Constraints

The restrictions used in this study are divided into 2 parts. On the one hand, health-related constraints for nutrient and food recommendations were considered in order to model a healthy diet. On the contrary, consumption-related constraints were included to ensure that food and beverage quantities were within consumable ranges.

The food baskets in this study were calculated for adult males and females with moderate activity levels. To consider nutrient-related constraints, the European Food Safety Authority reference values for adequate nutrient intakes were chosen [26] based on a physical activity level of 1.4. This corresponds to a sedentary lifestyle with little or no strenuous leisure activities. To ensure age-appropriate nutrient intakes for adults, reference values for 25–49-y-olds were taken. Recommendations based on body weight or energy intake were converted using the following assumptions: Body weight: 82 kg (male), 66 kg (female) [27]; energy content of energy-providing nutrients according to Regulation (EU) No 1169/2011 of the European Parliament and of the Council. Only vitamin D was not included at the full concentration of 15 μg/d. Because of the German consumption habits, which are the basis of this study, it is considered to be difficult to reach the vitamin D recommendation only through food intake. This is the reason why the German Society for Nutrition recommends taking supplements in case of insufficient sun exposure [28]. Because of the problem of reaching vitamin D recommendations through food intake, it is common in many studies that use the LP method to lower the vitamin D limits [29]. In this study, a lower limit of 5 μg/d was used. Besides lower limits, the European Food Safety Authority also sets upper limits for some nutrients that should be consumed in limited amounts (vitamins A, B₆, D, E, copper, iodine, zinc, and fluoride) [30]. These have also been considered.

In addition to the reference values for nutrient intake, there are some food-related recommendations that are important for a healthy diet. These relate to fruit, vegetables, water, salt, sugar, and caffeine. The food-related recommendations used in this study, their sources, and more detailed explanations are given in Table 1 [[31], [32], [33], [34], [35], [36]].

Food-related recommendations considered in the linear programming model

To ensure that the optimized food and drink quantities were within the range of consumption, the total quantity of food and drink was limited to the 90th percentile of observed consumption based on EVS data. In addition, lower and upper limits were set for 25 major food groups. The 10th percentile was used as the lower limit. Since several models were not solvable using the 90th percentile as the upper limit, the 95th percentile was taken instead. This is because the diets observed in the population tend to be unhealthy (e.g., too fatty, too salty) and, therefore, require a greater deviation from existing consumption patterns.