Distributionally robust facility location with bimodal random demand

In this paper, we study a facility location problem in which customer demand is bimodal, i.e., display, or belong to, two spatially distinct distributions. We assume that these two distributions are ambiguous (unknown), and only their mean values and ranges are known.
Therefore, we propose a distributionally robust facility location (DRFL) problem that seeks to find a subset of locations from a given set of candidate sites to open facilities to minimize the fixed cost of opening
facilities, and worst-case (maximum) expected costs of transportation and
unmet demand over a family of distributions characterized through the known means and support of these distributions. We propose a
decomposition-based algorithm to solve DRFL, which include valid lower
bound inequalities to accelerate the convergence of the algorithm. In a
series of numerical experiments, we demonstrate the superior computational and operational performance of our approach as compared with the stochastic programming approach and a DR approach that does not
consider bimodality of the demand. Our results draw attention to the need
to consider the impact of uncertainty of customer demand when it does not
follow one distinct and known distribution in many strategic real-world problems.