Annals of Operations Research

, Volume 17, Issue 1, pp 105–118 | Cite as

A model to study the relationship between forecast error, inventory investment, and customer service level in a multiperiod, probabilistic environment

  • Krishnan Srinivasan
  • William S. Duff
Chapter 2 Production Planning And Control


With the advent of Just-In-Time manufacturing strategies, reduction of inventory costs have once again become the focus of all attention. However, efforts to reduce inventory while continuing to live with poor forecasts and unduly high service level requirements, is likely to be futile.

This work uses a dynamic programming approach to establish trade-off curves, tying in forecast error, customer service level, and inventory investment. This work applies to realistic, dynamic settings wherein there is uncertainty associated with demand, and lead time could be fixed or probabilistic. This work further assumes form-free probability distributions and thus avoids errors introduced into the analysis from estimating parameters of the distribution from limited data.


Probability Distribution Dynamic Programming Lead Time Forecast Error Service Level 
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.


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  1. [1]
    J.S. Armstrong, The ombudsman: research on forecasting: A Quarter-Century Review, 1960–1984. Interfaces 16-1 (1986) 89–109.Google Scholar
  2. [2]
    E.V. Denardo,Dynamic Programming: Models and Applications (Prentice-Hall, Inc., Englewood Cliffs, NJ, 1982).Google Scholar
  3. [3]
    S.E. Dreyfus and A.M. Law,The Art and Theory of Dynamic Programming (Academic Press, New York, NY, 1977).Google Scholar
  4. [4]
    D.W. Fogarty and T.R. Hoffman, Customer service, Production and Inventory Management (1st Quarter, 1980).Google Scholar
  5. [5]
    G.K. Groff and L.W. Rue, Reorder point decision rules for service objectives, Production and Inventory Management (2nd Quarter, 1976).Google Scholar
  6. [6]
    F.S. Hillier and G.J. Liberman,Introduction to Operations Research, 4th ed. (Holden-Day, Inc., Oakland, CA: 1969).Google Scholar
  7. [7]
    R.M. Hogarth and S. Makridakis, Forecasting and planning: an evaluation, Management Science 27 (1981) 115–138.Google Scholar
  8. [8]
    G.M. Jenkins, Some practical aspects of forecasting in organizations, Journal of Forecasting, Number 1 (1982).Google Scholar
  9. [9]
    T.S. Lee, E.E. Adam, Jr., Forecasting error evaluation in material requirements planning (MRP) production-inventory systems, Management Science 32 (1986) 1186–1205.Google Scholar
  10. [10]
    C.G. Lumpert and C.C. Vaeck, Projection customer service, Production and Inventory Management (4th Quarter, 1977).Google Scholar
  11. [11]
    S. Makridakis and M. Hibbon, Accuracy of forecasting: an empirical investigation, J. of Royal Statistical Society A, 142 (1979) 97–145.Google Scholar
  12. [12]
    P.G. Moore, The manager's struggles with uncertainty, J. of Royal Statistical Society A, 140 (1977) 129–165.Google Scholar
  13. [13]
    G.L. Nemhauser,Introduction to Dynamic Programming (John Wiley & Sons, Inc., New York, NY: 1966).Google Scholar
  14. [14]
    C. New, Safety stocks for requirements planning, production and Inventory Management (2nd Quarter, 1975).Google Scholar
  15. [15]
    J. Orlicky,Material Requirements Planning (McGraw Hill Book Company, New York, NY, 1975).Google Scholar
  16. [16]
    H. Scarf, K.J. Arrow, S. Karlin and P. Suppes,Mathematical methods in social sciences (Stanford University Press, Stanford, CA: 1960) pp. 196–202.Google Scholar
  17. [17]
    H. Scneider, Effects of service levels on order points or order levels in inventory models, International Journal of Production Research 19(6) (November/December 1981) 615–631.Google Scholar
  18. [18]
    E.A. Silver, Operations research in inventory management: a review and critique, Operations Research 29(4) (July/August 1981) 628–45.Google Scholar
  19. [19]
    R.J. Tersine,Materials Management and Inventory Control Systems (North Holland Publishing Company, 1976).Google Scholar
  20. [20]
    T.E. Vollman, W.L. Berry and D.C. Whybark,Manufacturing Planning and Control Systems (Dow Jones-Irwin, Homewood, IL, 1984).Google Scholar
  21. [21]
    H.M. Wagner, Research portfolio for inventory management and production planning systems, Operations Research 28(3) (May/June 1980) 445–475.Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1989

Authors and Affiliations

  • Krishnan Srinivasan
    • 1
  • William S. Duff
    • 2
  1. 1.Department of Industrial EngineeringNorthern Illinois UniversityDeKalbU.S.A.
  2. 2.Department of Mechanical EngineeringColorado State UniversityFort CollinsU.S.A.

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