A priori parallel machines scheduling

We address the probabilistic generalization of weighted flow time on parallel machines. We present some results for situations which ask for “long-term robust” schedules of n jobs (tasks) on m parallel machines (processors): on any given day, only a random subset of jobs needs to be processed. The goal is to design robust a priori schedules (before we know which jobs need to be processed) which, on a long-term horizon, are optimal (or near optimal) with respect to total weighted flow time. The originality of this work is that probabilities are explicitly associated with data such that further classical properties of a task (processing time and weight) we consider a probability of presence. After motivating this investigation we analyze the computational complexity, analytical properties, and solution procedures for these problems. Special care is also devoted to assess experimentally the performance of a priori strategies.