendations, tackle food security issues, and promote sustainable dietary patterns. This review emphasizes the importance of carefully choosing the model parameters (variables, objective function, constraints) and input data and the need for appropriate expertise to correctly interpret and communicate the results. Future research should make improvements in the choice of metrics used to assess each aspect of a sustainable diet, especially the cultural dimension, to improve the practicability of the results.

Measuring the Affordability of Nutritious Diets in Africa: Price Indexes for Diet Diversity and the Cost of Nutrient Adequacy

Policies and programs often aim to improve the affordability of nutritious diets, but existing food price indexes are based on observed quantities that may not meet nutritional goals. To measure changes in the cost of reaching international standards of diet quality, we introduce a new cost of diet diversity index based on the lowest-cost way to include at least five different food groups as defined by the widely used minimum dietary diversity for women (MDD-W) indicator and compare that to a Cost of Nutrient Adequacy indicator for the lowest-cost way to meet estimated average requirements of essential nutrients and dietary energy. We demonstrate application of both indexes using national average monthly prices from two very different sources: an agricultural market information system in Ghana (2009-14) and the data used for national consumer price indexes in Tanzania (2011-15). We find that the cost of diet diversity index for Ghana fluctuated seasonally and since mid-2010 rose about 10% per year faster than national inflation, due to rising relative prices for fruit, which also drove up the cost of nutrient adequacy. In Tanzania there were much smaller changes in total daily costs, but more adjustment in the mix of food groups used for the least-cost diet. These methods can show where and when nutritious diets are increasingly (un)affordable, and which nutritional criteria account for the change. These results are based on monthly national average prices, but the method is generalizable to other contexts for monitoring, evaluation, and assessment of changing food environments. JEL codes: I15, Q11, Q18.

Stunting and Its Determinants among Children Aged 6-59 Months in Northern Ethiopia: A Cross-Sectional Study

Background

Stunting reflects chronic undernutrition during the most critical periods of growth and development in early life. The study was aimed at assessing the magnitude of stunting and associated factors among children aged 6–59 month in central Ethiopia.

Methods

A community-based cross-sectional study was conducted among 410 children aged between 6 and 59 months. Systematic random sampling technique was employed to select study participants. Interviewer-administered structured questionnaire was used to collect data. The data were entered using EPI INFO version 3.5.1, and analysis was done by SPSS version 21 and ENA, 2007 software for anthropometric calculation. World Health Organization standard 2006 was used to analyse anthropometric data. Bivariate and multivariable logistic regression analyses were also carried out to identify predictors of stunting. Statistical significance was declared at p < 0.05 and 95% CI.

Results

Overall magnitude of stunting was 52.4 (95% CI: 47.6–57.2). Being female (AOR: 2.8, 95% CI: 1.503–5.099), belonging to age group of 25–59 months (AOR: 4, 95% CI: 1.881–8.424) and birth weight of <2.5 kg (AOR: 5, 95% CI: 1.450–17.309), mothers' lack of ANC visits (AOR: 3.2 95% CI: 1.40–7.10), and mistimed complementary feeding initiation (AOR: 2.4, 95% CI: 1.266–4.606) were positively associated with child stunting, whereas educational status of the mother (AOR: 0.01, 95% CI: 0.001–0.063) showed negative association.

Conclusion

Stunting was a highly prevalent problem in the study area. Low weight at birth, female sex, older age, mistimed initiation of complimentary feeding, and mothers' lack of ANC visit were found to have significant relation with children's chronic malnutrition. Thus, interventions shall effectively address those factors to alleviate the problem.

A Review of the Use of Linear Programming to Optimize Diets, Nutritiously, Economically and Environmentally

The "Diet Problem" (the search of a low-cost diet that would meet the nutritional needs of a US Army soldier) is characterized by a long history, whereas most solutions for comparable diet problems were developed in 2000 or later, during which computers with large calculation capacities became widely available and linear programming (LP) tools were developed. Based on the selected literature (52 papers), LP can be applied to a variety of diet problems, from food aid, national food programmes, and dietary guidelines to individual issues. This review describes the developments in the search for constraints. After nutritional constraints, costs constraints, acceptability constraints and ecological constraints were introduced. The 12 studies that apply ecological constraints were analyzed and compared in detail. Most studies have used nutritional constraints and cost constraints in the analysis of dietary problems and solutions, but such research begin showing weaknesses under situations featuring a small number of food items and/or nutritional constraints. Introducing acceptability constraints is recommended, but no study has provided the ultimate solution to calculating acceptability. Future possibilities lie in finding LP solutions for diets by combining nutritional, costs, ecological and acceptability constraints. LP is an important tool for environmental optimization and shows considerable potential as an instrument for finding solutions to a variety of very complex diet problems.

Nutritionally Optimized, Culturally Acceptable, Cost-Minimized Diets for Low Income Ghanaian Families Using Linear Programming

The Ghanaian population suffers from a double burden of malnutrition. Cost of food is considered a barrier to achieving a health-promoting diet. Food prices were collected in major cities and in rural areas in southern Ghana. Linear programming (LP) was used to calculate nutritionally optimized diets (food baskets (FBs)) for a low-income Ghanaian family of four that fulfilled energy and nutrient recommendations in both rural and urban settings. Calculations included implementing cultural acceptability for families living in extreme and moderate poverty (food budget under USD 1.9 and 3.1 per day respectively). Energy-appropriate FBs minimized for cost, following Food Balance Sheets (FBS), lacked key micronutrients such as iodine, vitamin B12 and iron for the mothers. Nutritionally adequate FBs were achieved in all settings when optimizing for a diet cheaper than USD 3.1. However, when delimiting cost to USD 1.9 in rural areas, wild foods had to be included in order to meet nutritional adequacy. Optimization suggested to reduce roots, tubers and fruits and to increase cereals, vegetables and oil-bearing crops compared with FBS. LP is a useful tool to design culturally acceptable diets at minimum cost for low-income Ghanaian families to help advise national authorities how to overcome the double burden of malnutrition.

Optimal formulations of local foods to achieve nutritional adequacy for 6-23-month-old rural Tanzanian children

Background: Achieving nutritional goals of infants and young children while maintaining the intake of local and culture-specific foods can be a daunting task. Diet optimisation using linear goal programming (LP) can effectively generate optimal formulations incorporating local and culturally acceptable foods.

Objective: The primary objective of this study was to determine whether a realistic and affordable diet that achieves dietary recommended intakes (DRIs) for 22 selected nutrients can be formulated for rural 6–23-month-old children in Tanzania.

Design: Dietary intakes of 400 children aged 6–23 months were assessed using a weighed dietary record (WDR), 24-hour dietary recalls and a 7-days food record. A market survey was also carried out to estimate the cost per 100 g of edible portion of foods that are commonly consumed in the study area. Dietary and market survey data were then used to define LP model parameters for diet optimisation. All LP analyses were done using linear program solver (LiPS) version 1.9.4 to generate optimal food formulations.

Results: Optimal formulations that achieved DRIs for 20 nutrients for children aged 6–11 months and all selected nutrients for children aged 12–23 months were successfully developed at a twofold cost of the observed food purchase across age groups. Optimal formulations contained a mixture of ingredients such as wholegrain cereals, Irish potatoes, pulses and seeds, fish and poultry meat as well as fruits and vegetables that can be sourced locally.

Conclusions: Our findings revealed that given the available food choices, it is possible to develop optimal formulations that can improve dietary adequacy for rural 6–23-month-old children if food budget for the child’s diets is doubled. These findings suggest the need for setting alternative interventions which can help households increase access to nutrient-dense foods that can fill the identified nutrient gaps.