Content

Introduction

At the moment, thanks to the development of Internet technologies and delivery vehicles, obtaining the necessary things is not difficult. For more efficient quick and cost-effective implementation of this work, companies need, among other things, to optimize their logistics operations.

You can optimize almost any element of the transport and logistics system, therefore, the range of work in this area is very wide. [1]

The following is not a complete list of possible optimizations:

  • stock optimization;
  • location selection for logistics facilities;
  • choice of packaging and mode of transport;
  • optimization of the railway infrastructure of the enterprise;
  • selection and optimization of transportation schemes;
  • terminal infrastructure optimization for new market requirements.

1. Topic urgency

The urgency of the problem is expressed in the dynamic development of retail trade and is associated with constantly changing environmental factors and increased competition. Product distribution is a rather complex system, dynamically changing under the influence of internal and external factors having diversification interactions. Thus, the optimization and rationalization of product distribution do not always achieve the highest results, due to the difficulty of obtaining or processing information, the ability to make decisions. The transformation of the logistics systems of goods distribution of retail trade enterprises in recent years has been largely associated with the transformation of relations in the context of elements of the logistics system.

To date, existing software systems are tailored to specific features of enterprises. At the same time, software products are little known, and it is either impossible to find them in the general access or extremely unlikely. However, the products that hit the network are not open source projects, and their functionality either does not correspond to modern platforms, or is limited.

2. Goal and tasks of the research

The aim of the study is to develop and implement a method for solving the problem of supplying products with different conditions.

The main objectives of research:

  1. formalization of supply tasks with advanced functionality, due to various groups of requirements;
  2. analyze existing methods for solving such problems;
  3. develop or improve existing methods for solving the problem and adapt them to the conditions of the problem;
  4. implementation of development in the form of an algorithm in a programming language;
  5. analysis of the results with an assessment of the complexity of the algorithm.

Object of research: models and methods for solving combinatorial optimization problems on graphs associated with deliveries to the distribution network.

Subject of research: speed and functionality of the final software product.

3. The problem of solving NP-complete problems

At the moment, there are many types of tasks related to logistics optimizations in the field of supplying products to retail outlets. They, as a rule, have various meaningful statements and are diverse in terms of mathematical statements.

The tasks of greatest interest, and therefore more studied, relate to classical linear programming problems. For them, the only problem may be the correct formalization and selection of the most suitable methods from the series of quite effective methods available in sufficient numbers to solve any problems, and of a sufficiently large dimension.

Tasks that are combinatorial, optimization or mixed type with elements of combinatorics by their models are mainly NP-complete. The class of NP-complete problems has the following properties [2]:

  • no NP-complete problem can be solved by any polynomial algorithm, despite the persistent efforts of many brilliant researchers;
  • if we could construct a polynomial algorithm for some NP-complete problem, then this would mean the polynomial solvability of each NP-complete problem.

Therefore, methods that solve problems of this type, depending on the requirements, can be effective in various directions and relevant for study, since today they do not have an ideal method and algorithm for solving. In this regard, the question arises of developing sufficiently effective methods that can cope with real tasks and the large data sets that they operate on. More often than not, the basic requirement is speed. This requirement is contrary to the nature and structure of these tasks. This means that the growth rate of solution time with increasing dimension makes them unacceptable for solving real problems. This explains the emergence of a large number of heuristic algorithms for solving optimization problems of combinatorial type, which are focused on obtaining acceptable solutions.

Basically, the various options for setting logistics tasks come down to the traveling salesman problem with additional requirements and restrictions depending on various factors. For example, due to the load limit, it may be necessary to split the graph with the recipient points into subgraphs, which leads to the problem of several traveling salesmen. Also, now, in connection with the development of catering networks, it is becoming important to limit the delivery time to maintain the product and its temperature in the best possible way.

Conclusion

The solution to the problem of optimizing the logistics of freight transportation is relevant: it is widely used in optimizing the functioning of many enterprises and can be used to improve the quality of services and reduce costs. In addition to commercial interest, the solution to this problem attracted the attention of the scientific community, as evidenced by the large number of constantly developing methods for solving it.

Unfortunately, the problem belongs to the class of NP-complete ones; therefore, its exact solution on large data sets in an acceptable time is impossible. By resolving this situation is the implementation of more efficient software, which, sooner or later, will face the problem of performance. The solution is to create heuristic algorithms that do not pursue the goal of finding a global optimum, but a solution that is high enough for a specific application.

The master's thesis analyzes possible ways to optimize existing heuristic methods in order to maximize their speed. Particular attention in the work is focused on optimizing the Clark-Wright algorithm, since it is one of the most efficient for this class of problems and, as a result, popular at the moment.[6]

References

  1. Оптимизация логистики — [Электронный ресурс]. — Режим доступа: https://morproekt.ru/articles/materialy-po-tekhnologii/optimizatsiya-logistiki
  2. Гэри М., Джонсон Д. Вычислительные машины и труднорешаемые задачи. М.: Мир, 1982.
  3. A.H. Land and A.G. Doig. An automatic method of solving discrete programming problems, С. 497-520.
  4. С. Гудман. Введение в разработку и анализ алгоритмов / С. Гудман, С. Хидетниеми. — М. : Мир, 1981.
  5. Макконелл Дж. Основы современных алгоритмов: учебное пособие / Дж. Макконелл; пер. с англ. С.К. Ландо. — [3-е изд.]. — М.: Техносфера, 2004. — 368 c.
  6. Л.Н. Шилин. Эвристический алгоритм как средство оптимизации транспортных потоков предприятия / Л.Н. Шилин, А.А. Навроцкий, Р.В. Козарь // Пятая Международная научно-практическая конференция «BIG DATA and Advanced Analytics. BIG DATA и анализ высокого уровня» — 2019.