Robust Solution Approach to CLSP Problem with an Uncertain Demand

  • Wilhelm DangelmaierEmail author
  • Ekaterina Kaganova
Conference paper
Part of the Lecture Notes in Production Engineering book series (LNPE)


In this paper, we consider a production planning problem where demand for production is not exactly known, and only its lower and upper bounds are provided. Section 1 comprises an introduction to the production planning field, whereas the detailed problem statement is given in Sect. 2. Modeling aspects are contained within Sect. 3. The mathematical model of capacitated lot-sizing problem (CLSP) was considered as a basis. A demand uncertainty is included into the mathematical model by means of an uncertainty set D, which consists of corresponding demand uncertainty intervals in each planning period. We describe the solution approach in Sect. 4. The robust optimization techniques were chosen for solving, which allowed to construct the solution immunized against uncertainty. A computational example, comparison with the solution from stochastic optimization approach and analysis of obtained results are encompassed in Sect. 5. Conclusions and directions of future research are presented in Sect. 6.


Production planning Demand uncertainty Robust optimization 


  1. 1.
    Karimi, B., Fatemi Ghomi, S.M.T., Wilson, J.M.: The capacitated lot sizing problem: a review of models and algorithms. OMEGA, Int. J. Manag. Sci. 31, 365–378 (2003)CrossRefGoogle Scholar
  2. 2.
    Ho, C.: Evaluating the impact of operating environments on MRP system nervousness. Int. J. Prod. Res. 27, 1115–1135 (1989)CrossRefGoogle Scholar
  3. 3.
    Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.:Global sensitivity analysis. The primer (2008)Google Scholar
  4. 4.
    Shapiro, A.: Stochastic programming approach to optimization under uncertainty. Math. Program. Ser., B 112, 183–220 (2008)Google Scholar
  5. 5.
    Ben-Tal, A., Nemirovski, A.: Robust convex optimization. Math. Oper. Res. 23(4), 769–805 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Beyera, H.G., Sendhoff, B.: Robust optimization—a comprehensive survey. Comput. Methods Appl. Mech. Eng. 196, 3190–3218 (2007)CrossRefGoogle Scholar
  7. 7.
    Quadt, D., Kuhn, H.: Capacitated lot-sizing with extensions: a review. 4OR, 6(1), 61–83 (2008)Google Scholar
  8. 8.
    Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton University Press, Princeton, New Jersey (2009)Google Scholar
  9. 9.
    Rockafellar, R.T.: Convex Analysis, pp. 342–346. Princeton University Press, Princeton, New Jersey (1972)Google Scholar
  10. 10.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge, UK (2005)Google Scholar
  11. 11.
    Krumke, S.: Online Optimization, Competitive Analysis and Beyond. Technical University, Berlin (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of PaderbornPaderbornGermany

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