In this paper, we consider a decision-maker who wants to determine a subset of locations from a given set of candidate sites to open facilities and accordingly assign customer demand to these open facilities. Unlike classical facility location settings, we focus on a new setting where customer demand is bimodal, i.e., display, or belong to, two spatially distinct probability distributions. We assume that these two distributions are ambiguous, and only their mean values and ranges are known. Therefore, we construct a scenario-wise ambiguity set with two scenarios corresponding to the demand’s two distinct distributions. Then, we formulate a distributionally robust facility location (DRFL) model that seeks to find the number and locations of facilities to open that minimize the fixed cost of opening facilities and the worst-case (maximum) expectation of transportation and unmet demand costs. We take the worst-case expectations over all possible demand distributions residing in the scenario-wise ambiguity set. We propose a decomposition-based algorithm to solve our min-max DRFL model and derive lower bound inequalities that accelerate the algorithm’s convergence. In a series of numerical experiments, we demonstrate our approach’s superior computational and operational performance compared with the stochastic programming approach and a DR approach that does not consider the demand’s bimodality. Our results draw attention to the need to consider the multi-modality and ambiguity of the demand distribution in many strategic real-world problems.
Shehadeh, K.S., & Sanci, E. (2021). Distributionally Robust Facility Location with Bimodal Random Demand. Computers and Operations ResearchComputers & Operations Research, 134, 105257.