Reverse logistics network design with stochastic lead times.

*(English)*Zbl 1113.90023Summary: 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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##### References:

[1] | Guide, V.D.R.; Jayaraman, V.; Srivastava, R.; Benton, W.C., Supply-chain management for recoverable manufacturing systems, Interfaces, 30, 2, 125-142, (2000) |

[2] | Babu BV, Angira R. A differential evolution approach for global optimization of MINLP problems. Proceedings of fourth Asia-Pacific conference on simulated evolution and learning, vol. 2, 2002. p. 880-4. |

[3] | Marianov, V.; ReVelle, C., The queueing maximal availability location problem: a model for the siting of emergency vehicles, European journal of operational research, 93, 110-120, (1996) · Zbl 0912.90195 |

[4] | Marianov, V.; Serra, D., Probabilistic, maximal covering location-allocation models for congested systems, Journal of regional science, 38, 401-424, (1998) |

[5] | Amiri, A., The design of service systems with queueing time cost, workload capacities and backup service, European journal of operational research, 104, 201-217, (1998) · Zbl 0955.90016 |

[6] | Krikke HR. Recovery strategies and reverse logistic network design. Disertation, University of Twente, The Netherlands; 1998. |

[7] | Fleischmann M. Quantitative models for reverse logistics. Disertation, Erasmus University Rotterdam, The Netherlands; 2000. |

[8] | Hopp, W.J.; Spearman, M.L., Factory physics, (2000), McGraw-Hill New York |

[9] | Whitt, W., Approximations for the \(\mathit{GI} / G / m\) queue, Production and operations management, 2, 2, 114-161, (1993) |

[10] | Shanthikumar, J.G.; Buzacott, J.A., Open queueing network models of dynamic job shops, International journal of production research, 19, 2, 255-266, (1981) |

[11] | Bitran, G.R.; Tirupati, D., Multiproduct queueing networks with deterministic routing: decomposition approach and the notion of interference, Management science, 34, 1, 75-100, (1988) · Zbl 0636.60101 |

[12] | Ryoo, H.S.; Sahinidis, N.V., Global optimization of nonconvex nlps and minlps with applications in process design, Computers & chemical engineering, 19, 5, 551-566, (1995) |

[13] | Ryoo, H.S.; Sahinidis, N.V., A branch-and-reduce approach to global optimization, Journal of global optimization, 8, 2, 107-138, (1996) · Zbl 0856.90103 |

[14] | Adjiman, C.S.; Androulakis, I.P.; Floudas, C.A., Global optimization of MINLP problems in process synthesis and design, Computers & chemical engineering, 21, S445-S450, (1997) |

[15] | Androulakis, I.P.; Maranas, C.D.; Floudas, C.A., Alpha bb: a global optimization method for general constrained nonconvex problems, Journal of global optimization, 7, 3, 337-363, (1995) · Zbl 0846.90087 |

[16] | Kesavan, P.; Barton, P.I., Generalized branch-and-cut framework for mixed-integer nonlinear optimization problems, Computers & chemical engineering, 24, 1361-1366, (2000) |

[17] | Vaidyanathan, R.; El-Halwagi, M., Global optimization of nonconvex minlps by interval analysis, (), 175-193 · Zbl 0874.90141 |

[18] | Westerlund, T.; Skrifvars, H.; Harjunkoski, I.; Pörn, R., An extended cutting plane method for a class of non-convex MINLP problems, Computers & chemical engineering, 22, 3, 357-365, (1998) |

[19] | Storn, R.; Price, K., Differential evolution—a simple end efficient heuristic for global optimization over continuous spaces, Journal of global optimization, 11, 341-359, (1997) · Zbl 0888.90135 |

[20] | Wah, B.W.; Wang, T., Efficient and adaptive Lagrange-multiplier methods for nonlinear continuous global optimization, Journal of global optimization, 14, 1-25, (1999) · Zbl 0917.90278 |

[21] | Rajasekaran, S., On simulated annealing and nested annealing, Journal of global optimization, 16, 43-56, (2000) · Zbl 1112.90383 |

[22] | Mathur, M.; Karale, S.B.; Priye, S.; Jayaraman, V.; Kulkarni, B., Ant colony approach to continuous function optimization, Industrial and engineering chemistry research, 39, 3814-3822, (2000) |

[23] | Chelouah, R.; Siarry, P., Tabu search applied to global optimization, European journal of operational research, 123, 256-270, (2000) · Zbl 0961.90037 |

[24] | Salcedo, R.L., Solving nonconvex nonlinear programming problems with adaptive random search, Industrial & engineering chemistry research, 31, 262, (1992) |

[25] | Price, K.V., An introduction to differential evolution, (), 79-108 |

[26] | Lampinen, J.; Zelinka, I., Mechanical engineering design optimization by differential evolution, (), 127-146 |

[27] | Lambrecht, M.R.; Ivens, P.L.; Vandaele, N.J., ACLIPS: a capacity and lead time integrated procedure for scheduling, Management science, 44, 10, 1548-1561, (1998) · Zbl 0989.90524 |

[28] | Vandaele, N.; Vannieuwenhuyse, I.; Cupers, S., Optimal grouping for a nuclear magnetic resonance scanner by means of an open queueing model, European journal of operational research, 151, 1, 181-192, (2003) · Zbl 1033.90018 |

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