A math-heuristic for the warehouse location-routing problem in disaster relief.

*(English)*Zbl 1348.90119Summary: We consider a problem faced by international aid organizations after the occurrence of a natural disaster. A supply system with intermediate warehouses has to be established to provide affected people with relief goods. A three-objective optimization model with a medium-term economic, a short-term economic, and a humanitarian objective function is used. We apply the epsilon constraint method to determine the Pareto frontier. To solve the single-objective constrained optimization problem, we propose an exact solution method as well as a “math-heuristic” technique building on a MILP formulation with a heuristically generated constraint pool. As a subproblem, the multiple-depot, multiple-trip capacitated team orienteering problem is solved. We present a MIP formulation and a VNS procedure for this problem. Synthetically generated instances and a real-world illustration case are used for our computational studies. The results of the math-heuristic technique are compared to those obtained from an application of the NSGA-II metaheuristic and, where possible, to those of the exact solution approach.

##### MSC:

90B06 | Transportation, logistics and supply chain management |

90B80 | Discrete location and assignment |

90C29 | Multi-objective and goal programming |

90C59 | Approximation methods and heuristics in mathematical programming |

##### Keywords:

humanitarian logistics; warehouse location-routing problem; multi-objective optimization; mathematical programming##### Software:

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\textit{S. Rath} and \textit{W. J. Gutjahr}, Comput. Oper. Res. 42, 25--39 (2014; Zbl 1348.90119)

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##### References:

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