In this talk, we present two distributionally robust optimization (DRO) models for a mobile facility (MF) fleet sizing, routing, and scheduling problem (MFRSP) with time-dependent and random demand, as well as methodologies for solving these models. Specifically, given a set of MFs, a planning horizon, and a service region, our models aim to find the number of MFs to use (i.e., fleet size) within the planning horizon and a route and time schedule for each MF in the fleet. The objective is to minimize the fixed cost of establishing the MF fleet plus a risk measure (expectation or mean conditional value-at-risk) of the random operational costs over all demand distributions defined by an ambiguity set. In the first model, we use an ambiguity set based on the demand’s mean, support, and mean absolute deviation. In the second model, we use an ambiguity set that incorporates all distributions within a 1-Wasserstein distance from a reference (empirical) distribution. To solve these DRO models, we propose a decomposition-based algorithm. In addition, we derive valid lower bound inequalities that efficiently strengthen the master problem in the decomposition algorithm, thus improving convergence. We also derive two families of symmetry-breaking constraints that improve the solvability of the proposed models. Finally, we present extensive computational experiments comparing the operational and computational performance of the proposed models and a stochastic programming model, demonstrating where significant performance improvements could be gained and derive insights into the MFRSP.

Presenter Bio:
Dr. Karmel S. Shehadeh is an Assistant Professor of Industrial Systems and Engineering (ISE) at Lehigh University. She currently serves as one of the directors of the Operations Research Division at the Institute of Industrial and Systems Engineers. Before joining Lehigh, she was a Presidential and Dean Postdoctoral Fellow at Heinz College of Information Systems and Public Policy at Carnegie Mellon University. She holds a doctoral degree in Industrial and Operations Engineering from the University of Michigan, a master's degree in Systems Science and Industrial Engineering from Binghamton University, and a bachelor's in Biomedical Engineering from Jordan University of Science and Technology.

Shehadeh’s broad methodological research expertise and interests include integer programming, stochastic optimization, and scheduling theory and algorithms development. Her primary application areas and expertise are in healthcare operations and analytics. Her research group is currently working on solving emerging and challenging real-world optimization problems within and outside healthcare operations. These include healthcare scheduling and capacity planning, home care, hospital readmission, facility location, and disaster response operations.