Abstract: 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.

Bio: Siqian Shen is an Associate Professor of Industrial and Operations Engineering at the University of Michigan and also serves as an Associate Director in the Michigan Institute for Computational Discovery & Engineering (MICDE).