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**Analyzing the effect of the inventory policy on order and inventory variability with linear control theory.**
*(English)*
Zbl 1109.90049

Summary: We apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.

### MSC:

90B50 | Management decision making, including multiple objectives |

90B05 | Inventory, storage, reservoirs |

### Keywords:

supply chain management; control theory; multi-echelon inventory control; echelon-stock policy; Bullwhip effect
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\textit{K. Hoberg} et al., Eur. J. Oper. Res. 176, No. 3, 1620--1642 (2007; Zbl 1109.90049)

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