Optimal and Heuristic Solutions for the Spare Parts Inventory Control Problem

  • Ibrahim S. Kurtulus


One inventory problem that has not changed much with the advent of supply chains is the control of spare parts which still involves managing a very large number of parts that face erratic demand which occurs far in between. For most items it has not been feasible to establish a control system based on the individual item’s demand history. Hence either the parts have beenbundled into one group as Wagner did and only one demand distribution has been used for all or they have been divided into different groups and group distributions have been used as in Razi. We picked two popular rules by Wagner and extensively tested their performance on data obtained from a Fortune 500 company. Comparisons were made with the optimal solution and optimal cost obtained from our procedure based on the Archibald and Silver’s optimizing algorithm. For some problems with very small mean demand and small average number of demand occurrences, finding the optimal solution required an inordinate amount of CPU time, thus justifying the need to use heuristics.


Optimal Cost Average Inventory Demand Distribution Reorder Point Work Stoppage 
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  1. Adelson RM (1966) Compound Poisson distributions. Oper Res Q 17:73–75CrossRefGoogle Scholar
  2. Archibald BC (1976) Continuous review (s, S) policies for discrete compound poisson demand processes. Unpublished Ph.D. thesis, University of Waterloo, WaterlooGoogle Scholar
  3. Archibald BC, Silver EA (1978) (s, S) policies under continuous review and discrete compound Poisson demand. Manag Sci 24:899–904CrossRefMATHGoogle Scholar
  4. Bartakke MN (1981) A method of spare parts inventory planning. Omega 9:51–58CrossRefGoogle Scholar
  5. Beckmann M (1961) An inventory model for arbitrary interval and quantity distributions of demands. Manag Sci 8:35–37CrossRefGoogle Scholar
  6. Bollapragada S, Morton TE (1999) A simple heuristic for computing nonstationary (s,S) policies. Oper. Res. 47:576–584 CrossRefMATHGoogle Scholar
  7. Croston JD (1972) Forecasting and inventory control for intermittent demands. Oper Res Q 23:289–303CrossRefMATHGoogle Scholar
  8. Dunsmuir WTM, Snyder RD (1989) Control of inventories with intermittent demand. Eur J Oper Res 40:16–21CrossRefMATHMathSciNetGoogle Scholar
  9. Ehrhard R (1979) The power approximation for computing (s, S) inventory policies. Manag Sci 25:777–786CrossRefGoogle Scholar
  10. Feeney GJ, Sherbrooke CC (1966) The (s-1, s) inventory policy under compound Poisson demand. Manag Sci 12:391–411CrossRefMathSciNetGoogle Scholar
  11. Feller W (1968) An introduction to probability theory and its applications. Wiley, New YorkMATHGoogle Scholar
  12. Gelders LF, Van Looy PM (1978) An inventory policy for slow and fast movers in a petrochemical plant: a case study. J Oper Res Soc 29:867–874MATHGoogle Scholar
  13. Hadley G, Whitin TM (1963) Analysis of inventory control systems. Prentice-Hall, New JerseyGoogle Scholar
  14. Iglehart D (1963) Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Manag Sci 9:259–267CrossRefGoogle Scholar
  15. Kurtulus IS (2004) Programming the (s, S) Archibald–Silver algorithm for the modern day PCs. In: National DSI proceedings, pp 291–296Google Scholar
  16. Peterson DK (1987) The (s, S) inventory model under low demand. Unpublished Ph.D. thesis, University of North Carolina, Chapel HillGoogle Scholar
  17. Peterson DK, Wagner HM, Ehrhardt RA (2000) The (s, S) periodic review inventory model under low mean demand and the impact of constrained reorder points. In: National DSI proceedings, pp 1014–1016Google Scholar
  18. Porteus EL (1985) Numerical comparison of inventory policies for periodic review systems. Oper Res 33:134–152CrossRefMATHMathSciNetGoogle Scholar
  19. Razi M, Kurtulus IS (1997) Development of a spare parts inventory control model for a Fortune 500 company. In: National DSI proceedings, pp 1402–1404Google Scholar
  20. Sani B, Kingsman BG (1997) Selecting the best periodic inventory control and demand forecasting methods for low demand items. J Oper Res Soc 48:700–713MATHGoogle Scholar
  21. Schultz CR (1987) Forecasting and inventory control for sporadic demand under periodic review. J Oper Res Soc 38:453–458MATHGoogle Scholar
  22. Segerstedt A (1994) Inventory control with variation in lead time, especially when demand is intermittent. Int J Prod Econ 35:365–372CrossRefGoogle Scholar
  23. Silver EA, Peterson R (1985) Decision systems for inventory management and production planning, 2nd edn. Wiley, New YorkGoogle Scholar
  24. Veinot AF, Wagner HM (1965) Computing optimal (s, S) inventory policies. Manag Sci 11:525–552CrossRefGoogle Scholar
  25. Vereecke A, Verstraeten P (1994) An inventory management model for an inventory consisting of lumpy items, slow movers, and fast movers. Int J Prod Econ 35:379–389CrossRefGoogle Scholar
  26. Wagner HM (1975) Principles of management science with applications to executive decisions. Prentice Hall, New JerseyMATHGoogle Scholar
  27. Yeh QJ (1997) A practical implementation of gamma distribution to the reordering decision of an inventory control problem. Prod Inventory Manag J 38:51–57Google Scholar
  28. Zheng YS, Federgruen A (1991) Finding optimal (s,S) policies is about as simple as evaluating a single policy. Oper. Res. 39 no.4, pp 654-665CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.School of BusinessVirginia Commonwealth UniversityRichmondUSA

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