2.3 Analysis of the results
‘Biogen’ LLC is a producer of medicines and biomedical products in the region. It is known that the peak demand for some drugs accounted for the summer period (cardiovascular drugs and analgesics) – 20 tenge; the second group (anti-infective, inflammatory drugs) – 15 tenge. According to the observations of the last few years, service marketing firm found that it can be implemented within two months considered in warm weather 3050 conv. u products of the first group 1100 conv. u production of the second group, in cold weather – 1525 conv. u products of the first group and 3690 conv. u the second group.
Due to possible changes in weather the task – to determine the firm’s strategy in output, ensuring maximum revenue from the sale of the sale price at 40 tenge per 1 conv. u products of the first group and 30 tenge. – The second group.
Problem. To determine the production program of the company in case of possible changes in weather, using matrix games.
Characteristics |
Value |
The first group drugs producing cost |
20 |
The second group drugs producing cost |
15 |
Warm weather amount of first group drugs released |
3050 |
Warm weather amount of second group drugs released |
1100 |
Cold weather amount of first group drugs released |
1525 |
Cold weather amount of second group drugs released |
3690 |
Price of the products of the first group |
40 |
Price of the products of the second group |
30 |
Table 2. Input information
To solve the problem firstly we need to run a program. The window will pop up. Then we need to input our information according to given task. (Figure 5).
Figure 5. Input information
By proceeding to the next form we get the PayOff matrix
Figure 6. Formed PayOff matrix in the second form
We solve our problem in Delphi by referring to the method described in 1.3 The algorithm and the block diagram of the solution. These methods are: Wald’s maximin criterion, maximin criterion, Hurwitz criterion, Savaga Criterion.
To calculate the input information we need to click ‘Calculate’ button. The program finds four solutions for our linear programming problem. It gives us several criterions: Wald'’ maximin model, Criterion of maximum, Hurwitz criterion, Savage criterion. See Figure 7.
Figure 7. Problem solution
By looking at the executed application we see the results: Wald’s maximin criterion is equal to 16 500 tenge. This means that firm should adapt the A1 strategy. Comparing two results from criterion of maximum we know that A2 is the best strategy in this case. Hurwitz criterion implemented several loops, and it tells us that in case of best solution – A2 strategy, a firm will obtain more profit – 54 770 tenge. There is a Risk matrix formed for Savage criterion which is necessary for calculations. By choosing the minimal element which is 69 350, we see that A1 and A2 strategies are both appropriate for the firm to use.
Conclusion
The mathematical economy studies properties of economic dynamics and balance by means of mathematical models of these phenomena and exact research of models. At the same time conditions of positive economic growth and a condition of balance of economy at various assumptions of the nature of production and distribution of products, of the mechanism of the market and establishment of the prices, a rent and other economic sizes can be received.
At the same time mathematical methods allow to prove more effectively the production program of the enterprise leaning on mathematical methods, such as linear programming, a simplex a method, etc. Mathematical methods allow to make calculations more quickly and reliably. They can be applied to the solution of any economic tasks.
The production program of the enterprise is understood as the evidence-based plan target on the volume, the nomenclature, the range and quality of products developed on the basis of the signed contracts and approved at the enterprise by appropriate authority. Basis for development of the production program are results of market researches, a stock of orders, presence of production capacities and resources at the enterprise.
The production program consists of the following sections:
— plan target on the volume, the nomenclature and the range of products.
— plan target on quality of products.
— plan for specialization and cooperation.
In this term paper the problem of linear programming with use of the Delphi programming language has been solved. Handwritten solution answers completely correspond with the results of solving in a Delphi application. This tells that economists can use software in their work field to increase the speed of their job.
Concerning results, favorable strategy of the production program when using a technique of the solution of problems of linear programming has been defined, that is when determining the production program of drugs focused on receiving target profit. So, based on results of a problem of definition of the production program consisting of production of 3050 and 1100 units of production of the first and second group of drugs in cold and 1525 and 3690 units in warm time we see that the firm should accept strategy of A2.
The mathematical economy studies properties of economic dynamics and balance by means of mathematical models of these phenomena and exact research of models. At the same time conditions of positive economic growth and a condition of balance of economy at various assumptions of the nature of production and distribution of products, of the mechanism of the market and establishment of the prices, a rent and other economic sizes can be received.
At the same time mathematical methods allow to prove more effectively the production program of the enterprise leaning on mathematical methods, such as linear programming, a simplex a method, etc. Mathematical methods allow to make calculations more quickly and reliably. They can be applied to the solution of any economic tasks.
References
Chripach V.Y., Golovalev A.S. Enterprise economy. – Minsk. 1997. – 448 p.
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Wald, A. Statistical decision functions which minimize the maximum risk. The Annals of Mathematics, 1946. – 265p.
Sniedovich, M. A bird's view of info-gap decision theory. Journal of Risk Finance, 2010. – 268p.
Resnik, M.D. Choices: an Introduction to Decision Theory, University of Minnesota Press, Minneapolis. 1987 – 189p.
Rustem, B. and Howe, M. Algorithms for Worst-case Design and Applications to Risk Management, Princeton University Press, Princeton. 1989 – 311p.
Ben-Tal, A, El Gaoui, L, Nemirovski, A. Robust Optimization. Princeton University Press, Princeton, 2009. – 123 p.
French, S. Decision Theory: An Introduction to the Mathematics of Rationality. 1994 – 312p.
Embarcadero. Extending the IDE Using the Tools API. 2015. – 78p.
Rozlog, Michael. RAD, Delphi and C++Builder Roadmap. 2014. – 178p.
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Appendix A (Text of the program)
unit Unit13;
interface
uses
Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants, System.Classes, Vcl.Graphics,
Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.StdCtrls;
type
TForm13 = class(TForm)
Button1: TButton;
Edit1: TEdit;
Edit2: TEdit;
Edit3: TEdit;
Edit4: TEdit;
Edit5: TEdit;
Edit6: TEdit;
Label1: TLabel;
Label2: TLabel;
Label3: TLabel;
Label4: TLabel;
Label5: TLabel;
Label6: TLabel;
Edit7: TEdit;
Edit8: TEdit;
Label7: TLabel;