Facility location models are ubiquitously involved in modern transportation and logistics problems. We present new results of three sequential facility-location models that involve (i) competition and probabilistic customer choice, (ii) location prioritization given uncertain budget, and (iii) location-dependent uncertain demand with ambiguously known distribution. For (i), we utilize submodularity and outer approximation to derive valid inequalities used as cuts to efficiently solve an exact mixed-integer nonlinear programming (MINLP) reformulation of the bilevel Stackelberg game. For (ii) and (iii), we derive multi-stage mixed-integer linear programming (MILP) and MINLP formulations based on moment ambiguity sets of unknown distribution of the stochastic demand. We employ the Stochastic Dual Dynamic integer Programming (SDDiP) for solving the multi-stage MILP/MINLP formulations using scenario-tree representations of the uncertainty. Via numerical studies, we show the computational efficacy of our approach as well as managerial insights of the new facility location models.

Joint work with: Shabbir Ahmed, Beste Basciftci, Ruiwei Jiang, Mingyao Qi, and Xian Yu