Automation and Remote Control

, Volume 73, Issue 6, pp 1046–1055 | Cite as

On the calendar planning problem with renewable resource

  • Yu. V. Kovalenko
Computer-Aided Information Control Systems, Process Control Systems


We consider a strongly NP-hard calendar planning problem with constraints on resource consumption and job ordering. One characteristic feature of our problem setting is that resource consumption intensities by different jobs may change during their processing, and resource availability depends on time. To solve the problem, we construct an integer programming model and develop a dynamic programming algorithm. We distinguish a special case of the problem that can be solved in pseudopolynomial time. We show numerical experiments on randomly generated test examples.


Remote Control Planning Horizon Renewable Resource Time Moment Dynamic Programming Algorithm 
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.
    Servakh, V.V., An Efficiently Solvable Case of Calendar Planning Problems with Renewable Resource, Diskret. Anal. Issled. Oper., 2000, ser. 2, vol. 7, no. 1, pp. 75–82.MathSciNetzbMATHGoogle Scholar
  2. 2.
    Garey, M.R. and Johnson, D.S., Complexity Results for Multiprocessor Scheduling under Resource Constraints, SIAM J. Comput., 1975, vol. 4, no. 4, pp. 397–411.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Servah, V.V. and Shcherbinina, T.A., A Fully Polynomial Time Approximation Scheme for Two Project Scheduling Problems, Proc. 12th IFAC Int. Sympos., Dolgui, A., Morel, G., and Pereira, C.E., Eds., Elsevier, 2007, vol. 3, pp. 129–134.Google Scholar
  4. 4.
    Gimadi, E.Kh., Zalyubovskii, V.V., and Sevast’yanov, S.V., Polynomial Solvability of Calendar Planning Problems with Stored Resources and Directive Deadlines, Diskret. Anal. Issled. Oper., 2000, ser. 2, vol. 7, no. 1, pp. 9–34.MathSciNetzbMATHGoogle Scholar
  5. 5.
    Kallrath, J., Borisovsky, P., and Kovalenko, J., Scheduling Using Continuous-Time Formulations, Technical Report, BASF SE, Scientific Computing, 2010.Google Scholar
  6. 6.
    Kovalenko, Yu.V., Solving the Calendar Planning Problem with a Production with Continuous Raw Material Intake, in Youth of the Third Millenium: XXXIV Regional Sci.-Pract. Student Conf., “Phys.-Mat. Sci.” Section Proceedings, Omsk: Omsk. Gos. Univ., 2010, pp. 21–24.Google Scholar
  7. 7.
    Sprecher, A., Kolisch, R., and Drexl, A., Semi-Active, Active, and Non-Delay Schedules for the Resource-Constrained Project Scheduling Problem, Eur. J. Oper. Res., 1995, vol. 80, pp. 94–102.zbMATHCrossRefGoogle Scholar
  8. 8.
    Gimadi, E.Kh. and Glebov, N.I., Diskretnye ekstremal’nye zadachi prinyatiya reshenii (Discrete Extremal Decision Problems), Novosibirsk: Novosib. Gos. Univ., 1991.Google Scholar
  9. 9.
    Garey, M.R. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NP-Completeness, San Francisco: Freeman, 1979. Translation under the title Vychislitel’nye mashiny i trudnoreshaemye zadachi, Moscow: Mir, 1982.zbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  • Yu. V. Kovalenko
    • 1
  1. 1.Dostoevsky Omsk State UniversityOmskRussia

Personalised recommendations