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**Designing a supply chain network under the risk of disruptions.**
*(English)*
Zbl 1264.90017

Summary: We study a supply chain design problem with the risk of disruptions at facilities. At any point of time, the facilities are subject to various types of disruptions caused by natural disasters, man-made defections, and equipment breakdowns. We formulate the problem as a mixed-integer nonlinear program which maximizes the total profit for the whole system. The model simultaneously determines the number and location of facilities, the subset of customers to serve, the assignment of customers to facilities, and the cycle-order quantities at facilities. In order to obtain near-optimal solutions with reasonable computational requirements for large problem instances, two solution methods based on Lagrangian relaxation and genetic algorithm are developed. The effectiveness of the proposed solution approaches is shown using numerical experiments. The computational results, in addition, demonstrate that the benefits of considering disruptions in the supply chain design model can be significant.

### MSC:

90B06 | Transportation, logistics and supply chain management |

90B50 | Management decision making, including multiple objectives |

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\textit{A. Jabbarzadeh} et al., Math. Probl. Eng. 2012, Article ID 234324, 23 p. (2012; Zbl 1264.90017)

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