Technical science/4.Transport

c.t.s. Kabikenov S. Zh.

Kyzylbaeva E. Zh.

Kukesheva A.B.

Karaganda State Technical University, Kazakhstan

Mathematical model of management of reserves of spare parts on mining enterprises

Calculation of the need for spare parts (units, aggregates) by the statistical modeling method will be considered on the example of the work of a warehouse, from which at an arbitrary time t, are issued a random number of aggregates (units, spare parts) of one name Vt. If at the moment t the stock X in the warehouse is sufficient, then the Vt request is satisfied completely. If the stock is insufficient to fully satisfy the requirement, then it is satisfied only by the amount of the stock in the warehouse. In the latter case, the enterprise bears losses due to a deficit, the value of which is proportional to the number of units not supplied to the technical service of aggregates, i. e. Сdef = к(Vt – X), where к – s the loss of the enterprise due to the idle time of one car with a deficit of units in the warehouse.

The supply of aggregates to the enterprise warehouse from suppliers also occurs at random instants of time τ and in a random volume Yt. Expenses for the maintenance and storage of aggregates in the warehouse Cstor = λХ, where λ - cost of storage and maintenance of one unit in the warehouse for the period T; X - average stock in the warehouse for the period T.

It is necessary to find such a planned level of the initial stock of X0 units in the warehouse, at which the total costs of the enterprise will be minimal: (Cdef + Cstor) → min (Figure 1).

Thus, here there are four random variables: the moment of receipt of the demand for the issue of aggregates from warehouse t; the volume of this requirement Vt; the moment of aggregates arrival to the warehouse from suppliers τ and the volume of this supply Yτ.

Figure 1 - The dependence of the enterprises costs on the initial stock

The laws of distribution of these random variables are established on the basis of processing information contained in the warehouse accounting records.

To solve the problem further, we introduce the quantities:

Vi+1 = ti+1 – ti – the duration of the interval between (i + 1)-st и i issue of aggregates from a warehouse;

μi+1 = τi+1 – τi – the duration of the interval between (i + 1) -st и i supply of aggregates from a warehouse.

Since τi and ti are random quantities, therefore, the quantities νi + 1 and μi + 1 are also random.

To solve this problem, the initial data are needed, which can serve as various values of the planned level of the initial stock of Х_о units.

Calculations on a computer (Figure 2) with different initial data for the entire plan period T (year) allow to simulate the actual processes occurring at the enterprise, for which the values of random variables are established with the help of a random number generator, distribution law of which should correspond to the distribution law of random variables on the given enterprise.

As a result of calculations for all selected levels of initial stock Хо, we reveal the dependence of total costs for the whole period on storage of the aggregate stock and because of a deficit in case of failure to meet the requirements due to the lack of aggregates in the warehouse.

Modeling of the needs of the enterprise in spare parts
	Modeling of the needs of the enterprise in spare parts
Modelling period days P=		30
Conditions for modeling the consumption of parts				Conditions for replenishment modeling
Number of requests for spare parts N1=			8	How many times to restock N4=				7
Min number of requested spare parts N2=			5	Min quantity of spare parts in consignment N5=				6
Max number of requested parts (N3˃N2) N3=			10	Max quantity of spare parts in consignment (N6˃N5) N6=				12
Resulrs of modeling				Initial stock	Losses due to deficits	Storage costs	Total losses	End-of-period stock
Initial stock in modeling X0=			3	3	22456	3,200	22459,200	-59
Step of changing the initial stock D=			5	8	17936	8,533	17944,500	-54
Number of steps for modeling X2=			10	13	14040	17,067	14057,100	-49
Loss of a trucking company from idle vehicles K1=			8	18	10560	27,733	10587,700	-44
Spare parts storage costs L1=			8	23	7608	40,000	7648,000	-39
				28	5328	54,400	5382,400	-34
				33	3528	70,400	3598,400	-29
				38	2448	94,400	2542,400	-24
CALCULATE

Figure 2- The program for modeling the needs of the enterprise in spare parts

References

1. Bykov A. Optimizacija zapasov na osnove imitacionnogo modelirovanija [Optimization of reserves based on simulation modeling] Logistika-Logistics, 2004, no. 1.

2. Anilovich V.Ja. K raschjotu zapasnyh chastej. Traktory i s/hozjajstvennye mashiny [To the calculation of spare parts. Tractors and agricultural machinery] 1975, no. 1.

3. Berg A.I. Osnovnye voprosy teorii i praktiki nadjozhnosti [Main issues of reliability theory and practice] Moscow, Sovetskoe radio Publ., 1975. 408 p.