International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 11337-11348 © TJPRC Pvt. Ltd
SOLUTION OF THE PROBLEM OF OPTIMAL DISTRIBUTION OF CARGO FLOWS IN THE REGION AND THE DEVELOPMENT OF ITS TRANSPORT NETWORK
ABDULAZIZ A. SHERMUKHAMEDOV1 & ABDIMUROT U. KUZIEV2 1*Doctor of Technical Sciences, Professor of Department Road-Building Machines and Equipment, Tashkent Institute of Design, Construction and Maintenance of Automobile Roads, Tashkent, Uzbekistan 2Schalor, Docent, Head of Department of Transport Systems and Constructions, Termez State University, Termez, Uzbekistan ABSTRACT
This paper discusses the problem of optimal distribution of freight traffic with the best use of vehicles of road and rail transport, transport network, as well as their development, taking into account the prospective growth of freight traffic in the conditions of the Surkhandarya region of the Republic of Uzbekistan.
The mathematical model and a technique for solving the problem of optimal distribution of freight traffic in the region under consideration by types of land transport and transport networks are proposed.
Using the example of the region under consideration, the results of effective distribution of the flow of cargo
in the regional multimodal network, including taking into account the growth of traffic volumes, were obtained, areas Article Original were identified where the network capacity should be increased, their reconstruction and construction of new sections, taking into account various options.
KEYWORDS: Multimodal Transportation, Road and Rail Transport, Freight Traffic, Transport Network, Modified Multi-Network Method, Solution Algorithm & Transport Infrastructure
Received: Jun 10, 2020; Accepted: Jun 30, 2020; Published: Sep 05, 2020; Paper Id.: IJMPERDJUN20201083
1. INTRODUCTION
It is known that the modernization and further development of production entails the expansion and efficiency of the transport infrastructure – all elements of the railway and road transport networks, technical and technological means. Such an infrastructure for the development of the transport services market is a multimodal transport network, including international transport corridors [1].
Multimodal transportation is internal transportation with at least two modes of transport [2]. It is known that multimodal transportation combines the advantages of several types of transport (road, rail, sea).
An analyzes of the literature on the development of multimodal networks and the planning of multimodal transportation shows that researchers use three main levels in planning, strategic, tactical and operational, with extensive study of tactical level issues, followed by strategic and operational levels. Despite the great attention paid to the above problems, there are still many questions and tasks that need to be solved [3]. In particular, the tasks of optimizing traffic flows and transport networks, the development or selection of methods for substantiating and solving mathematical models are the most relevant problems of our time.
In articles [4] – [8] using simulation networks Petri Net (E-Net), Firework, and others, the problems of a multimodal transport network with multi-purpose optimization for regional transit multimodal transport are solved.
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The article [9] discusses the methodological basis for the design and throughput of a multimodal transport network.
The article [10] analyzes ways to increase transport capacity in Slovakia, the construction of broadband routes in Europe to reduce transshipment stations and reduce the flow of goods from Eastern Europe and Asia.
Based on an analysis of the existing literature, this article discusses the development of freight flows with the best use of road and rail vehicles, the transportation network, as well as their development, taking into account the prospective growth of freight flows in the conditions of the Surkhandarya region of the Republic of Uzbekistan.
Surkhandarya region is located in the southernmost part of Uzbekistan, it borders with the Republic of Tajikistan in the north-east, Kashkadarya region in the north-west, the Republic of Turkmenistan in the west and the Republic of Afghanistan in the south through the Amu Darya river. The geographical location may create a new promising southern alternative transport corridor with access to the ports of Iran (Bandar-Abbas, Chahbahar) and Pakistan (Gwadar, Karachi) in transit through Afghanistan.
The area of the region is 20.1 thousand km2, which is 4.7% of the country's territory, according to official statistics, the population as of January 1, 2018 was 2513.1 thousand people, which is 7.5% of the population. The population density of the Surkhandarya region is 125 people per km2, this figure in the country averages 74.3 people per km2.
As a result of the growth of the population and manufacturing enterprises, it is necessary to deliver products to the domestic and foreign markets with the best use of transportation means of automobile and railway transport, the transport network, and to reduce its cost, it is necessary to develop transport infrastructure.
The development of the transport network in the region should be based on an appropriate science-based basis. In particular, to optimize the transport security of settlements, it is advisable to use the methodology of optimizing cargo flows in transport networks and the development of the transport network [11]. In addition, the introduction of intelligent transport systems will expand the opportunities for the development of a multimodal transport network and its effective use.
Thus, we can distinguish the following ways of developing a transport network [12]:
construction of road infrastructure;
use of an intelligent transport system (ITS) to optimize and control traffic flow.
Effective planning and investment in transport infrastructure systems is seen as the key to economic development in both developed and developing countries. However, planning such strategic transport investments is difficult due to their high cost and public profile, long asset life and uncertainties regarding future models and technologies of transport demand. Taking into account that only a limited amount of funds is available for transport investments, it is important that this financing be used in the right places and in the right way to ensure the best return on limited public resources [13].
Therefore, there is a need for a model capable of evaluating network demand and performance over a wide range of possible future options so that reliable decisions can be made as to which schemes will be adopted.
As a rule, it is envisaged that the development of local road networks will be carried out in stages on separate
Impact Factor (JCC): 8.8746 SCOPUS Indexed Journal NAAS Rating: 3.11 Solution of The Problem of Optimal Distribution of Cargo Flows in 11339 the Region and the Development of its Transport Network networks, given the limited financial resources. At the same time, the improvement of the transport and operational characteristics of transport links will be achieved through the conversion of road paved lower type of pavement into a transition type paved road [5].
Research on this issue is carried out in the framework of the project №OT-Atex-2018-352 on the topic: “Optimal development of the regional transport network and widespread application of the principles of logistics in the effective development of promising freight flows”.
2. MATERIALS AND METHODS
The adoption of road development plans based on the following considerations: each stage of a road development means either improving the road category, or improving the type of road surface, or simultaneously improving the road category and improving the type of road surface.
To formulate the problem and develop the model, we introduce the basic concepts and indicators in the field of the transport network.
The basic concepts of the automobile and railway networks are nodes (peaks), from where various road connections originate. At nodes (peaks) - consignees or senders transfer goods from one mode of transport to another, rail or road networks intersect in different directions.
We assume that a plurality of N available or possible nodes (peaks) are given that represent the current or future state of the transport network in the economic zone. This set contains a certain number of senders ( S ) and recipients (t ), that is, S , t N .
A large-scale transport-transit system can be represented in the form of graphs representing ordered pairs with a limited set of peaks (airport, railway, automobile terminals, bicycle stations, logistics centers) and arcs (transport lines between different terminals) [13].
Let us denote the variable parameter that characterizes the value of the l-th type of cargo flow over the transport network section ij (ij-oriented link connecting node i to network node j) with a possible level of development of section p,
p by X ij,l . For each node i = 1,2, ...n, index of the address of the sender, j = 1, 2, ... m, index of the address of the recipient,
l l ai - the volume of the shipment from point i, bj - the volume of arrival of the goods at point j, l = 1,2, ... k, index indicating the type of cargo.
Now we turn to the analysis of the characteristics of the throughput of cargo flows in the arcs of the transport
p network. One of these parameters is the indicator Cij , i.e. the cost of transporting a unit of cargo in section ij at the p-th level of development. In the general case, as the optimization criterion, we can take the sum of the products of the elements
p of transport costs for l-types of cargo in all arcs ij of the network and parameters X ij . However, it should be noted that the value of the parameter will be different, depending on what level of development of the transport network p is considered in the problem. For example, if the problem is solved for an existing network, that is, p=0, then
p p(m) p(m) Cij,l Cij,l . Moreover, Cij,l the cost of transportation at current costs per unit volume of transportation. And vice www.tjprc.org SCOPUS Indexed Journal [email protected] 11340 Abdulaziz A. Shermukhamedov* & Abdimurot U. Kuziev
p p(mk) p(mk) versa, if p 0 then Cij,l Cij,l , and Cij,l it will consist of the sum of current costs and capital investments per unit volume.
p Another important aspect in formulating the mathematical model of the problem [3] is a parameter X ij,l that must be optimized to ensure that the cargo flows in the arcs ij do not exceed the permissible value set for each arc of the transport network in accordance with its level of development. This restriction is expressed by various parameters for each type of transport. For example, the level of development of the automobile road network is determined by the categories of
p ma x roads and that is characterized by the maximum possible number of vehicles Dij traveling per day for each category ij of road sections. To characterize this restriction in the model, it is necessary to go from the parameter of the cargo flow to the parameter of the maximum number of vehicles . This transition can be expressed by the following expression:
1 p p , X ij,l p Kij Dc qij
p where qij is the average carrying capacity of vehicles passing through the arc ij at the p - th level of
p development, t; Kij a coefficient reflecting the proportion of non-freight vehicles in the stream of transport passing through this section; Dc calendar days.
p max The restriction of cargo flows for arcs of railway transport is characterized by the parameter Qij , the maximum throughput of this section per day. Due to various restrictions on cargo flows in arcs of various transport networks, the arcs of IJ territory must be divided into local arcs for each type of transport, that is, into - IJ AR arcs of highways (automobile roads) and IJ RW - arcs of railways. Thus, the statement of the problem and the mathematical model are as follows: determine non-negative freight X ij,l flows through the inter-node arcs ij in the territory of the economic zone, i.e.
p Xij,l 0, ij IJ , (1)
at the same time, the intensity of the flow passing through the arcs of the highways (automobile roads) should not exceed the maximum throughput of the traffic flow in this section, i.e.
k 1 p p p max ; (2) X ij,l p Kij Dij ,ij IJ AR l1 Dc qij
The cargo flow for all types of goods transported along all the arcs of the railway network should not exceed the
p max maximum throughput of the cargo flow through this section Qij :
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k p p X ij,l Qij , ij IJ RW ; (3) l 1
The volume of flows sent from the departure node along all arcs is equal to the volume of flows received at the arrival node
i 1,2,. .. ,n; ai bj (4) i j j 1,2,. .. ,m;
where i = 1,2, ..., n - for each node and l = 1,2, ..., k - for each cargo;
ai,if ,i S; (5) X ij,l X ji,l 0,if ,i S,t; j l j l b j ,if ,i t.
current (FC) or full (FF) costs of territorial freight transportation are minimal.
p(m) FC Cij,l X ij,l MIN . (6) ij l
p(mk) FF Cij,l X ij,l MIN . (7) ij l
Such a formulation of the problem of the optimal development of the transport network involves expanding the capabilities of the links in existing networks, their reconstruction and the construction of new ones, taking into account various options. At the same time, it is possible to include new lines for various types of transport in the network. In general, a section of any type of transport can be included in the model as a link ij with the corresponding transportation cost. It is only important to find this value correctly.
When solving this problem, specific difficulties arise, the main ones are: a lot of variation and a large dimension; the nonlinear nature of the change in the function of the costs of transporting goods from the volume of freight traffic; the need to solve the problem in dynamics; the difficulty of calculating the cost of transporting goods between comparable modes of transport.
Therefore, it is necessary to solve the problem in a somewhat simplified form. For example, you can reduce the dimension of the problem by averaging some variable parameters: type of cargo; utilization rate of mileage; car loading capacity; type of rolling stock; transportation distance; type of car; the ratio of the empty run of cars to the loaded; the use of wagon capacity and a number of others. Naturally, the values of the selected variables that are averaged should, if possible, have little effect on the optimality of the solution, i.e. this effect on the value of the target functional should be within the permissible error range from the optimal value.
The main reason for the complexity of this task is the non-linearity of the function of transport costs depending on the volume of cargo flows.
The growth of traffic flows in the economic zone requires the development of the capacity of the transport network. The existing capacity of the transport network and its compliance with the required levels is an ever-changing factor. Thus, the task of the optimal development of the transport network is considered a very variable dynamic system. www.tjprc.org SCOPUS Indexed Journal [email protected] 11342 Abdulaziz A. Shermukhamedov* & Abdimurot U. Kuziev
A dynamic system requires the use of dynamic programming methods, which creates additional problems due to its large size. Therefore, it is recommended that the solution of a dynamic problem be considered as a solution of static problems at specific stages of long-term planning (for example, 5,10,15,20 years).
The prospective volume, composition and direction of freight traffic are the most important information for solving the problems of developing a transport network. The composition of the transported cargo determines the possible options for using certain types of transport during transportation. Due to the location of the production, cargo flow parameters are known in advance. To reduce the size of the task, we can assume that the cargo flow is uniform in composition, while the average load capacity is used in the calculations.
Thus, it may not be practical to use accurate computational methods to solve this problem, since the original data can often contain significant errors. In these cases, approximate methods can be more efficient and faster than exact methods. However, the effectiveness of using approximate methods does not reduce the need and importance of developing accurate algorithms. They may be necessary to evaluate the accuracy of approximate methods.
Consider the problem of the optimal distribution of freight traffic on road and rail networks and the development of the transport network of the Surkhandarya region of the Republic of Uzbekistan (figure 1).
а) b)
Figure 1: Map a) and Scheme b) of the Transport Networks of the Surkhandarya Region of Uzbekistan: - Railways; Automobeli Roads: - International, - Republican, - Various
As noted, the search for a rational option for the transport network is carried out by optimizing flows on the extended network. The source data for solving the distribution of cargo flows are the transport network and the size of traffic. The size of transportation can be set either by the volumes of production and consumption of each homogeneous cargo at specific points or by the transportation plan for the sum of all goods in the form of cargo transportation, where data is displayed for each point of the sender and recipient.
The task is posed as follows. It is required for as short a time as possible to approximately distribute the flows over the network with the simultaneous receipt of the “density” of movement on each arc. In this case, it is necessary to
Impact Factor (JCC): 8.8746 SCOPUS Indexed Journal NAAS Rating: 3.11 Solution of The Problem of Optimal Distribution of Cargo Flows in 11343 the Region and the Development of its Transport Network fulfill the following criterion (minimization of the functional) [14]:
m F Cij Xij or F Cst X st min. ij st
The idea of this method is as follows. A tree of profitable paths is built, the throughput of the route is determined
St , i.e. (S,...i, j...t) as dst mindij . ij
When sending (distributing) the next cargo Xst along the most advantageous arc, the throughput of the arcs is reduced by this value at the same time. With full satisfaction, the arc closes and is excluded from further consideration. After each arc closure, a new tree of profitable paths is built.
In the process of solving the problem, the characteristic of the arcs connecting the settlements (nodes) in the transport network is distributed over the sections and the passage of the cargo flow (transport) through the shortest arcs is ensured. The block diagram of the algorithm for the approximate distribution of cargo flows is shown in Figure 2 [14].
The compiled unified transport multi-network and cargo transportation matrix were the initial information for solving the problem of developing the transport network of the Surkhandarya region. It should be noted that the constructed initial multi-network can also be used to solve the problems of developing a transport network for a more distant future (2030, 2040, 2050 etc.), for which it is enough to compose the corresponding matrices.
3. RESULTS
Cargo flows were optimized using the approximate method of traffic distribution taking into account capacity limitations.
The software implementation of this algorithm is based on the algorithmic language Pascal [15].
The program consists of the following main blocks:
Block for describing variables and source data used in the program for calculations and outputting results;
Block for specifying the source data;
Block search for ways of minimum cost on a given transport network;
Block distribution of cargo flow on the path of minimum cost, followed by adjusting the capacity of the network arcs;
Block introducing new arcs to solve the problem of rational development of the transport network;
Block issuing calculation results.
Block for the Description of Variables and Source Data
This block describes the variables necessary for the program to work, and the variables used to display the calculation results. In addition, the initial data describing the number of network nodes, communication between network nodes, throughput capacity of arcs, the cost of transshipment of cargo at a railway station and the transportation of cargo on each individual arc are described.
Block for Specifying the Source Data www.tjprc.org SCOPUS Indexed Journal [email protected] 11344 Abdulaziz A. Shermukhamedov* & Abdimurot U. Kuziev
The main source data for the program are:
N is the number of network nodes;
K is the number of corresponding network nodes;
MAP [1. N, 1. N] - a matrix describing the direct connection between two network nodes by setting the appropriate freight cost;
D [1. N, 1. N] - a matrix used to set the bandwidth of the network arcs;
MK [1. K, 1. K] - a matrix used to set the values of flows between the corresponding nodes of the network.
Input of the initial data is carried out in the program editing mode.
Figure 2: Flowchart for the Approximate Distribution of Cargo Flows.
Block Search Paths of Minimum Cost on a Given Transport Network
This block is implemented on the basis of the well-known Dijkstra's algorithm, known from the literature [7], as an algorithm for searching for shortest circuits.
Impact Factor (JCC): 8.8746 SCOPUS Indexed Journal NAAS Rating: 3.11 Solution of The Problem of Optimal Distribution of Cargo Flows in 11345 the Region and the Development of its Transport Network The algorithm for finding the minimum cost paths is implemented as a separate STEP procedure, which is accessed from the main part of the program.
Block Distribution of Cargo Flow
This block distributes the cargo flow along the minimum cost path connecting the two corresponding network nodes. By the distribution of cargo flow is meant the transportation of a certain amount of cargo along a selected route, which is carried out in the program by taking into account the used capacity of each arc of the route and adjusting the correspondence matrix making up this route.
Block Introducing new ARCS to Solve the Problem of Rational Development of the Transport Network
In this block, the introduction of new arcs between two adjacent nodes of the network is organized when the capacity of the original arcs is exhausted. Thus, various options for the development of the transport network are considered.
Block for Issuing Calculation Results
The operators of this unit fix individual results of calculations, then calculate integrated indicators and display them on a monitor screen and print them as a separate file, convenient for analyzing the results.
The main output results are:
The numbers of the corresponding nodes, between which the search for the path of minimum cost;
The number and numbers of nodes included in the search path;
Minimum bandwidth;
The cost of transportation along this route;
The value of the distributed cargo flow;
The presence of the remainder or the fact of exhaustion of the throughput of a separate arc included in the path;
The output of the value of the optimized functional at the end of the distribution of the entire specified cargo flow on the network or the exhaustion of the network bandwidth.
The problem of distribution of cargo flow in a regional multimodal network using the proposed computer program is considered. At the first stage, in order to verify the correctness of the initial information, to clarify the bottlenecks of transportation without restrictions on throughput, several options for the distribution of transportation on a multimodal network were decided, including taking into account the growth in traffic volumes. At the same time, the functional amounted to F = 1099777 thousand Uzbek soums. An analysis of the results of the decision showed that some sections have an additional rolling estimate, i.e. additional costs due to lack of road capacity. The value of the rolling estimate characterizes the cost overrun for a round trip, therefore, the larger it is, the greater the cost overrun per unit; It is necessary to increase the throughput first of all for arcs with a rolling estimate. As a result, an additional path with a higher level of development is provided for this condition. At the same time, the cost of transportation increases due to the high likelihood of movement between adjacent points on a round trip and the solution to the flow distribution process may not be optimal.
The next step in solving the traffic distribution in the multimodal network carried out in descending order (decrease) in distance of transportation, that is, the shortest distance transport to the movement of road transport. www.tjprc.org SCOPUS Indexed Journal [email protected] 11346 Abdulaziz A. Shermukhamedov* & Abdimurot U. Kuziev
4. DISCUSSION AND CONCLUSIONS
At the same time, the functional amounted to F = 893602 thousand Uzbek soums. This will reduce the cost of transportation by 19.7%. Based on the analysis of the results of the distribution of cargo, the following conclusions were made:
It is better to use road transport to develop the freight flows of the region in question.
It was found that the regional road network has the capacity to meet the growing flow of goods: the districts of Kumkurgan-Shurchi, Shurchi-Denov, Denau-Sariasiya. Therefore, it is necessary to gradually expand and reconstruct road sections of the road network.
It is advisable to transport goods at enterprises directly connected with the Termez-Sariasia, Termez-Denau railway, by rail, since the cost of transportation is low, and this measure reduces traffic flows in these congested sections.
Transit traffic from the Surkhandarya region to the Republic of Tajikistan is carried out mainly along the Darband-Sherabad-Denov route. If the Darband-Baysun-Denov route is laid, the distance will be reduced to 85.6 km, which will increase the transit potential.
The Darband-Baysun-Denov highway is suitable not only for transit goods, but also for traffic flows in the areas of Shurchi, Denau, Altynsay, Sariasia and Uzun. To do this, it is necessary to reconstruct this section of the road as a 4- lane (category 1).
Automobile vehicles allow door-to-door cargo transportation. At the same time, the process of loading and unloading goods required for a mixed transport system does not occur. Studies have shown that for domestic transport in the area under consideration and for transporting small agricultural goods through the region, motor vehicles should be used. In addition, small production enterprises, firms and farms are currently being created, which further increases the demand for small volumes of traffic. Thus, it is necessary to gradually develop road transport and road transport networks in the region.
Transportation of large volumes of household goods transported to and from the region by the Tashguzar-Baysun- Kumkurgan railway is cheaper and easier than road transport.
Also, from the analysis of the results, it was found out at which railway stations it is better to unload goods arriving from other regions of the republic, to reload them by road for the purpose of delivery to their destination. For example:
• Darband railway station for goods in the Angora and Sherabad regions;
• Boysunsky railway station for the Altinsay region of freight traffic;
• Tangimush railway station is convenient for luggage in the Kyzyryk region.
Thus, a mathematical model and methods for solving the problem of the optimal distribution of cargo flows in the region under consideration by types of ground transport and transport networks are proposed. A feature of this method of solution is that the distribution of freight flows and the development plan for transport networks were obtained with the joint and coordinated participation of modes of transport and transport networks.
Impact Factor (JCC): 8.8746 SCOPUS Indexed Journal NAAS Rating: 3.11 Solution of The Problem of Optimal Distribution of Cargo Flows in 11347 the Region and the Development of its Transport Network At the final stage of making a decision on the problem of optimizing freight traffic, areas where road capacity should be increased will be identified, and promising freight traffic for the road and rail networks will be determined.
According to the study, the following conclusions were made about the development of the road network in the region (table I):
Table I: Stages and Length of the Existing Road Network № Stages of Development Length, km № Stages of Development Length, km 1 IIAL-IAC 115 4 IIIT-IIAL 72 2 IIIAL-IAC 67 5 IVLT-IIIAL 23 3 IIIAL-IIAC 39 6 IVT-IVAL 24 Notes: technical categories of the road: I, II, III, IV; types of coatings: AC-advanced capital, AL-advanced lightweight,LT-lightweight transitional, T-transitional.
Using the results of this study makes it possible to plan and design promising transport road and rail networks.
The development of the transport network will be carried out in accordance with the operational condition of the roads. This will allow rational distribution of capital resources for the development of the regional transport network.
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