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

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.