Robust location transportation problems under uncertain demands

In robust optimization, the multi-stage context (or dynamic decision-making) assumes that the information is revealed in stages. So, part of the decisions must be taken before knowing the real values of the uncertain parameters, and another part, called recourse decisions, is taken when the information is known. In this paper, we are interested in a robust version of the location transportation problem with an uncertain demand using a 2-stage formulation. The obtained robust formulation is a convex (not linear) program, and we apply a cutting plane algorithm to exactly solve the problem. At each iteration, we have to solve an NP-hard recourse problem in an exact way, which is time-consuming. Here, we go further in the analysis of the recourse problem of the location transportation problem. In particular, we propose a mixed integer program formulation to solve the quadratic recourse problem and we define a tight bound for this reformulation. We present an extensive computation analysis of the 2-stage robust location transportation problem. The proposed tight bound allows us to solve large size instances.