In a serial inventory system without fixed costs, an echelon base-stock policy is known to be optimal if there is no stockout cost at any stage except the last stage. (This was proved for finite-horizon problems by Clark and Scarf (1960)1 and for infinite-horizon problems by Federgruen and Zipkin (1984)2.)

What is known about the case in which there are non-zero stockout costs at upstream stages? Is an echelon base-stock policy known to be optimal or non-optimal?

Whether or not a base-stock policy is optimal, if we assume such a policy is used, are there algorithms for optimizing the base-stock levels, analogous to those by Clark and Scarf (1960) or Chen and Zheng (1994)3?


[1] Clark, A. J., Scarf, H. (1960). Optimal Policies for a Multi-Echelon Inventory Problem. Management Science. 6(4):475-490.

[2] Federgruen, A., Zipkin, P. (1984). Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model. Operations Research. 32(4):818-836.

[3] Chen, F., Zheng, Y-S. (1994). Lower Bounds for Multi-Echelon Stochastic Inventory Systems. Management Science. 40(11):1426-1443.

  • $\begingroup$ have you checked the reference 'stochastic inventory control' of Evan Porteus? $\endgroup$ – Steven01123581321 Jan 13 at 18:36
  • $\begingroup$ @Steven31415 Not recently, but as I recall, that book doesn't cover much (or anything) about multi-echelon inventory optimization -- only single-stage models. $\endgroup$ – LarrySnyder610 Jan 15 at 1:45

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