Parameterized Multi-Scenario Single-Machine Scheduling Problems

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.