Service Parts Management pp 221-231 | Cite as

# Optimal and Heuristic Solutions for the Spare Parts Inventory Control Problem

## Abstract

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.

## Keywords

Optimal Cost Average Inventory Demand Distribution Reorder Point Work Stoppage## References

- Adelson RM (1966) Compound Poisson distributions. Oper Res Q 17:73–75CrossRefGoogle Scholar
- Archibald BC (1976) Continuous review (s, S) policies for discrete compound poisson demand processes. Unpublished Ph.D. thesis, University of Waterloo, WaterlooGoogle Scholar
- Archibald BC, Silver EA (1978) (s, S) policies under continuous review and discrete compound Poisson demand. Manag Sci 24:899–904CrossRefMATHGoogle Scholar
- Bartakke MN (1981) A method of spare parts inventory planning. Omega 9:51–58CrossRefGoogle Scholar
- Beckmann M (1961) An inventory model for arbitrary interval and quantity distributions of demands. Manag Sci 8:35–37CrossRefGoogle Scholar
- Bollapragada S, Morton TE (1999) A simple heuristic for computing nonstationary (s,S) policies. Oper. Res. 47:576–584 CrossRefMATHGoogle Scholar
- Croston JD (1972) Forecasting and inventory control for intermittent demands. Oper Res Q 23:289–303CrossRefMATHGoogle Scholar
- Dunsmuir WTM, Snyder RD (1989) Control of inventories with intermittent demand. Eur J Oper Res 40:16–21CrossRefMATHMathSciNetGoogle Scholar
- Ehrhard R (1979) The power approximation for computing (s, S) inventory policies. Manag Sci 25:777–786CrossRefGoogle Scholar
- Feeney GJ, Sherbrooke CC (1966) The (s-1, s) inventory policy under compound Poisson demand. Manag Sci 12:391–411CrossRefMathSciNetGoogle Scholar
- Feller W (1968) An introduction to probability theory and its applications. Wiley, New YorkMATHGoogle Scholar
- 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
- Hadley G, Whitin TM (1963) Analysis of inventory control systems. Prentice-Hall, New JerseyGoogle Scholar
- Iglehart D (1963) Optimality of (s, S) policies in the infinite horizon dynamic inventory problem. Manag Sci 9:259–267CrossRefGoogle Scholar
- Kurtulus IS (2004) Programming the (s, S) Archibald–Silver algorithm for the modern day PCs. In: National DSI proceedings, pp 291–296Google Scholar
- Peterson DK (1987) The (s, S) inventory model under low demand. Unpublished Ph.D. thesis, University of North Carolina, Chapel HillGoogle Scholar
- 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
- Porteus EL (1985) Numerical comparison of inventory policies for periodic review systems. Oper Res 33:134–152CrossRefMATHMathSciNetGoogle Scholar
- 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
- 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
- Schultz CR (1987) Forecasting and inventory control for sporadic demand under periodic review. J Oper Res Soc 38:453–458MATHGoogle Scholar
- Segerstedt A (1994) Inventory control with variation in lead time, especially when demand is intermittent. Int J Prod Econ 35:365–372CrossRefGoogle Scholar
- Silver EA, Peterson R (1985) Decision systems for inventory management and production planning, 2nd edn. Wiley, New YorkGoogle Scholar
- Veinot AF, Wagner HM (1965) Computing optimal (s, S) inventory policies. Manag Sci 11:525–552CrossRefGoogle Scholar
- 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
- Wagner HM (1975) Principles of management science with applications to executive decisions. Prentice Hall, New JerseyMATHGoogle Scholar
- 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
- 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