OPTIMUM DISTRIBUTION OF REPAIRS IN ТS-8 OF ELECTRIC LOCOMOTIVES VL80 BETWEEN REPAIR DEPOTS IN THE REPUBLIC OF KAZAKHSTAN

The article presents the solution for the problem of optimal distribution of electric locomotives in repair enterprises for carrying out repairs in the frame of technical service 8 (ТS-8) and increased technical service 8 (ITS-8). The aim of the study is to improve the efficacy of a rolling stock with a simultaneous decrease in the total expenses connected with the repair of locomotives and their transportation in repair enterprises. This is possible due to a reduction in the requirement for repairs by optimization of a resource before change of wheel bandages in electric locomotives VL80С that promotes an increase in their between-repairs run.


INTRODUCTION
At present, in the Republic of Kazakhstan, repair enterprises are dispersed across several repair depots, which leads to a shortage of equipment and component parts, long idle times, poor-quality repair, and expensive repair processes. Further, in the Republic, there are practically no enterprises performing qualitative technical checkup (TC) and major repairs (MR) of locomotives, nor are there enterprises manufacturing the necessary spare parts and components.
In Kazakhstan, the scheme of alternation of repairs and between-repairs run of locomotives -the structure of a repair cycle -is regulated by the specifications of order №536-C from 8/19/1999 and №202-1 of the Ministry of transport and communications (MT&C) of the Republic of Kazakhstan. Thus, the basic system of maintenance service and repair of locomotives is one of scheduled preventive maintenance [1,2].

THE ANALYSIS OF DISTRIBUTION OF LOCOMOTIVES IN RAILWAY REPAIR ENTERPRISES
An analysis of the railway transport system in the Republic of Kazakhstan has revealed the necessity for a scientific approach to define the optimum distribution of locomotives among railway repair enterprises.
As there is a lack of research on the optimum distribution of electric locomotives in railway repair enterprises, a study to determine the optimum distribution of electric locomotives VL80 С , and the subsequent application of results in the industry, was of both scientific and practical interest. This entailed generating certain mathematical models reflecting the technical and economic aspects of the investigation, correlation of communication between different elements and systems as a whole, and creating special programs and algorithms [3].
Thus, this study aimed to investigate the problem of optimum distribution of electric locomotives in railway repair enterprises in the Republic of Kazakhstan for carrying out repairs in volume technical service-8 (ТS-8) and increased technical service-8 (ITS-8) depots in order to improve the efficacy of use of a rolling stock that leads to a decrease in the total expenses connected with the repair of locomotives and their transportation in repair enterprises, as well as a reduction in the requirement for repairs by optimizing a resource before change of bandages of wheel pairs of electric locomotives VL80 С that promotes an increase in their between-repairs run [4,5].
Our analysis revealed the following: 1. Various aspects of the problem of development of a repair base has been investigated in many studies, wherein scientists and experts on railway transportation have studied the dilemma of optimum development and placement of enterprises for the repair of rolling stocks and its knots. 2. Optimum distribution of locomotives in railway repair enterprises was not researched. Therefore, the purpose of the present study was to find a solution to the dilemma of optimum distribution of electric locomotives VL80 С in railway repair enterprises in the Republic of Kazakhstan. According to the joint-stock company "NC" KTZH data, there are two base repair enterprises, "Altyn Orda 2004" LLC and "Tulpar At" LLC, which are in the cities of Astana and Zhambyl, which carry out repairs of electric locomotives of series VL80 С in volume ТS-8 and -9 operational depots (distances between which are presented in table 1). The comparative analysis of Altyn Orda 2004" LLC and "Tulpar At" LLC carrying out repairs in volume ТS-8 depots of electric locomotives VL80 С has shown that they differ in terms of repair technology, auxiliary configuration, and personnel qualification, which in turn was reflected in an idle time for electric locomotives under repair: 8, 5 and 7 days; therefore, the annual program of repairs of these enterprises is 60 and 72 electric locomotives (table 2).
The simplex method of linear programming was used to determine the optimum distribution of electric locomotives VL80 С in the repair enterprises undertaking repair in ТS-8 [6][7][8]. As a criterion for optimizing the distribution of locomotives of operational depots between repair enterprises, the minimum of the objective function -the total cost of repairs with transport costs was chosen.

APPLICATION OF THE SIMPLEX METHOD OF LINEAR PROGRAMMING DURING DEFINITION OF OPTIMUM DISTRIBUTION OF REPAIRS OF ELECTRIC LOCOMOTIVES VL80С IN RAILWAY REPAIR ENTERPRISES
The total cost of repair of the locomotive in volume ТS-8, taking into account transport expenses, is defined as where rep с is the cost of repair of 1 electric locomotive (45190 €) in volume ТS-8, which is a set jointstock company "Locomotive"; ij deliv с is the cost of delivery of the locomotive from i operational depot to repair enterprise j .
Expenses for electric locomotive delivery to the repair enterprise is defined as where cost of 1 loc.-km. is 0.7 €; ij l is the delivery distance of the locomotive from operational depot i to repair enterprise j in km.
The costs of delivery of electric locomotives calculated in (2) are related to repair enterprises in table 3.
Taking into account costs of delivery of electric locomotives in repair enterprises according to (1), expenses for repair and delivery of electric locomotives, ij c , which are presented in table 4, are defined.
where 255 is the number of working days per year; pj t is the entertaining repair time position for this type of repair in days (table 2); pj C is the quantity of repair positions in workshop ТS-8 in repair enterprises "Altyn Orda 2004" LLC and "Tulpar At" LLC (table 4).  Throughput of repair enterprises "Altyn Orda 2004" LLC and "Tulpar At" LLC equals 60 and 72 units per year, respectively.
The annual program flow and major repairs of electric locomotives in operational depots is defined by the following formula: where S year is the linear annual run of electric locomotives in km.; K L is the run of electric locomotives before repair of K volume; ∑ >К i i N is the total number of repairs having great volumes.
Actual (calculated on the between-repairs run established by order №536-C) and planned annual requirements for repairs of electric locomotives for volume TS-8 operational depots are presented in table 5. Table 5 The requirements for repairs in volume ТS-8 - Part Dislocation  To find a solution for the problem of linear programming, the simplex method creates an algorithm for a choice of the plan for solving the problem [9].
For the practical calculation by a simplex method of optimization of criterion function at linear restrictions, it is necessary to know the repair cost, cost of delivery of an electric locomotive, requirement of repair operational depots undertaking repairs, and the power of repair enterprises (tables 3 and 4).

THE DEFINITION OF OPTIMUM DISTRIBUTION OF REPAIRS OF ELECTRIC LOCOMOTIVES VL80С
As the criterion of optimum distribution of electric locomotives between repair enterprises and operational depots, the minimum criterion function of total expenses for repair and transportation of electric locomotives with restrictions on annual requirement of depot for repairs in ТS-8 of electric locomotives VL80 С and throughput (power) of repair enterprises is chosen.
Distribution of electric locomotives between the repair enterprises, set by the existing standard documentationorder №536-C, is presented in table 6.
Distribution of repairs of electric locomotives in the repair enterprises, set by order №536-C, is undertaken in the form of an order.
The optimum plan of distribution of electric locomotives VL80 С in repair enterprises is ascertained by the simplex method using the VBA program [1,2].
In an existing system of repair, according to order №536-C, the between-repairs run in ТS-8 is 350 thousand km. and requirements for repair on all nine operational depots is 132 units of electric locomotives corresponding to the annual program of repairs in ТS-8 of two repair enterprises. The sum of demands for repair equals the annual programme of repairs of electric locomotives of repair enterprises, i.e.    After introduction of a fictitious repair enterprise the problem of linear programming accepts the balanced (closed) type. In this case, the criterion function becomes ∑∑ = = → = The optimum distribution of electric locomotives on repair enterprises, taking into account actual requirements of operational depots, is presented in table 8.
The calculation of optimum distribution of repairs of electric locomotives VL80С has shown that at realization of the between-repairs run established by order №536-Ц, the repair enterprises "Altyn Orda 2004" LLC and "Tulpar At" LLC cannot cope with the number of actual electric locomotives under repair; therefore, annually there are 9 electric locomotives not repaired. Thus, the minimum total cost of repairs with delivery of electric locomotives is 5986 thousand €.
The operational depots of Almaty and Kostanai are at a great distance from the repair enterprises "Altyn Orda 2004" LLC and "Tulpar At" LLC. As the expenses for repair after delivery of electric locomotives from these depots are high from the point of view of the economy, it is possible that 4 and 5 repairs of electric locomotives in the operational depots of Almaty and Kostanaj were not carried out. From a practical point of view, this distribution of electric locomotives isn't entirely acceptable, but from the mathematical point of view it is the most optimal option. Therefore, due to inadequate power to repair, the optimum distribution of electric locomotives in repair shops needs to be calculated further to exclude a situation in which in one or several operational depots, the most remote from repair enterprises, most, or even all, electric locomotives needing repair remain unrepaired; i.e., it is necessary to distribute the unrepaired electric locomotives between all operational depots at more regular intervals, as presently required in the Kazakhstan railway system.
Carrying out a repair in ТS-8 is dictated by the necessity for the repair of wheel pairs by changing the worn out bandages, which between-repairs resource defines as the run before repair in ТS-8. Therefore, a major problem is the maintenance of wheel-pairs Locomotive Park in good condition and planning repairs in a timely and rational manner. The calculations made have shown that at a between-repairs run of 350 thousand km, established by order №536-C, the thickness of bandages of wheel pairs in depots at Zhambyl, Karaganda, Astana, and Almaty average 60 -65 mm. As the minimum admissible thickness for change of bandages for a wheel is 45 mm, it is obvious that the resource of wheel pair will be underused. Therefore, it is necessary to study whether it is really mandatory for the between-repairs run to objectively reflect actual requirements, or whether there is a possibility to increase the between-repairs run and, by that, reductions in the requirement for repairs.
Results [2] of the calculation of optimum run before repairs with change of bandages of wheelpairs of electric locomotives VL80 С for 4 operational depots are shown in table 9. Table 9 Results of calculation of optimum run before repairs with change of bandages of wheel pairs of electric locomotives VL80 С for 4 operational depots The optimum terms for the change of bandages of wheel pairs received as a result of calculations for the same value of factor of a parity of expenses for planned and unplanned repairs differ. It means that service conditions considerably influence the thickness of bandages of wheel pair electric locomotives VL80 С [7,11,12]. Therefore, terms for carrying out ТS-8 repairs are necessary to be defined, considering the actual technical condition of wheel pairs CE (composition of electric).
Offered schemes of formation of a repair cycle at optimum between-repairs run of electric locomotives in 4 operational depots are presented in Picture 1.
The received results of calculation of requirement for repairs in specified ТS-8 operational depots are presented in table 10.
Thus, thanks to the application of an optimum between-repairs run in operational depots at Zhambyl, Karaganda, Astana, and Almaty, it was possible to lower the requirements for repairs in ТS-8 on 20 units of electric locomotives in a year. As the requirement for locomotives under repair in 4 operational depots changed, the optimum distribution of repairs of electric locomotives of all 9 considered depots will also have to be changed. For the distribution of electric locomotives in repair enterprises, requirements for the repairs, calculated on the basis of the optimum between-repairs run in operational depots at Zhambyl, Karaganda, Astana, and Almaty (table 11), are used. For other operational depots -Zhana-Yesil, Shu, Arys, Kostanai, and Pavlodar -the actual requirements are presented in table 5. The total requirement for repairs is shown in table 11.
The total annual requirement is 112 units of electrical locomotives for repair, which doesn't correspond to the annual program of ТS-8 repair of two repair enterprises. The sum of demands for repair is less than the annual program of repairs of electric locomotives of repair enterprises, i.e.   For solving the linear programming problem, an additional fictitious operational depot was added with the need for repairs 20 0 = a which will send on repair electric locomotives with cost of their repair and delivery j с 0 equal to zero is entered [13,14].
In this case, criterion function becomes Optimum distribution of electric locomotives in repair enterprises at an optimum between-repairs run of 4 depots is presented in table 12. With an increase in the between-repairs run of electric locomotives of 4 depots, the requirement under repair decreases and 20 repairs of electric locomotives are in a reserve of repair enterprises: "Altyn Orda 2004" LLC -8 and "Tulpar At" LLC -12 repairs of electric locomotives in a year.
The total cost of repair with delivery in a case when the additional fictitious operational depot has been entered, and the requirements are balanced, equals 5080 thousand €.

CONCLUSIONS
According to investigations and calculations performed, the following points are defined: 1. With the help of the simplex method, an optimal variant of the VL-80 locomotive distribution in repair enterprises is defined. 2. Schemes of composition of the repair cycle with optimal mileages of locomotives in concrete operation depots are made.
Optimum distribution of repairs in тs-8 of electric locomotives… 29 3. As a consequence of the implementation of optimal inter-repair mileages in 4 operation depots, the need for TO-8 repair is reduced by 20 locomotives per year. 4. The annual economy from the application of an optimum between-repairs run in the operational depots of Zhambyl, Karaganda, Astana, and Almaty, at the expense of a decrease in requirement for repairs of electric locomotives, has made 906 thousand €.