Number of meal components, nutritional guidelines, vegetarian meals, avoiding ruminant meat: what is the best trade-off for improving school meal sustainability?

Abstract

Purpose

School meals have the potential to promote more sustainable diets. Our aim was to identify the best trade-off between nutrition and the environment by applying four levers to school meals: (i) reducing the number of meal components, (ii) complying with the French school nutritional guidelines, (iii) increasing the number of vegetarian meals, and/or (iv) avoiding ruminant meat.

Methods

Levers were analyzed alone or in combination in 17 scenarios. For each scenario, 100 series of 20 meals were generated from a database of 2316 school dishes using mathematical optimization. The nutritional quality of the series was assessed through the mean adequacy ratio (MAR/2000 kcal). Seven environmental impacts were considered such as greenhouse gas emissions (GHGE). One scenario, close to series usually served in French schools (containing four vegetarian meals, at least four ruminant meat-based meals, and at least four fish-based meals) was considered as the reference scenario.

Results

Reducing the number of meal components induced an important decrease of the energy content but the environmental impact was little altered. Complying with school-specific nutritional guidelines ensured nutritional quality but slightly increased GHGE. Increasing the number of vegetarian meals decreased GHGE (from 11.7 to 61.2%) but decreased nutritional quality, especially when all meals were vegetarian (MAR = 88.1% against 95.3% in the reference scenario). Compared to the reference scenario, series with 12 vegetarian meals, 4 meals containing fish and 4 meals containing pork or poultry reduced GHGE by 50% while maintaining good nutritional quality (MAR = 94.0%).

Conclusion

Updating French school nutritional guidelines by increasing the number of vegetarian meals up to 12 over 20 and serving non-ruminant meats and fish with the other meals would be the best trade-off for decreasing the environmental impacts of meals without altering their nutritional quality.

Appendix 1

Binary integer linear model used to generate one series of twenty meals according to one of the 17 scenarios

Variables and objective function:

The unknown were binary variables $x(d,m)$ where d is the dish ($d=1, ..,2136)$ and m is the meal ($m=1, ..,20)$ in the series. If $x\left(d,m\right)=1$,it means dish d was selected in meal m by the algorithm but if$x\left(d,m\right)=0$, it means dish d was not selected in meal m.

The optimization process was used to simulate random picking among school meal dishes. To do so, a coefficient $r\left(d,m\right)$ corresponding to a random continuous number between 1 and 1000 was assigned to each variable $x(d,m)$. The single-objective function consisted of minimizing the sum of each variable multiplied by its random coefficient as indicated in Eq. (1). To allow uniform distribution among complete dishes and protein and sides dishes, $r$ was divided by 2 for protein and side dishes.

$$f\left( x \right) = \min \mathop \sum \limits_{d = 1}^{2136} \mathop \sum \limits_{m = 1}^{20} x\left( {d,m} \right) \times s\left( {d,m} \right), s\left( {d,m} \right) = \frac{{ r \left( {d,m} \right)}}{n}, r \left( {d,m} \right) \in \left[ {1;1000} \right]$$

(1)

$$n = 2\,\, if\,\, d \in \left\{ {\text{protein dishes, side dishes}} \right\}, n = 1\,\, if\,\, d \notin \left\{ {\text{protein dishes, side dishes}} \right\}.$$

Common constraints

Some constraints on the format of meals were shared by all the scenarios. There could be exactly one dairy product and one bread per meal as shown in Eqs. (2) and (3).

$$\mathop \sum \limits_{{d \in {\text{dairy}}\;{\text{products}} }} x\left( {d,m} \right){ } = 1,{ }m = 1, \ldots ,20,$$

(2)

$$\mathop \sum \limits_{{d = {\text{ bread}}}} x\left( {d,m} \right){ } = 1,{ }m = 1, \ldots ,20{ }.$$

(3)

At each meal, there could be only one main dish. Equation (4) showed there could be exactly one complete dish, or one combination of one protein dish and one side dish per meal, but not both.

$$\mathop \sum \limits_{{d\, \in {\text{complete}}\;{\text{dishes}} }} x\left( {d,m} \right){ } + { }0.5 \times \mathop \sum \limits_{{d\, \in {\text{protein dishes}}}} x\left( {d,m} \right) + 0.5 \times \mathop \sum \limits_{{d\, \in {\text{side}}\;{\text{dishes}} }} x\left( {d,m} \right) = 1,{ }m = 1,{ } \ldots ,{ }20,$$

(4)

$${\text{with }}\mathop \sum \limits_{{d\, \in {\text{protein}}\;{\text{dishes}} }} x\left( {d,m} \right) \le 1, \mathop \sum \limits_{{d\, \in {\text{side}}\;{\text{dishes}} }} x\left( {d,m} \right) \le 1 \;{\text{and }}\mathop \sum \limits_{{d\, \in {\text{complete}}\,{\text{dishes}} }} x\left( {d,m} \right) \le 1 .$$

Specific constraints

For ‘4C-’ and ‘5C-’ scenarios

In ‘5-C’ scenarios, every meal included both starter and a dessert as shown in Eq. (5) whereas in ‘4C- ‘ scenarios, exactly 10 meals over 20 included a starter and 10 meals over 20 included a dessert as shown in Eq. (6).

$$\mathop \sum \limits_{{d{ }\, \in {\text{ starters}}}} x\left( {d,m} \right){ } = 1{\text{ and }}\mathop \sum \limits_{{d{ }\, \in {\text{ desserts}}}} x\left( {d,m} \right){ } = 1,{ }m = 1,{ } \ldots ,20,$$

(5)

$$\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{{d{ }\, \in {\text{ starters}}}} x\left( {d,m} \right){ } = 10{\text{ and }}\;\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{{d{ }\, \in {\text{ desserts}}}} x\left( {d,m} \right){ } = 10.$$

(6)

For ‘-FR’, ‘FR*’ and ‘-FR*’ scenarios

The series of 20 meals must comply with the 15 mandatory FR and 5 recommended FR for vegetarian meals. For example, Eq. (7) shows the constraint for maximum FR and Eq. (8) for the minimum FR with $c_{i} \left( d \right)$ the compliance of dish d with the iest FR where $c_{i} \left( d \right) = 1$ if complied with, and $c_{i} \left( d \right) = 0$ otherwise.

$$\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{d = 1}^{2136} x\left( {d,m} \right) \times c_{i} \left( d \right) \le {\text{MAX}},$$

(7)

$$\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{d = 1}^{2136} x\left( {d,m} \right) \times c_{i} \left( d \right) \ge {\text{MIN}}.$$

(8)

For ‘nveg’, ‘4fish’ and ‘4PP’ scenarios

The scenarios with ‘nVeg’, ‘4Fish’ or ‘4PP’ must respect a frequency of n vegetarian meals, 4 fish meals and 4 PP meals, respectively, as specified in Eqs. (9), (10), and (11).

$$\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{{d \,\in {\text{vegetarian}}\;{\text{dish}} }} x\left( {d,m} \right){ } = n{ },\,\,{ }n \in \left\{ {0;4;8;12;16;20} \right\},$$

(9)

$$\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{{d\, \in {\text{fish}}\;{\text{dish}} }} x\left( {d,m} \right){ } = 4,$$

(10)

$$\mathop \sum \limits_{m = 1}^{20} \mathop \sum \limits_{{d{ } \in {\text{ PP dish}}}} x\left( {d,m} \right){ } = 4.$$

(11)

Moreover, starters in vegetarian meals also could not contain meat or fish (Eq. (12)), starters in meals containing a fish dish could not contain meat (Eq. (13)) and starters in meals containing a PP dish could not contain fish, red meat, or processed meat (Eq. (14)).

$$\mathop \sum \limits_{{d\, \in {\text{vegetarian}}\;{\text{dish}}}} x\left( {d,m} \right) + \mathop \sum \limits_{{d\, \in {\text{starter with}}\;{\text{fish or meat}} }} x\left( {d,m} \right) \le 1,\,\,{ }m = 1, \ldots ,20,$$

(12)

$$\mathop \sum \limits_{{d\, \in {\text{fish}}\;{\text{dish}} }} x\left( {d,m} \right) + \mathop \sum \limits_{{d \in {\text{starter with}}\;{\text{meat}} }} x\left( {d,m} \right) \le 1,\,\,{ }m = 1, \ldots ,20,$$

(13)

$$\mathop \sum \limits_{{d\, \in {\text{PP }}\;{\text{dish}}}} x\left( {d,m} \right) + \mathop \sum \limits_{{d\, \in {\text{starter with}}\;{\text{fish, red or processed meat}} }} x\left( {d,m} \right) \le 1,{ }m = 1, \ldots ,20.$$

(14)