Heuristic Solutions for a Class of Stochastic Uncapacitated p-Hub Median Problems

Abstract

In this work, we propose a heuristic procedure for a stochastic version of the uncapacitated r-allocation p-hub median problem with nonstop services. In particular, we assume that the number of hubs to which a terminal can be allocated is bounded from above by r. Additionally, we consider the possibility of shipping traffic directly between terminals (nonstop services). Uncertainty is associated with the traffic to be shipped between nodes and with the transportation costs. If we assume that such uncertainty can be captured by a finite set of scenarios, each of which with a probability known in advance, it is possible to develop a compact formulation for the deterministic equivalent problem. However, even for small instances of the problem, the model becomes too large to be tackled by a general solver. This fact motivates the development of a heuristic procedure, whose starting point is the determination of a feasible solution to every (deterministic) single-scenario problem. These solutions are then embedded into a process based on the path relinking methodology: gradually an initial solution to the overall problem is transformed by the incorporation of attributes from some guiding solutions. In our case, the guiding solutions are those found for the single-scenario problems. We report and discuss the results of the numerical experiments performed using instances randomly generated for the new problem from the well-known CAB and AP data sets.