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 “food laboratory” project

From 2017 to 2020, several organisations came together in the Meatylab project: innovative digital and food solutions to help with formulation for the charcuterie sector (presentation by Patrice Houizot). The consortium led by Solina was made up of Avril, Henaff, Inrae, Novelios, Adria Développement and Acsystème. The objective was to bring together agri-food manufacturers with digital companies (web, modelling, applied mathematics) to improve product knowledge through data.

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.

Olive cake recipe

Take the example of olive cake. It contains the following ingredients:

  • 5 g of nutritional yeast (score A)
  • 15 g dry white wine 11°
  • 200 g egg, raw (score A)
  • 50 g Gruyere IGP France (score D)
  • 250 g soft wheat flour or wheat T65 (score A)
  • 200 g pork, 80/20 lean, raw (D score)
  • 15 g extra virgin olive oil (score C)
  • 5 g black pepper, powder (score A)
  • 200 g green olives, in brine (score C)

When reading the scores, it is possible to observe that our olive cake may not have a very good overall score, due to the gruyere, pork, or olives for example. Our objective will therefore be to improve this score by using an optimisation algorithm. Before that, let’s review a few concepts together.

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×287.png

The nutri-score

Since 2016, the nutri-score has appeared in France, and then in other European countries, to help consumers select food products according to their nutritional value.

Each letter corresponds to a score. This ranges from grade A (from -15 to -2) for the so-called healthiest foods with the best score, to the worst score with grade E (from +17 to +40). The calculation method uses nutritional information by penalising calorie intake, sugar, saturated fat and salt contents, to favour on the contrary the fruit, vegetable, fibre, or protein content, for example.

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.

With the smoked trout avocado nutrition label, our tool determines a score of -4. According to the classification rules, this places this recipe in the nutri-score A category.

In addition to this classification, we have added a second classification rated out of 100, considering the presence of organic products and additives in the recipe. So for the same recipe, we find a positive rating of 90/100.

For comparison, we take our olive cake recipe which, after deliberation by the jury, obtains a nutri-score C with its score of +9 and a score of 21/100 according to our second nutritional score. No olives were incorrectly processed in this calculation and, of course, finishing the dish is still strongly advised.

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.

The knack: a case of applying mathematics for butchers-pork butchers-caterers

Knack or Strasbourg sausage is a culinary specialty of Alsace. Its composition is traditionally beef and pork seasoned with spices and salt, in a sheep sausage casing. Its name comes from the noise made by the sausage when bitten (knacken in German). During the project, we used our mathematical skills to work on this food product alongside food manufacturers.

The cost of making a knack

For an industrial, just like for a craftsman, it is important to preserve the properties of his product (ingredients, shape, texture, etc.). He also needs to track the cost of manufacturing his products against the selling price. Take the example of a 100 kg mixture for making knacks. The craftsman will integrate the composition of the recipe into the tool, indicate the ingredients on which the tool can “play” and those which it is not possible to modify (for example, an imperative to use an existing stock) and of course the price of each ingredient per kg.

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.


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

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