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**Reverse logistics network design with stochastic lead times.**
*(English)*
Zbl 1113.90023

Summary: This work is concerned with the efficient design of a reverse logistics network using an extended version of models currently found in the literature. Those traditional, basic models are formulated as mixed integer linear programs (MILP-model) and determine which facilities to open that minimize the investment, processing, transportation, disposal and penalty costs while supply, demand and capacity constraints are satisfied. However, we show that they can be improved when they are combined with a queueing model because it enables to account for (1) some dynamic aspects like lead time and inventory positions, and (2) the higher degree of uncertainty inherent to reverse logistics. Since this extension introduces nonlinear relationships, the problem is defined as a mixed integer nonlinear program (MINLP-model). Due to this additional complexity, the MINLP-model is presented for a single product-single-level network. Several examples are solved with a genetic algorithm based on the technique of differential evolution.

### MSC:

90B06 | Transportation, logistics and supply chain management |

90B10 | Deterministic network models in operations research |

91B70 | Stochastic models in economics |

90B22 | Queues and service in operations research |

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\textit{K. Lieckens} and \textit{N. Vandaele}, Comput. Oper. Res. 34, No. 2, 395--416 (2007; Zbl 1113.90023)

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