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    УдосконалСння ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ–Π² визначСння схСм ΠΎΠ±Ρ–Π³Ρƒ Π»ΠΎΠΊΠΎΠΌΠΎΡ‚ΠΈΠ²Ρ–Π² Π· урахуванням Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½ΠΈΡ… особливостСй Π²Π°Π³ΠΎΠ½ΠΎΠΏΠΎΡ‚ΠΎΠΊΡ–Π²

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    This paper focuses on new analytical solutions in the area of building locomotives’ circulation plans to handle individual applications for route transportation of freight. Such a domain has been little researched for the railway network of Ukraine, whereas the present study provides a basis for automating the planning process. The main aim is to improve the methods of determining the schemes of locomotives’ turnover in the railway network of Ukraine under the condition of an accelerated handling of individual railcar traffic and with regard to technological peculiarities. The developed mathematical model simultaneously makes it possible to determine the weight of trains on the routes they follow, to outline the circuity of locomotives with regard to deploying various series of locomotives within the network, and to regulate the system of locomotive crews’ operations in view of the existing technical and technological features of locomotive facilities and the railway infrastructure. The suggested mathematical model is processed in the study through the use of an integer genetic algorithm with its own system of coding the solution. The results have confirmed the adequacy of the developed mathematical model. The use of the suggested mathematical model on the basis of the genetic algorithm can help automate the complex process of determining the schemes of locomotives’ circulation with regard to the technological peculiarities of railcar traffic and, consequently, improve the accuracy and speed of decision-making for servicing individual applications for route transportation of freight.ΠŸΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎ ΡΠΎΠ²Π΅Ρ€ΡˆΠ΅Π½ΡΡ‚Π²ΠΎΠ²Π°Π½ΠΈΠ΅ ΠΌΠ΅Ρ‚ΠΎΠ΄ΠΎΠ² опрСдСлСния схСм обращСния Π»ΠΎΠΊΠΎΠΌΠΎΡ‚ΠΈΠ²ΠΎΠ² с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ тСхнологичСских особСнностСй Π²Π°Π³ΠΎΠ½ΠΎΠΏΠΎΡ‚ΠΎΠΊΠΎΠ². Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° матСматичСская модСль, которая позволяСт Π½Π°ΠΉΡ‚ΠΈ массу ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π½Π° ΠΌΠ°Ρ€ΡˆΡ€ΡƒΡ‚Π°Ρ… ΠΈΡ… слСдования, схСмы обращСния Π»ΠΎΠΊΠΎΠΌΠΎΡ‚ΠΈΠ²ΠΎΠ² ΠΈ Ρ€Π°Π±ΠΎΡ‚Ρ‹ Π±Ρ€ΠΈΠ³Π°Π΄ с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ дислокации ΠΏΠ°Ρ€ΠΊΠ° с Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹ΠΌΠΈ сСриями Π½Π° ΠΏΠΎΠ»ΠΈΠ³ΠΎΠ½Π΅ сСти. Для Ρ€Π΅ΡˆΠ΅Π½ΠΈΡ Π΄Π°Π½Π½ΠΎΠΉ матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ ΠΏΡ€ΠΈΠΌΠ΅Π½Π΅Π½ цСлочислСнный гСнСтичСский Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ с собствСнной схСмой кодирования Ρ€Π΅ΡˆΠ΅Π½ΠΈΡΠ—Π°ΠΏΡ€ΠΎΠΏΠΎΠ½ΠΎΠ²Π°Π½ΠΎ удосконалСння ΠΌΠ΅Ρ‚ΠΎΠ΄Ρ–Π² визначСння схСм ΠΎΠ±Ρ–Π³Ρƒ Π»ΠΎΠΊΠΎΠΌΠΎΡ‚ΠΈΠ²Ρ–Π² Π· урахуванням Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½ΠΈΡ… особливостСй Π²Π°Π³ΠΎΠ½ΠΎΠΏΠΎΡ‚ΠΎΠΊΡ–Π². Π ΠΎΠ·Ρ€ΠΎΠ±Π»Π΅Π½ΠΎ ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½Ρƒ модСль, яка дозволяє Π·Π½Π°ΠΉΡ‚ΠΈ масу ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π½Π° ΠΌΠ°Ρ€ΡˆΡ€ΡƒΡ‚Π°Ρ… Ρ—Ρ… слідування, схСми ΠΎΠ±Ρ–Π³Ρƒ Π»ΠΎΠΊΠΎΠΌΠΎΡ‚ΠΈΠ²Ρ–Π² Ρ‚Π° Ρ€ΠΎΠ±ΠΎΡ‚ΠΈ Π±Ρ€ΠΈΠ³Π°Π΄ Π· врахуванням дислокації ΠΏΠ°Ρ€ΠΊΡƒ Π· Ρ€Ρ–Π·Π½ΠΈΠΌΠΈ сСріями Π½Π° ΠΏΠΎΠ»Ρ–Π³ΠΎΠ½Ρ– ΠΌΠ΅Ρ€Π΅ΠΆΡ–. Для Ρ€Ρ–ΡˆΠ΅Π½Π½Ρ Π΄Π°Π½ΠΎΡ— ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΎΡ— ΠΌΠΎΠ΄Π΅Π»Ρ– застосовано Ρ†Ρ–Π»ΠΎΡ‡ΠΈΡΠ΅Π»ΡŒΠ½ΠΈΠΉ Π³Π΅Π½Π΅Ρ‚ΠΈΡ‡Π½ΠΈΠΉ Π°Π»Π³ΠΎΡ€ΠΈΡ‚ΠΌ Π· власною ΡΡ…Π΅ΠΌΠΎΡŽ кодування Ρ€Ρ–ΡˆΠ΅Π½Π½

    Π ΠΎΠ·Ρ€ΠΎΠ±ΠΊΠ° ΠΌΠ΅Ρ‚ΠΎΠ΄Ρƒ модСлювання Ρ€ΠΎΠ·ΠΏΠΎΠ²ΡΡŽΠ΄ΠΆΠ΅Π½Π½Ρ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ Ρƒ Π½Π΅Ρ†ΠΈΠΊΠ»Ρ–Ρ‡Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π½Π° залізницях Π·ΠΌΡ–ΡˆΠ°Π½ΠΎΠ³ΠΎ Ρ€ΡƒΡ…Ρƒ

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    The main goal of present study is to develop a method for modeling delay propagation in non-cyclic train scheduling on a railroad network with mixed traffic. This will make it possible to explore the dynamics of delay transfer between trains and to identify the most vulnerable points in the timetable of trains. We have devised a method for modeling delay propagation in non-cyclic train scheduling for the rail networks with mixed traffic. It is proposed to apply as a basis of the developed method a mathematical model for the construction of a non-cyclic train timetable. A distinctive feature of the objective function of the mathematical model is taking into consideration the patterns of building a non-cyclic train timetable under conditions of mixed traffic of passenger and heavy-weight or multi-car freight trains, for which it is important to minimize the cost of stopping during motion. The proposed mathematical model was solved based on the multiagent optimization. To account for delay propagation on the railroad network of great dimensionality, we devised a procedure for connecting interdependent sections, which makes it possible to decompose the general problem based on the construction of schedule of trains for separate estimated sections taking into consideration the network effect. We performed an analysis of the dynamics of propagation of secondary delays in non-cyclic train scheduling with detailed patterns of changes in all parameters in time and space. We obtained dependences of the number and duration of delayed trains on the point of occurrence in the timetable of trains along the estimated line of the Ukrainian railroad network. The approach proposed allows the automatization of determining a time reserve in the standard non-cyclic train scheduling based on forecasting the consequences of train delays.ΠŸΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΌΠ΅Ρ‚ΠΎΠ΄ модСлирования распространСния Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ Π² нСцикличСском Π³Ρ€Π°Ρ„ΠΈΠΊΠ΅ двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ тСхничСских ΠΈ тСхнологичСских особСностСй ΠΆΠ΅Π»Π΅Π·Π½ΠΎΠ΄ΠΎΡ€ΠΎΠΆΠ½ΠΎΠΉ сСти смСшанного пассаТирского ΠΈ Π³Ρ€ΡƒΠ·ΠΎΠ²ΠΎΠ³ΠΎ двиТСния. Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π° исслСдования влияния Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π² Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌ Π³Ρ€Π°Ρ„ΠΈΠΊΠ΅ двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π½Π° основС ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ построСния Π³Ρ€Π°Ρ„ΠΈΠΊΠ° двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ Π·Π°Π΄Π°Π½ΠΎΠΉ ΠΏΠ΅Ρ€Π²ΠΈΡ‡Π½ΠΎΠΉ Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π½Ρ‹Π΅ ΡΠΊΡΠΏΠ΅Ρ€ΠΈΠΌΠ΅Π½Ρ‚Π°Π»ΡŒΠ½Ρ‹Π΅ исслСдования модСлирования распространСния Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ Π² Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌ Π³Ρ€Π°Ρ„ΠΈΠΊΠ΅ двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π½Π° ΠΆΠ΅Π»Π΅Π·Π½ΠΎΠ΄ΠΎΡ€ΠΎΠΆΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠΈ Π·Π½Π°Ρ‡ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠΉ протяТСнностиЗапропоновано ΠΌΠ΅Ρ‚ΠΎΠ΄ модСлювання Ρ€ΠΎΠ·ΠΏΠΎΠ²ΡΡŽΠ΄ΠΆΠ΅Π½Π½Ρ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ Ρƒ Π½Π΅Ρ†ΠΈΠΊΠ»Ρ–Ρ‡Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π· урахуванням Ρ‚Π΅Ρ…Π½Ρ–Ρ‡Π½ΠΈΡ… Ρ‚Π° Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½ΠΈΡ… особливостСй Π·Π°Π»Ρ–Π·Π½ΠΈΡ‡Π½ΠΎΡ— ΠΌΠ΅Ρ€Π΅ΠΆΡ– Π·ΠΌΡ–ΡˆΠ°Π½ΠΎΠ³ΠΎ Ρ€ΡƒΡ…Ρƒ ΠΏΠ°ΡΠ°ΠΆΠΈΡ€ΡΡŒΠΊΠΈΡ… Ρ– Π²Π°Π½Ρ‚Π°ΠΆΠ½ΠΈΡ… ΠΏΠΎΡ—Π·Π΄Ρ–Π². Π ΠΎΠ·Ρ€ΠΎΠ±Π»Π΅Π½ΠΎ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Ρƒ дослідТСння Π²ΠΏΠ»ΠΈΠ²Ρƒ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Ρƒ Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π½Π° основі ΠΎΠΏΡ‚ΠΈΠΌΡ–Π·Π°Ρ†Ρ–ΠΉΠ½ΠΎΡ— ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΎΡ— ΠΌΠΎΠ΄Π΅Π»Ρ– ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²ΠΈ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π· урахування Π·Π°Π΄Π°Π½ΠΎΡ— ΠΏΠ΅Ρ€Π²ΠΈΠ½Π½ΠΎΡ— Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Ρ– Π΅ΠΊΡΠΏΠ΅Ρ€ΠΈΠΌΠ΅Π½Ρ‚Π°Π»ΡŒΠ½Ρ– дослідТСння модСлювання ΠΏΠΎΡˆΠΈΡ€Π΅Π½Π½Ρ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Ρƒ Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π· урахуванням взаємоув’язки Π·Π°Π»Ρ–Π·Π½ΠΈΡ‡Π½ΠΈΡ… Π΄Ρ–Π»ΡŒΠ½ΠΈΡ†

    Π ΠΎΠ·Ρ€ΠΎΠ±ΠΊΠ° ΠΌΠ΅Ρ‚ΠΎΠ΄Ρƒ модСлювання Ρ€ΠΎΠ·ΠΏΠΎΠ²ΡΡŽΠ΄ΠΆΠ΅Π½Π½Ρ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ Ρƒ Π½Π΅Ρ†ΠΈΠΊΠ»Ρ–Ρ‡Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π½Π° залізницях Π·ΠΌΡ–ΡˆΠ°Π½ΠΎΠ³ΠΎ Ρ€ΡƒΡ…Ρƒ

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    The main goal of present study is to develop a method for modeling delay propagation in non-cyclic train scheduling on a railroad network with mixed traffic. This will make it possible to explore the dynamics of delay transfer between trains and to identify the most vulnerable points in the timetable of trains. We have devised a method for modeling delay propagation in non-cyclic train scheduling for the rail networks with mixed traffic. It is proposed to apply as a basis of the developed method a mathematical model for the construction of a non-cyclic train timetable. A distinctive feature of the objective function of the mathematical model is taking into consideration the patterns of building a non-cyclic train timetable under conditions of mixed traffic of passenger and heavy-weight or multi-car freight trains, for which it is important to minimize the cost of stopping during motion. The proposed mathematical model was solved based on the multiagent optimization. To account for delay propagation on the railroad network of great dimensionality, we devised a procedure for connecting interdependent sections, which makes it possible to decompose the general problem based on the construction of schedule of trains for separate estimated sections taking into consideration the network effect. We performed an analysis of the dynamics of propagation of secondary delays in non-cyclic train scheduling with detailed patterns of changes in all parameters in time and space. We obtained dependences of the number and duration of delayed trains on the point of occurrence in the timetable of trains along the estimated line of the Ukrainian railroad network. The approach proposed allows the automatization of determining a time reserve in the standard non-cyclic train scheduling based on forecasting the consequences of train delays.ΠŸΡ€Π΅Π΄Π»ΠΎΠΆΠ΅Π½ ΠΌΠ΅Ρ‚ΠΎΠ΄ модСлирования распространСния Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ Π² нСцикличСском Π³Ρ€Π°Ρ„ΠΈΠΊΠ΅ двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ тСхничСских ΠΈ тСхнологичСских особСностСй ΠΆΠ΅Π»Π΅Π·Π½ΠΎΠ΄ΠΎΡ€ΠΎΠΆΠ½ΠΎΠΉ сСти смСшанного пассаТирского ΠΈ Π³Ρ€ΡƒΠ·ΠΎΠ²ΠΎΠ³ΠΎ двиТСния. Π Π°Π·Ρ€Π°Π±ΠΎΡ‚Π°Π½Π° ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Π° исслСдования влияния Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π² Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌ Π³Ρ€Π°Ρ„ΠΈΠΊΠ΅ двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π½Π° основС ΠΎΠΏΡ‚ΠΈΠΌΠΈΠ·Π°Ρ†ΠΈΠΎΠ½Π½ΠΎΠΉ матСматичСской ΠΌΠΎΠ΄Π΅Π»ΠΈ построСния Π³Ρ€Π°Ρ„ΠΈΠΊΠ° двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² с ΡƒΡ‡Π΅Ρ‚ΠΎΠΌ Π·Π°Π΄Π°Π½ΠΎΠΉ ΠΏΠ΅Ρ€Π²ΠΈΡ‡Π½ΠΎΠΉ Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Π½Ρ‹Π΅ ΡΠΊΡΠΏΠ΅Ρ€ΠΈΠΌΠ΅Π½Ρ‚Π°Π»ΡŒΠ½Ρ‹Π΅ исслСдования модСлирования распространСния Π·Π°Π΄Π΅Ρ€ΠΆΠΊΠΈ Π² Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌ Π³Ρ€Π°Ρ„ΠΈΠΊΠ΅ двиТСния ΠΏΠΎΠ΅Π·Π΄ΠΎΠ² Π½Π° ΠΆΠ΅Π»Π΅Π·Π½ΠΎΠ΄ΠΎΡ€ΠΎΠΆΠ½ΠΎΠΉ Π»ΠΈΠ½ΠΈΠΈ Π·Π½Π°Ρ‡ΠΈΡ‚Π΅Π»ΡŒΠ½ΠΎΠΉ протяТСнностиЗапропоновано ΠΌΠ΅Ρ‚ΠΎΠ΄ модСлювання Ρ€ΠΎΠ·ΠΏΠΎΠ²ΡΡŽΠ΄ΠΆΠ΅Π½Π½Ρ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ Ρƒ Π½Π΅Ρ†ΠΈΠΊΠ»Ρ–Ρ‡Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π· урахуванням Ρ‚Π΅Ρ…Π½Ρ–Ρ‡Π½ΠΈΡ… Ρ‚Π° Ρ‚Π΅Ρ…Π½ΠΎΠ»ΠΎΠ³Ρ–Ρ‡Π½ΠΈΡ… особливостСй Π·Π°Π»Ρ–Π·Π½ΠΈΡ‡Π½ΠΎΡ— ΠΌΠ΅Ρ€Π΅ΠΆΡ– Π·ΠΌΡ–ΡˆΠ°Π½ΠΎΠ³ΠΎ Ρ€ΡƒΡ…Ρƒ ΠΏΠ°ΡΠ°ΠΆΠΈΡ€ΡΡŒΠΊΠΈΡ… Ρ– Π²Π°Π½Ρ‚Π°ΠΆΠ½ΠΈΡ… ΠΏΠΎΡ—Π·Π΄Ρ–Π². Π ΠΎΠ·Ρ€ΠΎΠ±Π»Π΅Π½ΠΎ ΠΏΡ€ΠΎΡ†Π΅Π΄ΡƒΡ€Ρƒ дослідТСння Π²ΠΏΠ»ΠΈΠ²Ρƒ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Ρƒ Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π½Π° основі ΠΎΠΏΡ‚ΠΈΠΌΡ–Π·Π°Ρ†Ρ–ΠΉΠ½ΠΎΡ— ΠΌΠ°Ρ‚Π΅ΠΌΠ°Ρ‚ΠΈΡ‡Π½ΠΎΡ— ΠΌΠΎΠ΄Π΅Π»Ρ– ΠΏΠΎΠ±ΡƒΠ΄ΠΎΠ²ΠΈ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π· урахування Π·Π°Π΄Π°Π½ΠΎΡ— ΠΏΠ΅Ρ€Π²ΠΈΠ½Π½ΠΎΡ— Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ. ΠŸΡ€ΠΎΠ²Π΅Π΄Π΅Π½Ρ– Π΅ΠΊΡΠΏΠ΅Ρ€ΠΈΠΌΠ΅Π½Ρ‚Π°Π»ΡŒΠ½Ρ– дослідТСння модСлювання ΠΏΠΎΡˆΠΈΡ€Π΅Π½Π½Ρ Π·Π°Ρ‚Ρ€ΠΈΠΌΠΊΠΈ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Ρƒ Π½ΠΎΡ€ΠΌΠ°Ρ‚ΠΈΠ²Π½ΠΎΠΌΡƒ Π³Ρ€Π°Ρ„Ρ–ΠΊΡƒ Ρ€ΡƒΡ…Ρƒ ΠΏΠΎΡ—Π·Π΄Ρ–Π² Π· урахуванням взаємоув’язки Π·Π°Π»Ρ–Π·Π½ΠΈΡ‡Π½ΠΈΡ… Π΄Ρ–Π»ΡŒΠ½ΠΈΡ†

    An Improved Method of Determining the Schemes of Locomotive Circulation with Regard to the Technological Peculiarities of Railcar Traffic

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    This paper focuses on new analytical solutions in the area of building locomotives' circulation plans to handle individual applications for route transportation of freight. Such a domain has been little researched for the railway network of Ukraine, whereas the present study provides a basis for automating the planning process. The main aim is to improve the methods of determining the schemes of locomotives' turnover in the railway network of Ukraine under the condition of an accelerated handling of individual railcar traffic and with regard to technological peculiarities. The developed mathematical model simultaneously makes it possible to determine the weight of trains on the routes they follow, to outline the circuity of locomotives with regard to deploying various series of locomotives within the network, and to regulate the system of locomotive crews' operations in view of the existing technical and technological features of locomotive facilities and the railway infrastructure. The suggested mathematical model is processed in the study through the use of an integer genetic algorithm with its own system of coding the solution. The results have confirmed the adequacy of the developed mathematical model. The use of the suggested mathematical model on the basis of the genetic algorithm can help automate the complex process of determining the schemes of locomotives' circulation with regard to the technological peculiarities of railcar traffic and, consequently, improve the accuracy and speed of decision-making for servicing individual applications for route transportation of freight
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