Local Search Based Approximation Algorithms for Two-Stage Stochastic Location Problems

• Published in: Approximation and Online Algorithms Vol. 10138; pp. 197 - 209
• Main Authors: Willamowski, Felix J. L., Bley, Andreas
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 01.01.2017; Springer International Publishing
• Series: Lecture Notes in Computer Science
• ISBN: 9783319517407; 3319517406
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-51741-4_16

We present a nested local search algorithm to approximate several variants of metric two-stage stochastic facility location problems. These problems are generalizations of the well-studied metric uncapacitated facility location problem, taking uncertainties in demand values and costs into account. The proposed nested local search procedure uses three facility operations: adding, dropping, and swapping. To the best of our knowledge, this is the first constant-factor local search approximation for two-stage stochastic facility location problems. Besides traditional direct assignments from clients to facilities, we also investigate shared connections via capacitated trees and tours. We obtain the first constant-factor approximation algorithms for both connection types in the setting of two-stage stochastic optimization. Our algorithms admit order-preserving metrics and thus significantly generalize and improve the allowed mutability of the metric in comparison to previous algorithms, which only allow scenario-dependent inflation factors.