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COMBINATORIAL CALCULUS OF INGREDIENTS OF FUNCTIONAL FOODS

COMBINATORIAL CALCULUS OF INGREDIENTS OF FUNCTIONAL FOODS

Kiselev V. Vladimir

Prof.Dr.

Professor of chair of biotechnology, commodity researches and quality managements of the goods

The Kemerovo institute of technology of the food-processing industry

kisselev.vm@mail.ru

 

Reference: Kiselev, V. Combinatorial calculus of ingredients of functional foods/ V.M. Kiselev //Achieving Commodity & Service Excellence in the Age of Digital Convergence.- The 16th Symposium of IGWT.- Korea: Suwon, 2008.- Proceeding Vol.1.- P. 392-396

 

The following article presents the results of the optimization combinatorics of ingredients of functional foods in the sphere of food supply for industrial workers. The conducted mathematic and technologic experiments proved the possibility to organize coalminers’ dietary plan in underground environment in such a way that it would meet the body needs and provide necessary nutrients and energy. The article explores the arguments in favor of advantageous economic and social effect of optimization combinatorics and the mathematic model, developed by the author, as well as parity of needs.

Optimization combinatorics of ingredients, functional food products, and parity of needs

 

Introduction to the conditions of the experiment

The experiment involved optimisation of coalminers’ dietary plan through particular ingridients in various meals, targeted towards general health nutrition in underground environment.

The research covered three groups of dietary plans (employees falling under the fourth or fifth category of labour intensity, coalminers, and individuals following a dietary plan due to health issues) and three groups of meals (first and second courses of coalminers’ meal plan in underground envirornment and beverages). Total number of recipies, optimized with the suggested methodology is 146 (assortment list of food ingredients) [1].

The development of the optimal composition of ingredients, constituting ready-to-serve meals and dietary plans, was based on the reference values of nutrient content in raw materials, as well as acceptable loss allowances during cooking process and keeping the meals warm.

Economic criteria of the cost of recipies for employers and expected economic effeciency, generated from adding the meals to coalminers’ dietary plan were accepted as limiting fastors. The optimised ingredient compositions were systemised into the Collection of Recipies for the Underground Dietary Plan of Coalmiers. The Collection passed review by the Institute of Nutrition of the Russian Academy of Medical Sciences, as well as by the R&D Institute of Public Nutrition of the Ministry of Trade [1].

Food Combinatorics and Parity of Needs

As a result of series of experiments, expediency of optimization of ingredient composition of functional foods, accompanied by the priority of scoring nutrients against normal physiological quantities for the target consumers was scientifically grounded. The possibility of optimization of ingredients’ composition of functional foods was experimentally proved from the view point of concept of social and ethic aspects of marketing (enrichment of food products with vital nutrients and optimization of energy value) with the help of developed mathematic model which has been named «Parity of body needs in various nutrients».

Vital-concept

During the experiment to reach parity of body needs in various nutrients, not only economic interests of employers were taken into consideration but social criteria as well. We called such approach to building ingredients’ composition of functional and therapeutic foods — Vital-concept [2].

Among the number of needs of the target group of consumers, Vital-concept affirms the priority of rated indices of nutrients and energy, which with functional foods intake lead to increased body resistance and, as a result, reduce of morbidity rate (including work-related diseases) and increased performance.

The need for Vital-concept was based on the results of preliminary hygiege field research work that studied the correlation between coalminers’ nutrition plan (69 coal mines of Kuznetsk coal basin) and statistics of their disease rate. Statistically-valid positive correlation (r=0,9) was established between the nutrition factor of the coalminers and morbidity rate. This means that wide spread of hot meals served to coalminers in underground environment leads to higher rate of specific diseases, such as work-related diseases and digestive system diseases.

The methodoligy of forming ingredients’ composition of some mneals based on the Vital-concept and the developed model of «parity of body needs in various nutrients» was used for elimination of identified issues in organisation of coalminers’ dietary plan in underground environment. The food products created on its basis as well as diatary plans and separate meals are trully functional, created for supplying the customers’ established needs [5].

Mathematic modeling of parity of needs

The optimal structure (from the view point of parity of body needs in various nutrients) of ingredients’ composition of food products was reached via taking into account economic accessibility for consumers and their specific needs. This was the main point of the mathematic modeling on its way to reaching parity of the mentioned need.

The mathematic modeling method includes summary criteria of the needs’ evaluation in absolute and specific values. It optimizes the balance of needs, such as product composition of the whole ration or of separate dishes, in their established final criteria [3].

The final balance of needs can be presented as a vector in formula 1:

d = (d1, d2, …, dk)           (1), where di is optimization parameters.

Whereby summary criteria (m) is computed according to formula 2 and integral estimation – according to formula 3, where αis significance factor of an ingredient or a nutrient:

     (2);

       (3)

        (4), where i=1,2,…,k

Thereafter we will receive the following meanings for the component vector (see formula 4), where km is quantity of goods with m number (in percentage to 100).

Variation constraints of every ingredient are shown in formula 5. The selection conditions of the standard vector (d*) are reflected in formulae 6 and 7. There also some limiting factors presented (see formula 8).

αm ≤ km ≤ bm       (5);

    (6);

  (7);

    (8)

The mathematic model of needs balance is shown in formula 9 – 15.

am = (am1, am2,…, amk),          (9),

where m=1,2,…,n, which meets the requirements:

ami≥0     (10),

  (11).

The targeted vector is given in formula 12:

d*= (d*1,d*2,…,d*k)    (12)

and linear combination of vectors a1, a2,…,an with coeffs k1, k2,…,kn.

In these conditions d= k1*a1+k2*a2+…+kn*an     (13), where d- is also length vector n.

In terms of needs balance optimization the ki meanings are computed with the following limitations:

αi ≤ ki ≤ βi     (14),

where i=1,2,….,n, to have the minimum abnormity.

Extended Euclidean norm was used as a standard (formula 15):

(15).

 Example of specific execution

As an example, we will conside the results of optimization of ingredient’ composition of functional product. The taken recipe is the second course offered in coalminers’ therapeutic and dietary nutrition, and offered to the fifth category of labour intensity workers. Due to the fact that among coalminers there is a high level of digestive system diseases, the cooking process was based on mechanical, thermal and chemical sparing. This is a widely used technique, applied in dietary plans No.1 and 2 and is reflected in recipes, technological processing and temperature of hot food consumption [1]. An example of the optimized recipe is given in table 1.

Table 1 — Optimized recipe of ingredient’ composition of functional product

The name of ingredients

Quantity of products, 10-3 kg

Gross

Net

Hen processed

101

70

Carrots

19

15

Tomato mashed

10

10

Onions napiform

18

15

Margarine creamy

8

8

Potato

507

380

Salt

3

3

Water drinking

212

212

Cheese

42

40

Oil creamy

4

4

Weight of a boiled bird

-

55

Weight of a potato and vegetables

-

386

Exit

-

700

Some difficulty in reaching the parity of needs was caused by the necessity to supply technologically optimized composition of ingredients. In order to reach the goal, the ingredients were exposed to technological processing in the sequence adequate to the condition of the raw material as well as the mentioned dietary terms of nutrition.

According to the preliminary research, one of the reasons of the widely spread demand disbalance between the participants of this specific type of product distribution (from suppliers/chefs to consumers of goods — miners) was the fact that a ready-to serve meal was consumed 1-1,5 hours later from the time it was put in special individual thermal containers, used underground. During this time the dish lost its nutritional value – the components were disintegrated and their temperature lowered. These two circumstances combined led to a signified demand fall, i.e. to demand disbalance [4].

A technologic procedure was used to rid of the abovementioned negative element. The components were put to hot food containers without mixing while they were not fully cooked. During storage time, food products continued to cook with the help of accumulated energy until they were completely done. This procedure greatly increased parity of the needs among the participants of this special type of product distribution.

The ingredients were subject to technological processing in consequence, adequate to their initial raw material. Process regulations include recipes, loss allowances while cooking, technology of cooking and serving, organoleptic estimation indices, necessity and expediency in the usage of bread, hot beverages and vitamin pills in underground nutrition of this group of miners.

In order to supply the stable quality and nutrition value of such food commodity, process regulations were created. They include recipes, loss allowances while cooking, technology of cooking and serving, organoleptic estimation indices of the cooked food, necessity and expediency in the usage of bread, hot beverages and vitamin pills in underground nutrition of this group of miners [1].

To demonstrate the results of the optimization experiment according to hygiene standards, which are in priority of this type of product distribution (Vital— concept), the final ingredients’ composition of the funcitonal food products for coalminers’ nutrition in underground enviroment is given in table 2.

The name of indicators

The maintenance nutrients in 700 gramms of mixes

Deviation from norm, %

Reached actually

Norm

The basic food substances, gramms:

Fiber

30,8

28,0

9,89

Including animal

17,7

16,0

10,79

Fat

29,9

33,0

-9,45

Including vegetative

8,0

8,0

0,05

Assimilable carbohydrates

103,0

115,0

-10,44

Including starch

83,2

85,0

-2,06

Nonassimilable carbohydrates

13,0

20,0

-34,80

Ashes

12,0

it is not limited

-

Fat: fiber

1,0

1,4

-30,64

Carbohydrates: fiber

3,3

5,0

-33,05

Mineral substances, mg:

Potassium

2 690,2

it is not limited

-

Calcium

350,5

170,0

106,16

Phosphorus

669,6

300,0

123,20

Sodium

2 334,5

minimum

-

Magnesium

166,7

95,0

75,52

Iron

7,9

2,8

186,97

Potassium: calcium

7,7

4,0

91,90

Phosphorus: calcium

1,9

1,3

46,98

Magnesium: calcium

0,6

0,5

-4,84

Potassium: sodium

1,1

minimum

-

Vitamins, mg:

A + β-carotin

1,1

0,4

169,88

C

32,9

21,5

53,17

Д, mkg

1,0

0,5

90,80

РР

8,2

5,5

49,54

Е

4,2

4,0

4,46

В1

0,5

0,6

-7,84

В2

0,5

0,6

-15,23

В6

1,2

0,8

56,41

В12, mkg

0,4

0,6

-39,62

Power value, kilojoules

3 345,3

3 650,0

-8,35

As you can see in the table 2, the optimization experiment has brought us much closer to a cumulative value of nutrients and recommended amount of energy value. According to the most optimization parameters, loss allowances are not higher than 10%, which in the framework of this experiment characterizes high parity of body needs in various nutrients, which, in return, is the foundation of the Vital-concept.

Taking into consideration that the employers accepted the optimized cost of ingredients’ composition of funcitonal food products for miners’ undeground nutritional plan (compared to the cost of alternative market offer in food products) we can draw a conclusion about positive economic and social effect as a result of optimizaiton of food combinatorics [6,7].

 

References:

  1. Киселев В. М., Позняковский В. М. Питание шахтеров. Научные основы и практические рекомендации (монография).- Новосибирск: Сибирское университетское издательство, 2004
  2. Киселев В. М. Управление ассортиментом: маркетинговый и товароведный подходы (монография).- Объединенное издательство «Российские университеты», Москва-Кемерово.- 2004
  3. Киселев В. М., Астраков С. Н. Методология формирования функциональных продуктов питания.- Хранение и переработка сельхозсырья, 2005.- №2.- С. 43-46
  4. Киселев В. М. Конкурентоспособность продовольственных товаров.- Пищевая промышленность, 2005.- №1.- С. 10-11
  5. Киселев В. М., Мазанько Е. И. Управление ассортиментом товаров: учебное пособие.- Кемерово;М.: Издательское объединение «Российские университеты»: Кузбассвузиздат-АСШТ, 2006
  6. Киселев В. М. Теоретические выводы и практические рекомендации по применению концепции паритета потребностей и методологии управления ассортиментом товаров в сфере товародвижения.- Эксклюзивный маркетинг, 2006.- №3.- С. 61-62
  7. Киселев В. М. Теоретические основы концепции паритета потребностей и методологии формирования ассортимента товаров.- Эксклюзивный маркетинг, 2006.- №3.- С. 32-42

 

 

 

Киселев Владимир