RATIONAL RECOVERY MODEL OF DEPOT PROCESSING EQUIPMENT AT THE INDUSTRIAL ENTERPRISE

Dep. «Locomotives», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, 49010, Ukraine, tel. +38 (0562) 33 19 61, e-mail dnuzt@diit.edu.ua, ORCID 0000-0002-3800-2920 Dep. «Higher Mathematics», Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan, Lazaryan St., 2, Dnipropetrovsk, 49010, Ukraine, tel.+38 (0562) 36 26 04, e-mail gitann@rambler.ru, ORCID 0000-0003-1570-4150


Introduction
The major task of the industrial enterprise repair depot is ensuring maximum resource recovery of rolling stock with limited resources consumption that are used in the system [3,6].
The following factors affect essentially the work of industrial enterprise repair section: -Existing park units state of rolling stock [4]; -State of repair equipment sector [10]; -Planning and regulation system of repairs [7]; -Accounting procedure of materials and spares use [11].
Many different types of locomotives and cars that are operated, outdated methods of repairs planning and regulation, transparent accounting of materials lead to unproductive work of a repair sector.This is, in turn, affects the effectiveness of an enterprise performance as a whole [9].And one of the most important factors determining the performance quality of a repair sector is its workability of major repair equipment.

Purpose
The aim of this work is search and investigation of new methods and ways in order to improve Operable technical state depends on the quality and speed of its failures removal that occur during operation of the equipment [13].
Let us consider the case when a repair shop does not perform repair at a prescribed time due to equipment failure [1].There is a problem of finding a rational way of restoring its workability.That is, the repair shop equipment of a depot at the industrial enterprises needs to be recovered as quickly as possible and with minimal expenditure of money [2].This statement leads us to the following problem of vector optimization: where γ -is a method of (trajectory, plan) the equipment repairing; ( ) T γ -is time expenditure for the equipment repairing; ( ) C γ -is funds expenditure.

Methodology
We will discuss in more detail the problem (1) in the case of failure of a stand for armature shaft inspection of the traction motor (TM) (see Fig. 1).Function of the stand is to control the armature shaft of TM for transversal and longitudinal cracks.In case of the stand failure the plan concerning its repair will include several stages (phases): where i v -is the set of activities on the i stage; n -total number of repair stages.
That is, for the stand of armature shaft inspection of TM sequence γ may have the following form: 1 v -failure identification and preparation of equipment for the repair; 2 v -dismantling; 3 v - repair; 4 v -mounting; 5 v -testing and launch.At the each stage there is a plurality of actions that can be performed: Each of these actions is characterized as follows: ( ) Total time and overhaul cost are determined depending on the choice of action at each stage of repair: 1 ( ) ( ) The number of options N for repairing depends on the number of stages and activities at each stage: where i k -the number of operations on the i stage.So a problem of the vector optimization (1) assumes the following form: . Solving problem (1) we mean finding such sets of repair options that each of its elements (a repair plan γ ) will be effective so each pair 1 γ and 2 γ from this set are not comparable among themselves [5].
A repair plan γ is called effective, when any variation of it leads to increase one of the parameters (e.g.cost) and decrease the other (in this case, the runtime of repair).
Two sets 1 γ and 2 γ are not comparable, if there are at least two indexes from (1) such that one index is better (bigger) in terms of repair 1 γ , and the other is better under 2 γ .
A necessary and sufficient condition for the repairing plan effectiveness γ is described in [1] and is as follows.If there is any additional value of the coefficient λ at each stage of repair one should choose measures accordingly to conditions: Coefficient λ can be interpreted as a kind of «scales» that determine the importance of this or that index.
For example, if 0 λ = condition has the following veiw: This means that the company strives to minimize funds that are spent for repair.Time expenditure is not taken into account.
When λ → ∞ condition has the following form: That is, in this case a priority during the repairing is time of its conducting.

Findings
On the base on the proposed mathematical apparatus we will consider the following example.
Let the stand for armature shaft inspection of TM is in non-working state.We will divide its repair plan for five consecutive stages or phases.(Fig. 2).Matrix time expenditure: In this case the total number of options for the stand repair is: View of all options for repairing in space of functionals is presented in Fig. 4. Graphical interpretation of the obtained results is shown in Fig. 5.  Calculations are performed in the Maple mathematical package of symbolic computation.

Originality and practical value
The system of major equipment repair of a repair sector has been improved by solving the problem of vector optimization for rational repairing.In this case, the target functions are the monetary funds and time for repairing that a sector spends for repairing of their equipment.
Using the proposed model of rational repairing will improve the quality of a sector by increasing the efficiency of primary resources -time and funds -which a sector spends for repairing of their technical means.

Conclusions
The proposed model will provide the repair depot of industrial enterprises to higher levels of its functioning efficiency and reduce the resource intensity of its operation.Using the proposed method of the equipment efficient recovery, a repair depot of the industrial enterprise is able to distribute time and funds efficiently to carry out restoration works.This in turn will reallocate the enterprises savings.

Fig. 2 .
Fig. 2. Schematic representation of the phases The first stage is fault identification and preparation of the stand for repair.We select three options for preparing.The second stage is the dismantling.The next stage is directly repair.It can be conducted with five different modes, each of them differ by runtime and expences.The phase of mounting and debugging are the next.The last stage is testing and launch.Schematic representation of the repair trajectory is shown on Fig. 3.

Fig. 4 .
Fig. 4. Dependence of time expenditure for the repairing.Axis OX -time expenditure in hours.Axis SOfunds expenditure in UAH.

Fig. 5 .
Fig. 5. Best options for repairingUsing the mathematical model described above, we will find the best options for repairing: