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Computing globally optimal (s,S,T) inventory policies


  • Lagodimos, A.G.
  • Christou, I.T.
  • Skouri, K.


We consider a single-echelon inventory installation under the (s,S,T) periodic review ordering policy. Demand is stationary random and, when unsatisfied, is backordered. Under a standard cost structure, we seek to minimize total average cost in all three policy variables; namely, the reorder level s, the order-up-to level S and the review interval T. Considering time to be continuous, we first model average total cost per unit time in terms of the decision variables. We then show that the problem can be decomposed into two simpler sub-problems; namely, the determination of locally optimal solutions in s and S (for any T) and the determination of the optimal T. We establish simple bounds and properties that allow solving both these sub-problems and propose a procedure that guarantees global optimum determination in all policy variables via finite search. Computational results reveal that the usual practice of not treating the review interval as a decision variable may carry severe cost penalties. Moreover, cost differences between (s,S,T) and other standard periodic review policies, including the simple base stock policy, are rather marginal (or even zero), when all policies are globally optimized. We provide a physical interpretation of this behavior and discuss its practical implications.

Suggested Citation

  • Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:5:p:660-671
    DOI: 10.1016/

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    References listed on IDEAS

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    Cited by:

    1. repec:eee:ejores:v:266:y:2018:i:1:p:112-121 is not listed on IDEAS
    2. Avinadav, Tal & Henig, Mordecai I., 2015. "Exact accounting of inventory costs in stochastic periodic-review models," International Journal of Production Economics, Elsevier, vol. 169(C), pages 89-98.
    3. repec:eee:ejores:v:266:y:2018:i:1:p:72-87 is not listed on IDEAS
    4. Rossi, Roberto & Kilic, Onur A. & Tarim, S. Armagan, 2015. "Piecewise linear approximations for the static–dynamic uncertainty strategy in stochastic lot-sizing," Omega, Elsevier, vol. 50(C), pages 126-140.


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