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ROUTING ISSUES BASED ON MATHEMATICAL MODELS IN
TRANSPORT LOGISTICS
Kamalov Sherzodbek Sabirovich
Assistant of the "Automotive and Transport" department Andijan State Technical
Institute, (Andijan city)
kamalovsherzodbek1986@gmail.com
Annotation:
This article shows that routing can be done using techniques such
as using a surveying method, a safe, or a dispatcher table. In order to quantitatively
assess the effectiveness of the management of logistic systems, it is necessary to
develop a mathematical model of the process in the system. Mathematical models of
logistic processes can be conditionally divided into analytical and statistical models.
This illuminates the need for routing based on mathematical models.
Keywords:
logistics systems, motor transport, enterprise, freight forwarding,
routing, dispatcher, management, mathematical model, statistics, methods, linear
program.
Аннотация:
В этой статье показано, что маршрутизация может быть
выполнена с использованием технических методов, таких как метод
топографии, сейфа или панели управления. Для количественной оценки
эффективности
управления
логистическими
системами
необходимо
разработать математическую модель обработки данных в системе.
Математические модели логистических процессов условно можно разделить на
аналитические и статистические модели. Это объясняет необходимость
маршрутизации на основе математических моделей.
Ключевые слова:
логистические системы, автотранспорт, предприятие,
грузоперевозки, маршрутизация, диспетчер, управление, математическая
модель, статистика, методы, линейная программа.
Introduction
The constant development of World Trade requires fundamental changes in
transport markets, including in the transport system of our country. The development
of transport in accordance with international standards and the latest technologies has
increased the interest of specialists in the field of development of forwarding
services. The practical and theoretical problems of improving the efficiency of
Transport companies, improving the quality of Service and the complexity of the
services provided have not yet been considered. It determines its relevance in our
article, the purpose of which is to form new approaches to the management and
organization of the cargo delivery process [1].
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Literature analysis and methodology
In modern literature, in connection with the existing economic conditions, more
and more attention is paid to quality problems. Many foreign and domestic authors
have always distinguished an important place in their studies on the issues of speed
and quality of delivery of goods, especially A.Feigenbaum, E. Deming, K. Ishikawa,
S. Siro, J. The works of classics such as Harrington can be singled out. It was their
research and development, as well as their practical application in the creation of the
philosophy of universal management, that helped many countries that have developed
today (USA, Japan, etc.) to become the leaders of the world economy. But the
practical and theoretical problems of improving the efficiency of transport
companies, improving the quality of Service and the complexity of the services
provided have not yet been considered [2].
Methods.
When routing large batch freight traffic, there are two routes that differ from
each other. Routing in the first direction is addressed by citing the issue of
transportation, while in the second it is brought to the general issue of linear
programming. Let's look at the methods of the first direction. The transport issue of
linear programming had a somewhat simpler solution methodology, and the routing
issue had been brought to the point when it was first scientifically analyzed [3].
The issue of routing can be poured in several cases:
- routing of cargo transportation in a given Rayon without taking into account
the location of ATK of motor transport enterprises, and then connecting the found
routes to enterprises when drawing up routes for a single ATK, the issue can be put in
this view;
- drawing up routes taking into account the location of enterprises.
Since the main goal of the logistic system is to reduce costs associated with the
movement of products, it will be to establish the most optimal economic relations
between elements of the logistic system, in particular between providers, customers
and transport organizations [4].
It is impossible to develop and implement a logistic system without the
widespread use of modern economic mathematical methods and models, as well as
techniques of computational methods. Such confirmation is based on the fact that the
organization, functioning of the logistic system is associated with an enormous
amount of accounting operations required in the management of information and
material flows, as well as with multi-option calculations.
In order to quantitatively assess the effectiveness of the management of any
logistic systems, it is necessary to develop a mathematical model of the process in the
system. Today, mathematical models of logistic processes can be conditionally
International scientific journal
“Interpretation and researches”
Volume 1 issue 4 (50) | ISSN: 2181-4163 | Impact Factor: 8.2
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divided into two types of analytical and statistical models. In this case, let's dwell on
routing based on mathematical models [5].
Results and methods.
At the moment, a number of features related to this issue, such as the
technological nature of the need of the recipient or sender for the volume of
transportation of a contiguous address, the satisfaction of this need in the directions
of routes depends on the cargo flows that are being brought into it from the senders or
taken out of it, and these flows, the number of cars distributed to the routes should be
determined in accordance with the criteria for the full use of their shipping or
receiving capabilities and minimization of transportation costs, and such significant
circumstances were not taken into account. Routing can be done in a surveying
method, using techniques such as using a safe or a dispatcher tableau [6].
The topography method is a scheme of the rayon to be transported, in which all
shipping addresses, an auto shop and a road network connecting them are given. In
addition to this scheme, a table of inter-destination distances is included. On the basis
of the given orders, a daily shipping plan is drawn up, and the cargo flows that must
be carried out according to this plan are drawn on Lime paper. To do this, placing a
sheet of lime on top of the shipping scheme, the load flows that must be executed
between real destinations are drawn in the style of arrows. (Figure 1)
Figure 1.
Load inspection topogram (loaded and unloaded Road, ○-garage, load
receiving points)
The amount of cargo to be transported is indicated on the arrows. The freight is
then distributed over the routes. This takes into account the type of cargo transported
and the types of moving transport used. A plan with a graphical view of the cargo
transportation shown in the list is called a topogram, and it makes it much easier to
make a route. When making circular routes, it will be necessary to ensure that the
rolling stock on these routes reaches as high performance as possible. If the
coefficient of road use on the completed circular routes will be less than 0.5, then
freight transport should be organized on pendulum routes [7].
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Volume 1 issue 4 (50) | ISSN: 2181-4163 | Impact Factor: 8.2
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Another technical method of routing will be a Cabinet safe, divided into
mutually equal yachts. A rayon card or circuit will be placed in this safe where the
cargo will be transported. The scheme or card will also be divided into equal squares.
The magnification of squares depends on the density of points in the zone of cargo
transportation, which are numbered on the one hand with letters, and on the other
hand with numbers (1, 2, 3).
The compilation of routes is performed as follows. A card is taken from a yacht
and it is determined where to take the cargo. From the card in the yacht where this
cargo is carried, it is determined in which directions there is a cargo that is
transported. If there are no shipments from the same yacht, then the cards on the
adjacent yachts around it are checked. The first route is marked the second after the
structure, and so on. Each time the amount of cargo transported on the completed
routes is reduced from the cards, if the cargo on any card is completely transported,
this card is removed from the safe. It is also possible to automate this process.
Figure 2.
Routing safe It is used in other safes for loads that require special cars.
A different view of the safe method is to route using a dispatcher tableau. The
tabletop consists of two horizontal and vertical parts, and a load-bearing rayon card is
attached to the vertical part. These parts are the face of each 1 kv.km divided into
equal squares. Squares are marked by means of letters and numbers. The card
displays addresses that everyone sends and receives. Each yacht has two holes into
which nails can be inserted. Nails are painted in two different colors and indicate the
position of the cargo points: Red mih indicates the sender, and blue indicates the
cargo receivers. The tabletop will again have rubber threads of different lengths.
(Figure 3) the horizontal section of the Tableau is also available on Square yachts, as
in the vertical section of the Huddy, to which shipping orders are placed [8].
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Volume 1 issue 4 (50) | ISSN: 2181-4163 | Impact Factor: 8.2
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Figure 3.
Dispatcher table
When the dispatcher takes an order in one of the horizontal yachts and
determines where the cargo will be transported, and this determines the shipping
scheme by pulling a rubber cord on the mihchas. Then a load is used, which must be
transported in the opposite direction from the microdistrict in which the same load
went or from around it. In this way, all orders are checked and rational routes are
selected. It should be noted that the methods considered above provide effective
results when the shipping point and receiving point are not so numerous. In this case,
the quality of the compiled routes largely depends on the experience of the
dispatcher. With a much larger number of addresses, it becomes more difficult to
construct effective routes with these methods. Because there are extremely many
options for routes that can be drawn up in this, among which it is difficult to find the
optimal route system. In such cases, routing is carried out through mathematical
methods and modern computers [9].
Let I (iϵ{1:m}) be the set of address numbers for the sender and J(jϵ{1:n}) for
the receiver. The volumes of shipment from the addresses and the volumes of cargo
reception to the addresses are given ɑí and the volumes of cargo reception to the
addresses are given bj. Let the matrix of distances between the points of unloading
and increasing be given ‖c
ij
‖
n,m
we assume that for simplicity. The inter-point Inter-
destination freight plan is given {X
ij
}, where the X
ij
may also be given in the form of
the numbers of tons to be transported or the trains to be completed.
Routing - means finding such schemes of inter-point traffic so that the length of
the road without a load be the least, and the given load transport plan is executed.
We are given a load-walking plan {X
ij
}. Hence, one must find a load-free
walking plan {У
ji
} where {X
ij
} is the least of the sum of paths passed without load,
where: {У
ji
}- j is the load - free walking plan between drop i points; and У
ji
is the
number of load-free autotonnes or commutes performed between point j and point i.
unloaded services or motorways coming to points I will be equal to the number of
services or motorways going from this point to all points j J:
Ʃ
𝑛
𝑗=1
𝑦𝑗𝑖 = ɑ𝑖, (𝑖 = 1: 𝑚)
a
i
= Ʃjϵj X
ij
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The unloaded traffic or motorways coming out of point j will be equal to the
number of freight services or motorways coming to this point from all iϵj points.
Ʃ
𝑛
𝑖=1
𝑦𝑗𝑖 = 𝑏𝑗, (𝑗 = 1: 𝑛)
[2]
bi = Ʃiϵj Xij
The number of rides or autotonnes on the unloaded ride cannot be negative.
У
ji
≥ O, (i=1:m, j=1:n) [3]
The total road length to be run without load should be the shortest.
Ʃ
𝑚
𝑖=1
Ʃ
𝑛
𝑗=1
𝑐𝑗𝑖 𝑦𝑗𝑖 → 𝑀𝐼𝑁
[4]
L
0
=
Ʃ
𝑚
𝑖=1
Ʃ
𝑛
𝑗=1
𝑐𝑗𝑖 У𝑗𝑖
𝑞𝑗𝑖 У𝑐
=
1
𝑞𝑗𝑖 У𝑗𝑖 𝑄𝑗𝑖
Ʃ
𝑚
𝑖=1
Ʃ
𝑛
𝑗=1
𝑐𝑗𝑖 𝑌𝑗𝑖 → 𝑀𝐼𝑁
[4
*
]
In this case, the Y
ji
can be transported on non-cargo flights, which is the number
of tons. In addition, the amount of cargo brought into addresses and transported from
points is equal to each other.
Ʃ
𝑚
𝑖=1
ɑ𝑖 = Ʃ
𝑛
𝑗=1
𝑏𝑗
[5]
The number of goods and unloaded services, or the number of tons transported
on these services, is also equal.
Ʃ
𝑚
𝑖=1
Ʃ
𝑛
j=1
ɑ𝑖 = Ʃ
𝑚
𝑖=1
Ʃ
𝑛
𝑗=1
= 𝑏𝑗
[6]
Conclusion
Determining the optimal load-free walking plan in the view described above is
mathematically the transport problem of linear programming, while expressions 1-4
are mathematical models of the transport problem. Where 1.2 equalities are called
limiting equations, and 4 or 4* is called the optimality criterion or efficiency
function. Thus, finding the optimal plan for a load-free ride will lead to an optimal
solution to the transport issue.
References:
1.Под.ред. Л.Б.Миротина. Транспортная логистика. - М.:Издателство
―Экзамен‖, 2003-512 с.
3.B.A. Xо‗jayev «Avtomobillarda yuk va passajirlar tashish asoslari». T.,
«О‗zbekiston» 2002-240 b.
2.Butaev SH.A., Mirzaahmedov B.M., Jo‗raev M.N., Do‗rmanov A.SH.,
Bahodirov B. ―Tashish jarayoniarini modellashtirish va optimallashtirish‖,
Toshkent, 04 zR Fanlar akademiyasi, ―Fan‖ nashriyoti, 2009-268 b.
3.Ходжаев Б.А., Закиров Г.Т. ―Международние автомобилние перевозки‖,
Тошкент ―Фан‖, 2005- 310 б. s,
4.Butaev SH.A., Sidiqnazarov Q.M., Murodov A.S., Qoʻziev A.U. ―Logistika‖
(Etkazib berish zanjirida oqimlami boshqarish), Monografiya, Toshkent,
―EXTREMUM-PRESS‖ nashriyoti, 2012-580b.
International scientific journal
“Interpretation and researches”
Volume 1 issue 4 (50) | ISSN: 2181-4163 | Impact Factor: 8.2
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5.Sabirovich, Kamalov Sherzodbek. "ORGANIZATION OF DISTRIBUTION
OF MATERIAL AND INFORMATION FLOWS WITHIN THE LOGISTIC
SYSTEM."CREATIVE TEACHER 3.32 (2023): 127-133.
6.Sabirovich,
Kamalov
Sherzodbek.
"FACTORS
FOR
LIGHTING
INTELLECTUAL SYSTEMS IN INCREASING THE CAPABILITIES OF
TRASPORT TOOLS."JOURNAL OF INTERDISCIPLINARY INNOVATION
AND SCIENTIFIC RESEARCH IN UZBEKISTAN 2.16 (2023): 214-222.
7.Gaffarov, M. T., and Sh. S. Kamalov. "GUARANTEEING THE SAFE
CHARACTER IN ORGANIZING THE TRANSPORTATION OF KHALKARO TO
THE WORKING REGIME OF THE KHAYDOVITES."Journal of new century
innovations 18.5 (2022): 92-99.
8.Sabirovich, Kamalov Sherzodbek. "RELEVANCE OF VEHICLE FLOW
MODELING."JOURNAL OF INTERDISCIPLINARY INNOVATION AND
SCIENTIFIC RESEARCH IN UZBEKISTAN 2.16 (2023): 290-298.
9.Nasirov, Ilham Zakirovich, and Sherzodbek Sabirovich Kamolov. "Beaver
horn and S.INSTALLATION OF TRAFFIC LIGHTS AT THE INTERSECTION OF
ZUNNONOVA STREETS."JOURNAL OF NEW CENTURY INNOVATIONS 7:
102-107.
