## Algorithm for definition of quantity of fertilizers for achievement of necessary ratio of nutritious elements

*The Second International Conference “Problems of Cybernetics and Informatics” *
*September 10-12, 2008, Baku, Azerbaijan. Section #5 “Control and Optimization” *
**ALGORITHM FOR DEFINITION OF QUANTITY OF FERTILIZERS FOR **
**ACHIEVEMENT OF NECESSARY RATIO OF NUTRITIOUS ELEMENTS **
**Elkhan Sabziev1, Adalat Pashayev2, Vagif Guliyev3, Atamali Mammadov4 **
1Cybernetics Institute of ANAS, Baku, Azerbaijan,

*[email protected]*
2Kiber Ltd Company, Baku, Azerbaijan,

*[email protected]*
3Institute of Soil Science and Agrochemistry of ANAS, Baku, Azerbaijan,

*[email protected]*
4Cybernetics Institute of ANAS, Baku, Azerbaijan,

*[email protected]*
**Introduction**. One of main tasks of optimization of nutrition of hothouse plants is use

the standard, on phases of development of plants, solutions with the appropriate balanced parities of macro- and microelements. The allowable marginal levels of elements in the water for preparation of nutrition solutions should be in limits established by long-term laboratory and field experiments. They are given as standard units for each nutritious element, or as shares of percents. Besides the allowable limiting deviations as percentage parameters are given too.
One of industrial ways of cultivation of plants is hydroponics, meaning “job with water”
[1]. This method has wide application in hothouses and actually exempts from additional jobs on study of structure of soil and further updating of structure of fertilizers depending on it. Certainly, in each hothouse facility used spray water has the certain chemical structure and parameter pH, which it is necessary to take into account at definition of required quantity of nutritious elements for maintenance high (best) productivity. However, within the framework of this job, we shall consider, that required quantity of nutritious elements already are determined in view of these parameters.
It is necessary to notice, that the agriculturists first of all supervise such basic nutritious
elements, as nitrogen (NO3– and NH4+),, phosphorus (P2O5), potassium (K2O), magnesium (Mg2+), calcium (Ca2+), sulfur (SO 2-
4 ) etc. Then pay attention to a parity of microelements: Zn,
Thus, the quantitative portion of nutritious elements necessary for achievement of a
desirable crop, for each cultivate plant is considered as known. However, whereas the biological systems are flexible, the optimum parities of nutritious elements can be carried out with the some approximately.
On the other hand, quantities of available nutritious elements in structure of fertilizers
also are known. Now, in order to the farmer in the hothouse facilities applied method hydroponics, it is necessary to determine quantity of each accessible fertilizer for reception of required nutritious structure. Thus, it is desirable that most favorable was chosen from numerous variants of the decision with the economic point of view.

**Mathematical formulation of the problem.** Let's assume that it is required to receive

structure consisting of

*M * nutritious element, nitrogen, phosphorus, potassium, magnesium, calcium, sulfur etc., accordingly in the ratio

*C *:

*C *:

*C *:L:

*C*
1 K,

*M *−1 . For each

*j * the equality

*C *= 0 means that in the given
structure is no nutrition element with the same index.

*The Second International Conference “Problems of Cybernetics and Informatics” *
*September 10-12, 2008, Baku, Azerbaijan. Section #5 “Control and Optimization” *
the percentage share of

*j *-th nutritious element in structure of

*i *-th fertilizer, where

*N * is the total of accessible fertilizers,

*i *= ,
following natural conditions are carried out:

*a*
required to find such quantity of

*i *-th fertilizer that

*x *≥ 0 and
∑−

*a x *−

*C *≤ε

*C *,

*j *= ,0 ,1K,

*M *−1,
where 0 ≤ ε < 1 is the parameter of allowable deviations from normative meanings

*C *≥ 0 .

*F *(

*x *,

*x *,K,

*x*
=

*f x *+

*f x *+K+

*f x * (2)
will be minimum. The coefficients

*f *,

*f *, K,

*f*
fertilizers. The equality

*f *= 0 for some

*i * means, that these fertilizers are got free-of-charge
(for example, at the expense of the grants).

**The solving method**. Having copied inequalities (1) in the little bit modified kind, we

∑−

*a x *≤ 1+ε

*C *,

*j *= ,0 ,1K,

*M *−1,
∑−

*a x *≥ 1−ε

*C *,

*j *= ,0 ,1K,

*M *−1,

*F *(

*x *,

*x *,K,

*x*
=

*f x *+

*f x *+K+

*f x *→
The given problem we shall solve by the simplex method [2]. First of all by introduction
fictitious variable

*x *≥ 0 ,

*i *=

*N *,

*N *+ ,
1 K,

*N *+ 3

*M *−1 , we shall write (3a) and (3b) in the

*The Second International Conference “Problems of Cybernetics and Informatics” *
*September 10-12, 2008, Baku, Azerbaijan. Section #5 “Control and Optimization” *
*i *=

*N *+

*M*,

*N *+

*M *+ ,

*i *=

*N *+

*M*,

*N *+

*M *+ ,

*i *=

*N *+ 2

*M*,

*N *+ 2

*M *+ ,

*i *=

*j *+

*N *+

*M*,

*i *=

*N *+ 2

*M*,

*N *+ 2

*M *+ ,

*i *≠

*j *+

*N *+

*M*.

These dummy variables are simultaneously entered into the cost functional with some enough large coefficients

*Y *>> 0

*F *(

*x *,

*x *,K,

*x*
≡

*f x *+

*f x *+K+

*f x *+

*Y *⋅

*f x *+

*f x *+K+

*f*
Thus, we receive a problem which is equivalent to (3a) - (3c) and has been written in the
canonical form, that allows to apply the well known simplex-method.
It is necessary to note, that the solution (3) - (4) can not satisfy the initial agro-technical
requirements. For example, in structure considered fertilizers will not appear required nutrition elements. Therefore, the process of finding of the solution is necessary for finishing by checking of satisfaction of the solution to initial conditions.

**On the calculation program**. The described above problem was realized as the

program GUBRE2, on base MS Access. The initial data are saved in two tables.
The table GUBRELER contains the list of fertilizers, where the percentage parities of
nutritious elements, contained in them, its availability and price are resulted. The table TELEB contains the information on required structure of nutritious elements.
The program GUBRE2 works in the interactive mode, which allows, entering new
structures of nutritious elements, to correct them if necessary, to calculate quantities of fertilizers for achievement of a necessary parity of nutritious elements.

**Literature **
1. Belogubova Ye.N., Vasilyeva A.M., Gill L.S., and others. The modern vegetable-growing for
hothouse and open ground. Kiev, 2006, 528 p.
2. Yermolyev Yu.M., Lyashko I.I., Mikhaylevich V.S., Tyuptya B.I. Mathematical methods of
operational research. Kiev, 1979, 312 p.

Source: http://www.pci2008.science.az/5/15.pdf

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