Advertisement

Decision Processes in Continuous Time

  • Martin J. Beckmann
Part of the Ökonometrie und Unternehmensforschung book series (ÖKONOMETRIE, volume 9)

Abstract

Consider a system whose output rate decreases with time until corrective action (maintenance, replacement) is taken. Let

t denote the time elapsed since the last action,

a(t) the output rate

0≦a(t)≦A.

Keywords

Dynamic Program Continuous Time Inventory Level Preventive Maintenance Terminal Condition 
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.

References and Selected Reading to Part Four

  1. Barlow, R. E., F. Proschan, and L. C. Huraen: Mathematical Theory of Reliability. London: Wiley 1965.Google Scholar
  2. Barlow, R. E., and L. Hunter: Optimum Preventive Maintenance Policies. OR 8, 1, 90–100 (1960).CrossRefGoogle Scholar
  3. Beckenbach, E. F. (ed.): Modern Mathematics for the Engineer. 2nd series. New York: McGraw Hill 1961.Google Scholar
  4. Beckmann, M., and R. Muth: An Inventory Policy for a Case of Lagged Delivery. MS 2, 2, 145–155 (1956).Google Scholar
  5. Beckmann, M.: An Inventory Model for Arbitrary Interval and Quantity Distributions of Demand. MS 8, 1, 35–57 (1961).Google Scholar
  6. Bellman, R. E.: Equipment Replacement Policy. SIAM 3, 133–136 (1955).Google Scholar
  7. Bellman, R. E.: Dynamic Programming Ch. XII, 245–282. Princeton: Princeton University Press 1957.Google Scholar
  8. Bellman, R. E.: Some Applications of the Theory of Dynamic Programming. A Review. OR 2, 3, 275–288 (1954).CrossRefGoogle Scholar
  9. Bellman, R. E., I. L. Glicksberg, and O. A. Gross: Some Aspects of the Mathematical Theory of Control Processes. Santa Monica: RAND Corp. R-313, 1958.Google Scholar
  10. Bellman, R. E., and St. E. Dreyfus: Applied Dynamic Programming. Ch. V, 180–206. Princeton: Princeton University Press 1962.Google Scholar
  11. Bellman, R. E.: (ed.): Mathematical Optimization Techniques. Berkeley and Los Angeles: University of California Press 1963.Google Scholar
  12. Bellman, R. E., and R. Kalaba: Dynamic Programming and Modern Control Theory. New York: Academic Press 1965.Google Scholar
  13. Cartaino, T. F., and S. E. Dreyfus: Application of Dynamic Programming to the Airplane Minimum Time-to-climb Problem. Aeronautical Engineering Review 16, 6, 74–77 (1957).Google Scholar
  14. Descamps, R.: Remplacement et Programmation Dynamique. Métra 4, 2, 181–199 (1965).Google Scholar
  15. Dreyfus, S. E.: A Generalized Equipment Replacement Study. SIAM 8, 3, 425–435 (1960).Google Scholar
  16. Dreyfus, S. E.: Dynamic Programming and the Calculus of Variations. New York–London: Academic Press 1965.Google Scholar
  17. Feller, W.: An Introduction to Probability Theory and its Applications. II, p. 178. New York: Wiley 1966.Google Scholar
  18. Jorgenson, D. W., Mccall and Radner: Optimal Replacement Polity. Amsterdam: North Holland Publ. 1967.Google Scholar
  19. Maffei, R. B.: Planning Advertising Expenditures by Dynamic Programming Methods. Management Technology 1, 2, 94–100 (1960).Google Scholar
  20. Meij, J. L.: Depreciation and Replacement Policy. Amsterdam: North Holland Publishing Comp. 1961.Google Scholar
  21. Pontryagin, L. S. et al.: The Mathematical Theory of Optimal Processes. New York: Wiley 1962.Google Scholar
  22. Radner, R., and D. W. Jorgenson: Opportunistic Replacement of a Single Part in the Presence of Several Monitored Parts. RAND Corp., RM–3057–PR, Nov. 1962.Google Scholar
  23. Weiss, G. H.: On the Theory of Replacement of Machinery with a Random Failure Time, NRLQ 3, 279–293 (1956).CrossRefGoogle Scholar
  24. White, D. J.: Optimal Revision Periods, Journal Math. Anal. Appl. 4, 353–365 (1962).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1968

Authors and Affiliations

  • Martin J. Beckmann
    • 1
    • 2
  1. 1.Institut für Ökonometrie und UnternehmensforschungUniversität BonnGermany
  2. 2.Brown UniversityProvidenceUSA

Personalised recommendations