Advertisement

Mathematical Background

  • Konstantin Kogan
  • Eugene Khmelnitsky
Chapter
  • 273 Downloads
Part of the Applied Optimization book series (APOP, volume 43)

Abstract

The methodology suggested in this book is based on three mathematical tools — optimal control, combinatorics and mathematical programming — which are traditionally related to separate areas of research and application. The methodology involves, first, investigating a continuous-time problem with the aid of the maximum principle and then reducing it to a discrete combinatorial or mathematical programming problem solvable in polynomial time. The following sections present selected combinatorics, the maximum principle and a constructive approach for integrating both mathematical tools.

Keywords

Maximum Principle Optimal Control Problem Source Node Planning Horizon Linear Differential Equation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Selected Bibliograghy

  1. Arrow, K.J. and S. Karlin, 1958, “Smooth Production Plans” in Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, pp. 70–85.Google Scholar
  2. Blazewicz, J., K.H. Ecker, E. Pesch, G. Schmidt and J. Weglarz, 1996, Scheduling Computer and Manufacturing Processes, Springer-Verlag.Google Scholar
  3. Bollen, N.P.B., 1999, “Real Options and Product Life Cycles”, Management Science, 45(5), pp. 670–684.CrossRefGoogle Scholar
  4. Bollen, N.P.B., 1999, “Real Options and Product Life Cycles”, Management Science, 45(5), pp. 670–684. Bryson, A.E. and J.Y-C. Ho, 1975, Applied Optimal Control, Hemisphere Publishing Corporation, Washington. Burden, R.L. and J.D. Fares, 1989, Numerical Analysis, PWS-KENT, Boston.Google Scholar
  5. Collatz, L., 1986, Differential Equations: an Introduction with Applications, Wiley, Chichester.Google Scholar
  6. Dubovitsky, A.Y. and A.A. Milyutin, 1981, “Theory of the Maximum Principle” in Methods of Theory of Extremum Problems in Economy, V.L. Levin, ed., Nauka, Moscow, 6–47 (in Russian).Google Scholar
  7. Gershwin, S., 1994, Manufacturing Systems Engineering, Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  8. Gohberg, L P. Lancaster and L. Rodman, 1982, Matrix Polynomials, Academic Press, NY.Google Scholar
  9. Graves S.C. et al. (Eds.), 1993, Handbooks in OR and MS, Elsevier, Amsterdam.Google Scholar
  10. Hartl, R.F., S.P. Sethi and R.G.Vickson, 1995, “A survey of the maximum principles for optimal control problems with state constraints”, SIAM Review, 37(2), 181–218.CrossRefGoogle Scholar
  11. Holt, C.C., F. Modigliani, J.F. Muth, and H.A. Simon, 1960, Planning Production, Inventories and Work Force, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  12. Maimon, O., E. Khmelnitsky and K. Kogan, 1998, Optimal Flow Control in Manufacturing Systems: Production Planning and Scheduling, Kluwer Academic Publishers, Boston.CrossRefGoogle Scholar
  13. Milyutin, A.A., N. Osmolovsky, S. Chukanov and A. Ilyutovich, 1993, Optimal Control in Linear Systems, Nauka, Moscow (in Russian).Google Scholar
  14. Neapolitan, R. and K. Naimipour, 1996, Foundations ofAlgorithms, Heath, Lexington, MA.Google Scholar
  15. Ostwald, P.F., 1974, Cost Estimating for Engineering and Management, Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  16. Pinedo, M., 1995, Scheduling: Theory, Algorithms and Systems, Prentice Hall, Englewood Cliffs, NJ.Google Scholar
  17. Sethi, S.P. and Q., Zhang, 1995, Hierarchical Decision Making in Stochastic Manufacturing Systems, Birkhauser, Boston, MA.Google Scholar
  18. Sethi, S.P., M.I. Taksar and Q. Zhang, 1992, “Capacity and Production Decisions in Stochastic Manufacturing Systems: an Asymptotic Optimal Hierarchical Approach”, Production and Operations Management, 1(4), pp. 367–392.CrossRefGoogle Scholar
  19. Van Trees H.L., 1968, Detection, Estimation and Modulation Theory, Part I, John Wiley&Sons.Google Scholar
  20. Wagner, H.M., and T.M. Whitin, 1958, “A dynamic version of the economic lot size model”, Management Science, 5, pp. 89–96.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Konstantin Kogan
    • 1
  • Eugene Khmelnitsky
    • 2
  1. 1.Department of Computer ScienceCenter for Technological EducationHolonIsrael
  2. 2.Department of Industrial EngineeringTel-Aviv UniversityTel-AvivIsrael

Personalised recommendations