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**A coordinated location-inventory model.**
*(English)*
Zbl 1244.90012

Summary: We consider a coordinated location-inventory model where distribution centers (DCs) follow a periodic-review \((R, S)\) inventory policy and system coordination is achieved by choosing review intervals at the DCs from a menu of permissible choices. We introduce two types of coordination: partial coordination where each DC may choose its own review interval from the menu, and full coordination where all the DCs have an identical review interval. While full coordination increases the location and inventory costs, it likely reduces the overall costs of running the system (when the operational costs such as delivery scheduling are taken into account). The problem is to determine the location of the DCs to be opened, the assignment of retailers to DCs, and the inventory policy parameters at the DCs such that the total system-wide cost is minimized. The model is formulated as a nonlinear integer-programming problem and a Lagrangian relaxation algorithm is proposed to solve it. Computational results show that the proposed algorithm is very efficient. The results of our computational experiments and case study suggest that the location and inventory cost increase due to full coordination, when compared to partial coordination, is not significant. Thus, full coordination, while enhancing the practicality of the model, is economically justifiable.

### MSC:

90B05 | Inventory, storage, reservoirs |

90B06 | Transportation, logistics and supply chain management |

90C11 | Mixed integer programming |

90B80 | Discrete location and assignment |

### Keywords:

location-inventory model; risk pooling; periodic-review inventory; coordination; Lagrangian relaxation
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\textit{O. Berman} et al., Eur. J. Oper. Res. 217, No. 3, 500--508 (2012; Zbl 1244.90012)

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