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The Optimal Review Period in a Dynamic Inventory Model

Author

Listed:
  • James Flynn

    (Cleveland State University, Cleveland, Ohio)

  • Stanley Garstka

    (Yale University, New Haven, Connecticut)

Abstract

Consider a single-item, periodic review, infinite-horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one observes the current stock level and orders deliveries for the next T periods, thus incurring a fixed setup cost. The goal is to find a review period T and an ordering policy that minimize the long run expected average cost per period. Flynn and Garstka (Flynn, J., S. Garstka. 1990. A dynamic inventory model with periodic auditing. Opns. Res. 38 1089–1103.) characterize an optimal ordering policy when T is fixed and study a myopic policy whose cost is often close to the optimal cost. This paper covers the problem of selecting T . We prove an optimal review period T * exists, characterize its properties, and present methods for its computation. We also study an approximation to T * based on the myopic policy of our earlier paper and a crude but simple approximation expressing T * in terms of the two-thirds power of the model parameters. Analytic results (where the coefficient of variation of demand is small) and computational experiments suggest both approximations perform well when demands are normal.

Suggested Citation

  • James Flynn & Stanley Garstka, 1997. "The Optimal Review Period in a Dynamic Inventory Model," Operations Research, INFORMS, vol. 45(5), pages 736-750, October.
    • Handle: RePEc:inm:oropre:v:45:y:1997:i:5:p:736-750
    DOI: 10.1287/opre.45.5.736
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    Citations

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    Cited by:

    1. Lian, Zhaotong & Deshmukh, Abhijit & Wang, Jin, 2006. "The optimal frozen period in a dynamic production model," International Journal of Production Economics, Elsevier, vol. 103(2), pages 648-655, October.
    2. Hedenstierna, Carl Philip T. & Disney, Stephen M., 2016. "Inventory performance under staggered deliveries and autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1082-1091.
    3. Chiang, Chi, 2009. "A periodic review replenishment model with a refined delivery scenario," International Journal of Production Economics, Elsevier, vol. 118(1), pages 253-259, March.
    4. James Flynn, 2001. "Selecting review periods for a coordinated multi‐item inventory model with staggered deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 430-449, August.
    5. Hedenstierna, Carl Philip T. & Disney, Stephen M., 2018. "Avoiding the capacity cost trap: Three means of smoothing under cyclical production planning," International Journal of Production Economics, Elsevier, vol. 201(C), pages 149-162.
    6. Flynn, James, 2008. "An effective heuristic for the review period in an inventory model with staggered deliveries and normal demands," European Journal of Operational Research, Elsevier, vol. 186(2), pages 671-680, April.
    7. James Flynn, 2000. "Selecting T for a periodic review inventory model with staggered deliveries," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(4), pages 329-352, June.
    8. Xu, Kefeng & Leung, Mark T., 2009. "Stocking policy in a two-party vendor managed channel with space restrictions," International Journal of Production Economics, Elsevier, vol. 117(2), pages 271-285, February.

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