Preview

Mathematical notes of NEFU

Advanced search

Multistage production-distribution problem

https://doi.org/10.25587/2411-9326-2024-2-99-115

Abstract

The paper presents a new formulation of the production-distribution problem in networks with a complex structure of manufacturing the end product. The paper highlights different features of the problem, including the sequence of procedures for product manufacturing and delivery, taking into account various types of products at one stage, the distinction between a step and a stage. The concepts of "fictitious" and "real" parts (volumes) of product supply from real suppliers were introduced, which made it possible to avoid the use of heuristic methods in solving the problem. The paper presents a technique based on the simplex method for optimizing the production and supply of different types of products at each stage of the production chain, allowing the problem to be solved in one optimization procedure. The results of the study can be useful for planning in complex and multidisciplinary ("network") companies to make economically sound decisions in the field of production chain management.

About the Authors

V. V. Anisimov
Far Eastern State Transport University, Institute of Management, Automation and Telecommunications
Russian Federation

Vladimir V. Anisimov

47 Seryshev Street, Khabarovsk 680021



E. V. Sazanova
Far Eastern State Transport University, Institute of Management, Automation and Telecommunications
Russian Federation

Ekaterina V. Sazanova

47 Seryshev Street, Khabarovsk 680021



References

1. Shapiro J., Supply Chain Modeling, Piter, St. Petersburg (2006).

2. Lakhal S., Martel A., Oral M., and Montreuil B., “Network companies and competitiveness: a framework for analysis,” Eur. J. Oper. Res., 118, No. 2, 278–294 (1999).

3. Thomas D. J. and Griffin P. M., “Coordinated supply chain management,” Eur. J. Oper. Res., 94, No. 1, 1–15 (1996). DOI:10.1016/0377-2217(96)00098-7.

4. Meixell M. J. and Gargeya V. B., “Global supply chain design: A literature review and critique,” Transport. Res. Part E: Logistics Transport. Rev., 41, No. 6, 531–550 (2005). DOI:10.1016/j.tre.2005.06.003.

5. Mula J., Peidro D., Diaz-Madro˜nero M., and Vicens E., “Mathematical programming models for supply chain production and transport planning,” Eur. J. Oper. Res., 204, No. 3, 377–390 (2010).

6. Martel A., “The design of production-distribution networks: a mathematical programming approach,” in: Supply Chain Optimization (J. Geunes, P. M. Pardalos, eds.), pp. 265–305, Springer (2005).

7. Monge G., “Memoire sur la theorie des deblais et des remblais,” in: Hist. de l’Acad. Sci. Paris, pp. 666–704, Imprim. R. (1781).

8. Kantorovich L. V. and Gavurin M. K., “Application of mathematical methods in issues of analyzing cargo flows [in Russian],” in: Problems of Increasing the Efficiency of Transport, pp. 110–138, Izdat. Akad. Nauk SSSR, Moscow; Leningrad (1949).

9. Hitchcock F. L., “The distribution of a product from several sources to numerous localities,” MIT J. Math. Phys., 20, 224–230 (1941).

10. Trius E. B., Problems of Mathematical Programming of Transport Type [in Russian], Sov. Radio, Moscow (1967).

11. Golshtein E. G. and Yudin D. B., Transport-type Linear Programming Problems, Nauka, Moscow (1969).

12. Kuhn H. W., “The Hungarian method for the assignment problem,” Nav. Res. Logist. Q., 2, 83–97 (1955).

13. Ford L. R. and Fulkerrson D. R., “A simple algorithm for finding maximal network flows and an application to the Hitchcock problem,” Can. J. Math., 9, 210–218 (1957).

14. Munkres J., “Algorithms for the assignment and transportation problems,” J. Soc. Ind. Appl. Math., 5, No. 1, 32–38 (1957).

15. Dantzig G. B., “Application of the simplex method to a transportation problem,” in: Activity Analysis of Production and Allocation (T. C. Koopmans, ed.), pp. 359–373, John Wiley and Sons, New York (1951).

16. Alexandrov A. P., Lurie A. L., and Oleinik Yu. A., “Application of computer electronics in operational planning [in Russian],” Avtomob. Transp., No. 6, 31–35 (1959).

17. Lurie A. L., An Algorithm for Solving a Transport Problem by Approximating Conditionally Optimal Plans [in Russian], VINITI, Moscow (1959).

18. Brudno A. L., “Lurie’s method of differential rents for determining the optimal transportation plan [in Russian],” Dokl. Akad. Nauk SSSR, 131, No. 6, 1238–1241 (1960).

19. Orden A., “Transshipment problem,” Manage. Sci., 3, 276–285 (1956).

20. Lugger G. F., Artificial Intelligence: Strategies and Methods for Solving Complex Problems, Williams, Moscow (2004).

21. Arntzen B. C., Brown G. G., Harrison T. P., and Trafton L. L., “Global supply chain management at digital equipment corporation,” Interfaces, 25, 69–93 (1995).

22. Wagner G., Fundamentals of Operations Research, Mir, Moscow (1972). 23. Taha H. A., Introduction to Operations Research, Williams, Moscow (2006).


Review

For citations:


Anisimov V.V., Sazanova E.V. Multistage production-distribution problem. Mathematical notes of NEFU. 2024;31(2):99-115. (In Russ.) https://doi.org/10.25587/2411-9326-2024-2-99-115

Views: 6

JATS XML


Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.


ISSN 2411-9326 (Print)
ISSN 2587-876X (Online)