Analysis of dynamic processes

Nana Shakaia
Professor Izolda Khasaia (GSUSA), Ass. Professor Manana Chumburidze (ATSU)

Modern state of scientific-technical progress requires high responsibility from managers and businessmen for quality of decision-making process.

It is a principal cause which determines necessity of scientific decision–making process.
One of the essential features of a modern economy at all levels of administration is a dynamic factor that defines the realization of the various destination streams (material, human and financial) over the planning period.
The dynamic character of economic processes requires a comparison of future capital and other expenses with the current. At the same time, the dynamics should take into account other specific financial flows and the indirect economic ties in the balance calculations.
Hence, a dynamic process must be balanced and optimal – this is the specificity of market when the company (firm, company, industry) strives to maximize profit or to satisfy market demand volume, taking into account resource and time constraints, structure and quality or minimize the costs associated with this process.
Studies of the problem determine the necessity of elaborating an appropriate economic-mathematical model, since by means of computer modelling it can be timely determined the optimal type of management of the relevant trade or financial flows in order to realize it in a business plan.
Mathematical programming is one of the practical directions in this field. It is connected with practical processes of resource optimal distribution in various fields of production and services.
Optimal management system is constructed by means of well-known integrated optimization program – Solver integrated in MS Excel.
Before realizing dynamic programming tasks, including tasks of production resources optimal distribution as a mathematical model in Solver program, description of initial conditions of the problem in Excel should be done.
By means of Boolean operator we managed to construct the simplified procedure of describing task conditions. As a result we received the string of effective and dynamic data management structure. In case of information arrays, the last one ensures optimal management of RAM and improves the interface of the program.
For example, mathematical model of the classical Dynamic programming task is presented, about of optimal distribution of resources in the enterprises.
Suppose, n enterprise has m number of projects that are invested by s monetary unit.
Designate following: is investing for i production on the j projects. is profit for i manufacture on the j projects.
It is necessary to find the optimal distribution of the investment with maximal profitability for the enterprises i.e. we should construct such {Cij}n,mi=1,j=1 matrix of management operating factors in investment distribution dynamic process, which for the following constraints: guarantees optimal management or the maximal profit from the investment in the manufacture:
For better understanding of the process lest us discuss the realization of given problem in Excel with program Solver, for the following values of variables – n=3, m=4, S=5 , ,
At an initial stage of optimization problem, let’s describe initial data in Excel by following below instructions:
We have the distribution investment plane on the three manufactures, it is necessary to select the row B10:G10 with 6 elements. Put in cells B10,D10,F10 number 1, Put in cells C10 the instruction of logical operator IF: =IF(B10=1;5;6) which describe the alternative profit of investment plan for 1 manufacture , Put in cells E10 the instruction of logical operator IF: =IF(D10=1;0;(IF(D10=2;8;(IF(D10=3;9;12))))) which describe the alternative profit of investment plan for 2 manufacture, Put in cells G10 the instruction of logical operator IF: =IF(F10=0;0;3) which describe the alternative profit of investment plan for 3 manufacture.
According to condition of problems the quantity of investment is constraint by S(S=5), because of this in cells B12 using the formula of sum, for describe the sum appropriate for the entire alternative investment plan: =sum (B10; D10; F10)
In cells C12 using the formula of sum, total sum of all alternative profit appropriate for all the alternative investment plans: =sum(C10;E10;G10)

After that, the decision problems is possible using the program Solver: Tools ’! Solver, in the field of the windows Solver Parameters-determine address of the appropriate cells:
In the field Set Target Cell determine address cells of the target function: C12
In the field By Changing Cells determine address of the cells for iterations: B10;D10;G10,
In the field Subject to the Constraints click the mouse on the button Add, after this, in the window of the dialog Add Constraint determine the constraints.
Afterwards click the mouse on the button Options, the window of the Solver Options will be appeared:
Turn on the button Assume Non-Negative and click mouse on the button ok. The dialogue box of the Solver Options will be appeared.
In the field Equal To Turn on the button Max, which gives the maximal values of the target cells; after that click the mouse on the button Solver and we will get the solver process of problems and in the window of the dialog Solver Results choose from the option button: Keep Solver Solution-for Keep Solver or Restore Original Values-for Restore Original Values:
In the field Reports turn on the case Sensitivity-for analysis the sensitivity
Solve of problems. It is possible to choose several types of account by holding Ctrl key and clicking simulta-neously– by results – answer; by stability – sensitivity; by the limit – limit. Each account will pear on a separate sheet.
Click the mouse on the button ok and get the optimal distribution plan of the investment with the appropriate results sensitivity:
We have the following results approp-riate of optimal distribution plan of the investment:
for 1 manufacture is 1 monetary unit investment (cells B10) with maximal profit 5 monetary unit (cells C10); for 2 manufacture is 3 monetary unit investment (cells D10) with maximal profit 9 monetary unit (cells E10); for 3 manufacture is 1 monetary unit investment (cells F10) with maximal profit -3 monetary unit (cells G10); all maximal profit is 17 monetary unit (cells C12).
Thus, for financiers and managers is construed the optimal management system by means of program Solver built in program MS Excel