XVII Международная студенческая научная конференция Студенческий научный форум - 2025

Ардаширов Д.Р.,

Студент факультета управления процессами перевозок,УрГУПС

Марчукова O. A.,

Студент факультета управления процессами перевозок,УрГУПС

Филиппова Е.Г.

Relevance of the topic

One of the most important economic problems of the enterprise is a complete upgrade of the equipment or its partial replacement.

Consider the malfunctions in which the operation of railway tanks is prohibited:

1) Product leakage 2) Damage to the case 3) Deformation of the structure 4) Equipment malfunctions 5) Component wear

Consider the malfunctions in which the railway tank must be written off.

1) Critical damage to the hull 2) Malfunctions of the main systems 3) Inability to restore tightness 4) High level of wear and tear 5) Complex damage after accidents

Decommissioning a railway tanks a serious step that is usually applied only after a thorough assessment of its condition and the possibility of repair

Bellman's principle of optimality

Bellman's optimality principle states that if a certain sequence of decisions is optimal, then at any step subsequent decisions form an optimal strategy with respect to the outcome of previous decisions. Other words, if the control is optimal, then whatever the initial state of the system and the control of the system at the initial time, the subsequent control are optimal relative to the state that the system will assume as a result of the initial control.

Designations

1) r(t)-the cost of products produced per year per railway tank unit of age t years

2) u(t) -expenses related to the operation and repair of a railway tank aged t years

3) s(t)-the residual value of a railway tank of age t years

4) P-the purchase price of a new railway tank

5) N-the duration of the planned period

6) t = 0, 1, 2, ..., N is the number of the current period

7) t0-the initial condition and age of the equipment at the beginning of the planned period

The age of a railway tank is defined as the period of its operation after the last replacement, defined in years.

Elements of dynamic programming

Element 1: The system consists of equipment.

Element 2: The condition at the i - th stage is the service operation t (age) of the railway tank by the beginning of the i-th year.

Element 3: Stage i is represented by the ordinal number of the year i, i = 1, 2, ..., N.

Element 4: The solutions at stage i (i. e. for year i) are alternatives: to continue operation or to sell and buy a new railway tank at the beginning of the i-th year

To solve such problems, a system of equations is compiled that makes it possible to decide whether to save the equipment or replace it at this stage:

Let's consider the application of the Bellman optimality principle using the example of solving the following task.

Task

At a certain point in time, the Transneft company changes railway tanks. The dependence of annual production in value terms, as well as the dependence of the cost of maintenance and repair of railway tank-wagon at different times of their use is shown in the table. Knowing that the costs associated with the purchase of new railway tanks amount to 11 million rubles, and the replaced railway tanks, depending on their service operation, are sold (the cost of a used railway tank, depending on its service operation, is also shown in the table), it is necessary to draw up such a railway tank replacement plan for the next 10 years, if where the total profit of the Transneft company for a given period of time would be the maximum.

Age, t, during which the railway tanks are used, years	0	1	2	3	4	5	6	7	8	9	10
Annual costs, u(t), for the maintenance and repair of railway tanks	13	13,6	14,2	14,8	15,4	16	16,6	17,2	19,8	21,4	22
Cost, S(t), sales of the supported railway tank, millon rubles	-	6,05	5,5	4,95	4,4	3,85	3,3	2,75	2,2	1,65	1,1
Annual profit from the railway tank, r(t), in value terms	27	26,6	26,2	25,8	25,4	25	24,6	24,2	23,8	23,4	23

According to the task condition, work begins with a new railway tank. At the beginning of each subsequent year of work, it is necessary to make a decision: either we keep the railway tank and use it all year, or we sell the tank, buy a new one and use a new railway tank next year. In the figure below, the problem of replacing a railway tank for transporting petroleum products is presented as a network. For each year of operation of the railway tank, it’s possible age can be determined.

The solution to the problem contains conditional and unconditional optimization, and conditional optimization begins with the last stage. Thus, let's consider the last year of the planning period. According to the scheme, the age of the railway tank can be 1, 2, 3, 4, 5, 6, 7, 8 or 9 years old. We determine the conditionally optimal solution for each year.

Table 1(10 stage)

age of the railway tank, t, years	the maximum income for the last year, F1(t)	a conditionally optimal solution
1	18,50	save
2	16,95	save
3	15,40	save
4	13,85	save
5	12,90	sell
6	12,35	sell
7	11,8	sell
8	11,25	sell
9	10,70	sell

Similarly, we consider each subsequent year, moving from the end to the first year of the planned period of operation of the railway tank.

Table 2(9 stage)

age of the railway tank, t, years	the maximum income for the last year , F2(t)	a conditionally optimal solution
1	29,95	save
2	27,40	save
3	26,45	sell
4	25,90	sell
5	25,35	sell
6	24,80	sell
7	24,25	sell
8	23,70	sell

Table 3(8 stage)

age of the railway tank, t, years	the maximum income for the last year, F3(t)	a conditionally optimal solution
1	40,40	save
2	38,45	save
3	37,90	sell
4	37,35	sell
5	36,8	sell
6	36,25	sell
7	35,7	sell

Table 4 (7 stage)

age of the railway tank, t, years	the maximum income for the last year, F4(t)	a conditionally optimal solution
1	51,45	save
2	49,90	save
3	48,32	save/ sell
4	47,80	sell
5	47,25	sell
6	46,70	sell

Table 5 (6 stage)

age of the railway tank, t, years	the maximum income for the last year ,F5(t)	a conditionally optimal solution
1	62,90	save
2	60,35	save
3	59,40	sell
4	58,85	sell
5	58,30	sell

Table 6 (5 stage)

age of the railway tank, t, years	the maximum income for the last year,F6(t)	a conditionally optimal solution
1	73,35	save
2	71,40	save/sell
3	70,85	sell
4	70,30	sell

Table 7 (4 stage)

age of the railway tank, t, years	the maximum income for the last year, F7(t)	a conditionally optimal solution
1	84,40	save
2	82,85	save
3	81,30	save/sell

Table 8(3 stage)

age of the railway tank, t, years	the maximum income for the last year, ,F8(t)	a conditionally optimal solution
1	95,85	save
2	93,30	save

Table 9(2 stage)

age of the railway tank, t, years	the maximum income for the last year,F9(t)	a conditionally optimal solution
1	106,30	save

Table 10(1 stage)

age of the railway tank, t, years	the maximum income for the last year ,F10(t)	a conditionally optimal solution
0	115,35	save

Unconditional optimization

Thus, the maximum profit for 10 years of operation may amount to 115, 35 million rubles.

There are several strategies for replacing railway tank:

1) sell for 5 and 8 years of operation

2) sell for 4 and 8 years of operation

3) sell for 4 and 7 years of operation

Literature

1. T. V. Zavyalova, I. N. Pirogova, E.G. Filippova. Methods of making managerial decisions. The training manual. USURT Publishing House. 2014

2. The interstate standard. A railway tank . General technological conditions. GOST 10674-2022.

3. *A network of regional business portals. Catalog of railway tank in Yekaterinburg [electronic resource]. -Access mode: https://ekaterinburg.regtorg.ru/goods/vagon-cisterna/?ysclid=m3zpbj7s23445289880 , free- (11/20/2024)

4. Price list for works performed during the repair of freight wagons in the carriage repair depots of OMK Steel Way JSC[Electronic resource]. - Access mode: https://omk.ru/upload/iblock/554/PRICE LIST sign up for viewing Freight wagons (Appendix No. 4 to the text).pdf , free- (11/20/2024)

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