QUANTITATIVE ASPECTS OF ENTERPRISE RATIONAL MANAGEMENT IN THE AREA OF FOOD PRODUCTS SUPPLIES MANAGEMENT

The total economy is based on the choice between possible alternatives as rational combination of incoming factors with a goal to achieve business optimum. The modern econometry transfers managerial tasks into the language of mathematics and it primarily serves for performing of theoretical results on real examples in a way to balance the constant disequilibrium between actual and desired state of business system. The purpose of building and application of model in certain conditions is easier, faster and rational solving of various problems which can be met on all levels of management, and according to their type, specificity and way of solving it is necessary to construct appropriate models. The model of linear programming has wide used application.

scientific.The decisions brought on intuitive and practiced base have been shown as good in rear cases, but according to the rule the management should bring its decisions on the base of scientifically proved methods and models.
One of the problems typical for functioning of business systems is optimal number of supplies, whether is final product or by product supply, raw material or goods.These problems have general leading tendencies which come up to establishing of optimal supplies' level which ensure constant business running and minimize the expenses or maximize the incomes.

Rational management of trade enterprises' resources in case of optimizing supplies under certain conditions
Model and method of linear programming enable formulation of optimal program for products' purchase, while the models and methods of supplies enable deduction of optimal purchase number with optimal frame work of every purchase.This approach is possible if there is not even one additional restrictive factor which can influence the selection of optimal number and optimal volume of purchases, and if the variables from the model are not conditioned by whole numbers.
If there is only one additional limitation, the economic analysis of all three optimal solutions of described problem will confirm their incompatibility.This information shows none of the one solutions can be realized without making the additional correction.Complexity of problem is increased by adding of whole numbers condition to above mentioned sub problems.The above mentioned problem can be successfully solved by forming a unique model by which the optimal supplies' program is confirmed, subsequently optimal number and volume of every purchase.
Setting up a linear program model for searching of optimal purchases' assortment is described in the section of methods application and linear program model on programming of trade enterprises' running.
Confirmation of optimal goods' quantity on stock and in warehouses must be done in all enterprises.The search for appropriate goods must be totally satisfied and that is the basic assumption.Suggestion of optimal products' purchase regime of trade enterprise contains: The optimal program of purchase represents the quantity of products which can be the subject of purchase of trade enterprise during the observed period.Restrictive factors of optimal purchase program are: transport capacity, available money for purchase of products, market demands and capability of producer to deliver products.
Optimal quantity of every purchase is conditioned by: available warehouse capacity, available money for financing of products' supplies, agreed quantity for delivery to customers; The goal which enterprise wants to achieve is maxi profit.Profit is shown as a difference between income and expenses.Income is shown as a difference between selling price and buying price.
In observed time period starting and final supplies are equal to 0. Filling of warehouse is constant.
Condition of whole numbers stands for number of purchases, and in most cases for the number of products' units consisted in every purchase; Unique model contains optimum criteria and all restrictions for both sub problems.

Defining of supplies problem in trade enterprise
The trade enterprise must in some particular period T purchase particular products P1,P2, P3…Pn so the enterprise can sell these products further.Purchased products have the character of trade goods.The enterprise during the time T realizes many of purchases.
The sale of products is steady during the observed time period.Care must be taken about the following: − That enterprise can spend a certain amount of money for purchase, that amount will be а 10, and purchase prices for products are also known k 1 , k 2 , k 3 , ... , k n , − For deposit of purchased products, in the period between two successive purchases, total amount а 20 can be spent, and purchased goods come in time when the previous products are spent, so the starting and final supplies are equal to 0. − The purchased supplies must not be bigger than available warehouse which will be marked as а 30 unit of volume and а 31 , а 32 , а 33 , ... , а 3n, will be equations of particular products' volume.
− Available transport capacity marked as а 40, and equations of weight of some products are marked as а 41 , а 42 , а 43 , ... , а 4n , − The producers can ensure only m ј of Pj − On market you can sell only а 5ј units j of that product, and − Costs of purchase j of that product must not be higher than С 0ј of money units.
It is necessary to determine the program of purchase, number of purchase and content of every purchase in a way to achieve maximum profit.

Forming of supplies model
The unique model of supplies can be shown by the following mathematical model: a) the function of goal Where х ј -unknown quantities of j -product that is purchased by that trade company n ј -unknown number of purchases of j-product In the period of two purchases the average quantity of trade goods is stored and represents the half of purchased products.
The optimal regime of products' purchase informs about the number and content of products' purchases, so the maximum of profit can be achieved by the enterprise.The profit of enterprise is shown as differences between: -realized difference between selling and purchased value of product, and -expenses of purchase and storing The optimal purchase regime is modulated to restrictive factors which are adjusted to circumstances where the purchase is made, and one example is only shown here.

Interpretation of supplies model solution
The optimal solution, given by the solution of represented model, provides information about: -quantity of j-product that each purchase must have(х ј ) -how many purchases must be organized by enterprise (n ј ); -maximum that company can earn (z).
The solution of the model also shows what are the consequences when you don't do according to the optimal solution.This information is contained in difference of values (z ј -c ј ) in optimal solution.
Practical application of optimizing supplies on projecting enterprise running is given by the following problem.
The enterprise X purchases edible oil in various types of packaging from company Y and it is necessary to make the plan of purchase of these products for one year period.Care must be taken about the following: The total amount of edible oil that a producer can deliver in whatever packaging is 2 million l per year.
The company has a rule that warehouse must be empty at the end of every year, so supplies are equal to 0 at the end of every year.The demand for this type of product is constant during the year.Every purchase is delivered when the supplies are used.
The oil is transported by trucks which can carry 25,000 liters.Expenses for the purchase of one load are 1,500 КМ.The company must have at least 80 purchases per year.The company must have for paying of the purchase up to 32,000 КМ.The warehouse capacity is 1.000 m 3 which is enough for one load.
Possibility of selling some types of products during the year, purchased price (КМ/unit), volume per unit and expenses for storing for the period between two purchases are given in the following table 1. +х 12 -32,000n = 0 (1.9) `````````````` -х 13 + х 14 + n = 80 (1.10) ```````````х ј , n∈Ζ + , ∀j (ј = 1,2,3); (1.11) In the model given by relations (1.1) -(1.11), variables have the following meanings: n-number of purchases that company realizes during the year х 1 -quantity of edible oil that company purchases during the year х 2 -quantity of edible oil of 2l that company purchases during the year х 3 -quantity of edible oil of 5l that company purchases during the year х 4 -quantity of edible oil of 10l that company purchases during the year х 5 -difference between quantity of 1l oil which is possible to sell and purchased quantity of the same product х 6 difference between quantity of 2l oil which is possible to sell and purchased quantity of the same product х 7 difference between quantity of 5l oil which is possible to sell and purchased quantity of the same product х 8 difference between quantity of 10l oil which is possible to sell and purchased quantity of the same product х 9 -difference between total amount of oil offered by producer and purchased quantity х 10 unused transport capacity intended for purchase of products х 11 unused storage capacity intended for storing х 12 unused money intended for purchase of products х 13 number of purchase which is under the number of allowed number of purchases х 14 artificial variable without real meaning During the period between two successive purchases the average purchased products are stored, so the expenses of supplies are regarded to the half of purchased products in one delivery.Every delivery contains quantity of products: Optimal solution of whole numbers model programming is obtained by the application of appropriate methods.The optimal solution of problem is: n = 80; х 1 = 1,090,000; х 2 = 220,000; х 3 = 66,000 х 4 = 14,000 х 5 = 110,000 х 12 = 112,000.

C o n c l u s i o n
The task given to modern managers is to follow the functioning of business system of their company.To achieve the above mentioned, they must precisely define the criteria of efficiency of system's functioning and to see the factors that can restrict their performances.Some value of efficient criterion responds to some type of managing and the goal of optimal managing is to find one type for which the criterion will achieve the maximum value.Econometry models enable management to rely on them and involve them into the calculation of profitability because they include other useful information besides the best solution.
The best solution of optimizing products supplies in a trade enterprise X gives us the following information: − the company needs to organize 80 purchases of oil − the total number of oil purchase is 1,090,000 pieces of 1l, 220,000 pieces of 2l, 66,000 pieces of 5l, 14,000 pieces of 10l − every purchase will contain: 13,625 pieces of 1l, 2,750 pieces of 2l, 825 pieces of 5l and 175 pieces of 10l − the enterprise will spend 112,000KM less than predicted sum for financing of purchase during the year or 1400KM less than 32,000KM predicted for financing every purchase of oil − the enterprise will use all storing and transporting capacity − the enterprise will take over all oil quantity that can be offered by a supplier − by this regime the enterprise will create the profit of 89,400KM or 1,117.5KMper purchase − minimal number of purchases will be realized − if enterprise would purchase less than predicted quantity of 5l or 10l pieces, then the loss will be 0.1 or 0.2 KM per piece − if there are more than 80 purchases during the year, the enterprise will lose 1500KM of profit per every purchase − if enterprise purchases less than 220,000 pieces of 2l oil, the profit will stay the same.
On the basis of the modeled information the management has a background for organizing the purchase and storing of products in a way to realize the best possible profit.
It is necessary to see how many purchases the enterprise should make during the year and how many products should every purchase have.All conditions must be fulfilled and the difference between income and expenses must be at most.
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