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**Multi-source facility location-allocation and inventory problem.**
*(English)*
Zbl 1205.90178

Summary: We consider a joint facility location-allocation and inventory problem that incorporates multiple sources of warehouses. The problem is motivated by a real situation faced by a multinational applied chemistry company. In this problem, multiple products are produced in several plants. Warehouse can be replenished by several plants together because of capabilities and capacities of plants. Each customer in this problem has stochastic demand and certain amount of safety stock must be maintained in warehouses so as to achieve certain customer service level. The problem is to determine number and locations of warehouses, allocation of customers demand and inventory levels of warehouses. The objective is to minimize the expected total cost with the satisfaction of desired demand weighted average customer lead time and desired cycle service level. The problem is formulated as a mixed integer nonlinear programming model. Utilizing approximation and transformation techniques, we develop an iterative heuristic method for the problem. An experiment study shows that the proposed procedure performs well in comparison with a lower bound.

### MSC:

90B80 | Discrete location and assignment |

90B05 | Inventory, storage, reservoirs |

90C59 | Approximation methods and heuristics in mathematical programming |

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\textit{Z. Yao} et al., Eur. J. Oper. Res. 207, No. 2, 750--762 (2010; Zbl 1205.90178)

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