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EN
An algorithm for optimizing the routes of a set of vehicles used for the collection and removal of municipal solid waste in a metropolis is proposed. The algorithm eliminates the problem of applying heuristic methods for multi-agent optimization, which is NP non-deterministic polynomial-time-hard. The application of the algorithm leads to a guaranteed exact solution. Through the application of restrictions on the carrying capacity of vehicles, the size of the input matrix representing the transport network can be reduced to an adequate size. This process uses statistical information about the filling levels of container waste bins. The algorithm is applied to an example of two megacities. The shortest routes are built for different numbers of points (from 12 to 72) on the route. The dependence of the total mileage on the number of involved vehicles is studied.
EN
The article deals with the problem of increasing the productivity of trucks in the performance of international road freight transportation in Eastern Europe and the European Union. There are restrictions on cabotage transportation (domestic cabotage), as well as time limits for the execution of orders and penalties for the execution of the entire volume of transportation in this case in addition to the restrictions of the European Agreement E/ECE/TRANS/564. The task of optimizing the required number of vehicles, drivers/driving crews, and route configuration was formulated and solved by mathematical programming with time constraints. At the same time, a variable method of organizing the work of drivers on adjacent routes was applied, by which drivers/crews are not assigned to a specific vehicle but are changed after a certain number of work hours. This minimized the non-productive idling of trucks, ensured compliance with the work and rest regulations of drivers, and minimized truck mileage on routes. In contrast to known methods and research results, the problem is solved with a guaranteed achievement of the optimum in an acceptable search time. This result was achieved due to the appropriate formulation of the solution conditions. The results can be applied in the logistic planning of transport processes.
EN
The article deals with the modified Dijkstra’s algorithm of searching the shortest routes between all transport nodes of the road-transport network, which allows presenting the transport problem in the classical matrix form. This makes it possible to apply each of the known methods of optimal transport plans to solve it. The object of study is the transport process of freight transportation on the transport network by routes of international transport corridors. The purpose of the work is to improve the methods of solving the problems of finding the shortest routes on the transport network, including sections of international transport corridors. The research method is the analysis and modeling of freight transportation on road networks. The modified Dijkstra’s algorithm of finding the shortest paths between all nodes of the road-transport network was work out, which allows to represent the transport problem in the classical matrix form, i.e. in the form of a table of connections. This makes it possible to apply each of the known methods of constructing optimal plans of cargo transportation in the table of connections. The software complex based on the developed algorithm was designed in the algorithmic language Delphi, which was tested on the example of a transport problem set in the form of a road network, as well as complex testing and debugging of a computer system to support decision-making on the optimization of freight traffic on Ukrainian and Western Europe transport systems.
EN
This article is devoted to the coordination of single stages of the multimodal delivery process, taking into account the fact that the process is discrete in its content. The tact, which has the content of a time window for performing the operation is used for discrete processes. Due to the fact that multimodal transportation of goods is carried out on a large network, time is one of the most important criteria for their perfection. Two timing criteria are applied in the article, which take into account the fact that the multimodal process must be synchronized and that the transportation of a large group of goods can be carried out in separate parts. An estimation criterion was also applied, which takes into account constant, variable, contingent costs, which are carried out depending on the structure of the process. The goal of the study is to create such multimodal cargo delivery routes that are characterized by the highest level of selection criteria. In contrast to known studies, the dependence of the optimization criteria of the multimodal process on the total volume of cargo delivery was shown. The method of analyzing the transport scheme of multimodal transportation and the corresponding algorithm and computer program were developed. The methodology involves a complete review of all possible route options using three types of continent transport, namely road, rail, and river. The method of structural optimization is applied to the example of a transcontinental transport corridor.
EN
The importance of compliance with the schedule of work of road trains on the highway transport network of the European Union is shown. The possible options for work and rest modes for truck drivers on international routes have been analyzed. A model for optimizing the truck fleet operation plan has been developed. This model has two levels, that is, the general graph contains subgraphs designed with incompatible vertices to determine the active and shortest schedule. Each of the subgraphs reflects alternative routes and schedules of a truck. The model also includes restrictions on the total cycle time and active period duration of available unloading points. To find the shortest schedule, integer programming with a guaranteed optimal solution was applied. Testing of the proposed algorithm was performed for the example of serving orders for international freight transportation between the cities of Ukraine, Poland, and the Czech Republic. The active schedule is based on the criterion of the minimum of the total duration of drivers’ work. The results obtained are valid, consistent with the rules of the European Agreement. They indicate that the choice of the best schedule for a single car on a unitary route is not the best solution for the entire truck fleet and the entire flow of orders.
EN
This study considers the task of planning the routes of multimodal transnational cargo transportation. Due to the extremely long length of such routes, delivery times and costs per cargo unit are extremely important. Delays in various types of transport and in the case of cargo transshipment are associated not only with the growth of cargo flows but also with the inconsistency of vehicle schedules. The purpose of this study is to improve the previously developed methodology for optimizing multimodal cargo transportation, taking into account the need for its application to transnational transport corridors. The content of the formulated network problem is reduced to a modification of the traveling salesman problem with an unknown number of transport points the route should pass through. Such a problem is NP-hard due to the time complexity of the algorithms. A modified algorithm has been developed, according to which the general problem with the number of N points is divided into several subproblems. Transport points are grouped into consecutive subsets that are related by only one non-alternative way of transportation. This way can be any “bottleneck” of the transport network or an artificially created one. Such a decomposition of the problem gives a set of partial solutions, which were combined into the final optimal solution. The obtained solution to the routing problem of multimodal routes takes into account the cyclical schedules of the transport operation and gives a guaranteed exact optimum for calculations performed within the permissible time. In addition to determining the optimal route, the algorithm makes it possible to determine the required number of vehicles and their work schedules depending on the total cargo flow on the route.
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