Automation and Remote Control

, Volume 71, Issue 10, pp 2145–2151 | Cite as

Multiindex optimal production planning problems

  • L. G. Afraimovich
  • M. Kh. Prilutskii


We consider production planning problems formalized as optimization problems with a multi-index constraint system of the transport type. These problems arise, for instance, upon constructing a portfolio of orders, master scheduling, etc. We consider computational schemes of solving this problem for different kinds of optimization functions.


Remote Control Planning Problem Computational Step Transport Type Production Planning Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Tanaev, V.S. and Shkurba, V.V., Vvedenie v teoriyu raspisanii (Introduction to Scheduling Theory), Moscow: Nauka, 1975.Google Scholar
  2. 2.
    Tanaev, V.S., Gordon, V.S., and Shafransky, Ya.M., Teoriya raspisanii. Odnostadiinye sistemy (Scheduling Theory. Single-stage Systems), Moscow: Nauka, 1984.Google Scholar
  3. 3.
    Tanaev, V.S., Sotskov, Yu.N., and Strusevich, V.A., Teoriya raspisanii. Mnogostadiinye sistemy (Scheduling Theory. Multi-stage Systems), Moscow: Nauka, 1989.Google Scholar
  4. 4.
    Brucker, P., Scheduling Algorithms, New York: Springer, 1998.zbMATHGoogle Scholar
  5. 5.
    Pinedo, M., Scheduling: Theory, Algorithms, and Systems, New York: Springer, 2008.zbMATHGoogle Scholar
  6. 6.
    Prilutskii, M.Kh., Multicriteria Distribution of a Homogeneous Resource in Hierarchical Systems, Autom. Remote Control, 1996, no. 2, pp. 266–271.Google Scholar
  7. 7.
    Prilutskii, M.Kh. and Vlasov, S.E., Multicriterial Problems of Volume Planning. Lexicographic Schemes, Inform. Tekhnol., 2005, no. 7, pp. 61–66.Google Scholar
  8. 8.
    Afraimovich, L.G. and Prilutskii, M.Kh., Multiindex Resource Distributions for Hierarchical Systems, Autom. Remote Control, 2006, no. 6, pp. 1007–1016.Google Scholar
  9. 9.
    Prilutskii, M.Kh., Multicriteria Multi-index Resource Scheduling Problems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2007, no. 1, pp. 78–82.Google Scholar
  10. 10.
    Prilutskii, M.Kh. and Kostyukov, V.E., Optimization Problems of Volume Calendar Planning for Oil Refineries, Sist. Upravlen. Inform. Tekhnol., 2007, no. 2.1(28), pp. 188–192.Google Scholar
  11. 11.
    Alcaraz, J. and Maroto, C., A Robust Genetic Algorithm for Resource Allocation in Project Scheduling, Ann. Oper. Res., 2001, vol. 102, no. 1–4, pp. 83–109.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hunsaker, B., Kleywegt, A.J, Savelsbergh, M.W.P., and Tovey, C.A., Optimal Online Algorithms for Minimax Resource Scheduling, SIAM J. Discrete Math, 2003, vol. 16, no. 4, pp. 555–590.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Kochetov, Yu.A. and Stolyar, A.A., New Greedy Heuristics for the Calendar Planning Problem with Bounded Resources, Diskret. Anal. Issled. Oper., 2005, vol. 12, no. 1, pp. 12–36.MathSciNetGoogle Scholar
  14. 14.
    Eremeev, A.V., Romanova, A.A., Servakh, V.V., and Chaukhan, S.S., An Approximate Solution for the Delivery Management Problem, Diskret. Anal. Issled. Oper., 2006, vol. 13, no. 3, pp. 27–39.MathSciNetGoogle Scholar
  15. 15.
    Devyaterikova, M.V., Kolokolov, A.A., and Kolosov, A.P., On One Approach to Solving the Discrete Production Planning Problem with Interval Data, in Tr. Inst. Mat. Mekh., 2008, vol. 14, no. 2, pp. 48–57.Google Scholar
  16. 16.
    Galil, Z. and Tardos, E., An Mincost Flow Algorithm, J. ACM, 1988, vol. 35, no. 2, pp. 374–386.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Goldberg, A.V. and Rao, S., Beyond the Flow Decomposition Barrier, J. ACM, 1998, vol. 45, no. 5, pp. 783–797.zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Afraimovich, L.G. and Prilutskii, M.Kh., Searching for the Flow in Infeasible Transportation Networks, Upravlen. Bol’shimi Sist., Moscow: Inst. Probl. Upravlen., 2009, no. 24, pp. 258–280.Google Scholar
  19. 19.
    Agmon, S., The Relaxation Method for Linear Inequalities, Can. J. Math., 1954, vol. 6, no. 3, pp. 382–392.zbMATHMathSciNetGoogle Scholar
  20. 20.
    Motzkin, T.S. and Schoenberg, I.J., The Relaxation Method for Linear Inequalities, Can. J. Math., 1954, vol. 6, no. 3, pp. 393–404.zbMATHMathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • L. G. Afraimovich
    • 1
  • M. Kh. Prilutskii
    • 1
  1. 1.Nizhni Novgorod State UniversityNizhni NovgorodRussia

Personalised recommendations