Use mathematics in your kitchen

Millions of recipes on the production lines, and me and me and me. Hundreds of engineers designing potions, and now there’s mathematics!

Mathematics will probably never be part of the composition of a recipe and yet it is now one of the essential ingredients for agri-food engineers. No more wasting time and money testing millions of combinations yourself! Put maths directly into your recipe, it’s your secret ingredient. You will then focus on your expertise: the development of the recipe! A concrete example is the recipe for olive cake.

The requirements from recipe laboratories

At Solina (presentation by Hélène Féchant), more than 1,500 recipes are created each month, using several hundred pieces of information on raw materials. Faced with such complexity, having the calculations carried out by digital tools allows employees to focus on their high added value expertise. Data science makes it possible to solve very complex problems using automated data processing, mathematical modelling, optimisation algorithms and available calculation power.

Application of mathematics in food

During the project, different avenues were studied to meet the needs of the agri-food industry:

• generating a nutritional label on the basis of the recipe composition and based on nutritional databases (e.g. Anses-Ciqual),
• optimising the nutri-score of a recipe by modifying the distribution of ingredients,
• predicting the texture or optimising the manufacturing cost of a knack based on its composition.

Nutrition databases

Many databases exist globally to qualify the nutritional composition of food. With the help of INRAE, we used the Ciqual de l’Anses from ANSES here. In France, it is the reference table. It is available free of charge and, for more than 3,000 foods, provides the contents for lipids, fatty acids, carbohydrates, total sugars and profiles of individual sugars, proteins, salt, vitamins, and minerals. To take the example of our olive cake recipe, in nutrition the green olive is characterised by an average content of 75.8 g water, 1.31 g protein and 15.7 g lipids per 100 g.

Nutritional label

The nutritional label is mandatory information in France for consumers to assess the quantity of nutrients present in a food product. The nutritional composition can be calculated automatically using information from the Anses-Ciqual database and our olive cake recipe, and then be used to generate the label (see below), which can then be found on the packaging of the finished product

Nutri-score: smoked trout avocado or olive cake

Let’s take the example of 2 recipes from our database: smoked trout avocado and olive cake.

Nutri-score optimisation: take your score up a notch

For food manufacturers, it is essential to display information to the consumer that is an exact reflection of what the product contains. With the nutrition label and nutrition scores, it also becomes necessary to improve the nutritional quality of food products. With optimisation techniques derived from applied mathematics, we can now test many hypotheses very quickly, based on a recipe, and thus offer agri-food engineers an equivalent recipe with a better score.

The olive cake: from score C to B

Let’s go back to the olive cake recipe (white wine, pepper, eggs, oil, flour, olives, etc.), initially marked in our tool with a nutri-score C (mark of +9) and a nutritional score of 21/100. We are going to use our optimisation algorithm by leaving it some wiggle room to modify the doses of each of the ingredients. After just a few seconds, our tool offers us a new recipe with a nutri-score B (mark of +2) and a nutritional score of 42/100. To achieve this feat, our algorithm simply increased the amount of flour (+50 g), and white wine (+4 g) then decreased the amount of Gruyère IGP France (-35 g) and green olives (-30 g).) for an identical total weight of 1,040 g.

Although the operation of generating a nutritional label and calculating the nutri-score “by hand” is tedious for a food engineer, it becomes very easy with digital tools. Similarly, replaying multiple recipes with dozens of ingredients can quickly become an exponential problem that is difficult to format in Excel and very time-consuming. Here, with skills in applied mathematics integrated into a tool, hundreds of combinations are automatically tested to provide the engineer with two solutions that meet his requirements. His expertise then comes into play to select the best solution.

Composition of a knack mixture

In the composition, there are two types of ingredient to which we will be able to assign min, max or fixed quantity constraints:

• meat: shoulder fat 15/85 (between 0 and 90 kg), lean 80/20 No.3 (between 10 and 60 kg), rindless and lean jowl 90/10 n°1 (20 kg fixed),
• non-meat: a binder 2017/4382 from Solina (1.38 kg fixed), a type 1 seasoning from Solina (2.70 kg fixed), water/ice type 1 and sodium nitrite salt 0.6%.

The optimised recipe: products and cost price

From the elements provided, the maths will do its job and the tool will calculate different recipe possibilities, as well as the associated cost price, whilst considering the food properties to be adhered to before and after cooking (lipids, nitrites, sugars, sodium, etc.).

In the above example, we obtain the following result:

• cost of products: €77.12 per 100 kg
• shoulder fat 15/85: 7.94 kg
• lean 80/20 n°3: 29.68 kg
• rindless jowl: 21.24 kg
• lean 90/10 n°1: 0 kg
• binder 2017/4382: 1.38 kg
• type 1 seasoning: 2.70 kg
• water/ice type 1: 35.56 kg
• sodium nitrite salt 0.6%: 1.50 kg

The tool then deduces nutritional information after cooking:

• humidity: 62.40%
• lipids: 29.90%
• saturated fatty acids: 8.43%
• carbohydrates: 0.13%
• sugar: 1.17%
• protein: 9.57%
• collagen: 1.29%
• sodium: 0.83%

It is the same for engineers who wish to automate nutritional labels or improve a nutri-score, mathematics has helped the butcher-pork butcher-caterer here to determine the best combination for knack recipes quickly in relation to his available raw material, all at minimal cost.

Conclusion

Don’t be afraid of maths anymore! Digital tools, computing power and applied mathematics are superb tools for saving time on a daily basis, whether you are industrialists or craftsmen. You can finally focus on your business and provide consumers with qualitative information about your product to reassure them, whilst controlling your cost price.

Together, let’s spend time tasting!

Julien Jourdan