The Shelter Site Location Problem: Hedging Uncertainty
Bahar Yetiş Kara
Department of Industrial Engineering, Bilkent University
Abstract
In this work we develop a new modeling framework for the shelter site location problem under demand uncertainty. In particular, we propose a maxmin probabilistic programming model that includes two types of probabilistic constraints: one concerning the utilization rate of the selected shelters and the other concerning the capacity of those shelters. By invoking the central limit theorem we are able to obtain an optimization model with a single set of non-linear constraints which, can be approximated using a family of piecewise linear functions. The latter, in turn, can be modeled mathematically using integer variables. Eventually, an approximate model is obtained, which is a mixed integer linear programming model that can be tackled by an off-the-shelf solver. Using the proposed reformulation we are able to solve instances of the problem using data associated with the Kartal district in Istanbul, Turkey. We also consider a large-scale instance of the problem by making use of data for the whole Anatolian side of Istanbul. The results give clear evidence that capturing uncertainty in the shelter site location problem by means of probabilistic constraints may lead to solutions that are much different from those obtained when a deterministic counterpart is considered.
Furthermore, it is possible to observe that the probabilities embedded in the probabilistic constraints have a clear influence in the results, thus supporting the statement that a probabilistic programming modeling framework, if appropriately tuned by a decision maker, can make a full difference when it comes to find good solutions for the problem. We also investigate multi-criteria modeling frameworks for the shelter site location problem. Our results show that, the drawbacks of using only the Rawlsian approach can be smoothed by considering other objectives.
Short Bio
Dr. Bahar Yetis Kara is a Professor in the Department of Industrial Engineering at Bilkent University. Dr. Kara holds an M.S. and Ph.D. degree from Bilkent University Industrial Engineering Department, and she worked as a Postdoctoral Re- searcher at McGill University in Canada.
Dr. Kara holds “Best Dissertation Award” given by INFORMS - UPS-SOLA (2001), TUBAGEBIP
(National Young Researchers Career Development Grant) reward (2008), IAP Young Researchers Award (2009), and TÜBİTAK Young Scientist Incentive Award (2010).
Dr Kara’s current research interests include distribution logistics, humanitarian logistics, hub location and hub network design, and hazardous material logistics. She is currently an associate editor of IIE Transactions. Dr. Kara is also one of the founders and so one of the members of the current executive board of the EURO Working Group on Humanitarian Operations (HOpe).
Venue
Friday, March 2, 2018 at 4.00 pm in IE03