Parameterized Multi-Scenario Single-Machine Scheduling Problems Danny Hermelin 1 • George Manoussakis 1 • Michael Pinedo 2 • Dvir Shabtay 1 • Liron Yedidsion 1 Received: 29 April 2019 / Accepted: 16 March 2020 Ó Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract We study a class of multi-scenario single-machine scheduling problems. In this class of problems, we are given a set of scenarios with each one having a different realization of job characteristics. We consider these multi-scenario problems where the scheduling criterion can be any one of the following three: The total weighted completion time, the weighted number of tardy jobs, and the weighted number of jobs completed exactly at their due-date. As all the resulting problems are NP-hard, our analysis focuses on whether any one of the problems becomes tractable when some specific natural parameters are of limited size. The analysis includes the following parameters: The number of jobs with scenario-dependent processing times, the number of jobs with scenario-dependent weights, and the number of different due-dates. Keywords Single machine scheduling  Multi-scenario scheduling  Parameterized complexity  Fixed-parameter tractability  Robust job schedule & Dvir Shabtay dvirs@bgu.ac.il Danny Hermelin hermelin@bgu.ac.il George Manoussakis gomanous@gmail.com Michael Pinedo mpinedo@stern.nyu.edu Liron Yedidsion lirony@bgu.ac.il 1 Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, P.O.B. 653, 8410501 Beer-Sheva, Israel 2 Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012, USA 123 Algorithmica https://doi.org/10.1007/s00453-020-00702-w