Reactive scheduling of uncertain jobs with maximum time lags

This paper investigates a scheduling problem characterized by uncertain task durations and maximum time lags, a combination that has received little attention in the literature. The problem involves a set of jobs, each comprising a sequence of tasks where the penultimate task has uncertain duration, known only within a given range, and the final tasks are identical across all jobs. There must be no idle time between consecutive tasks of the same job, except for a bounded delay allowed between the penultimate and final tasks, which is consistent across all jobs. Each task requires a subset of renewable resources, and jobs have specific release dates and arrive in real time. The challenge is to determine the starting times of the tasks such that no resource or temporal constraints are violated, regardless of the realized task durations, with the goal of minimizing the total waiting time of the jobs. This problem is particularly relevant to bio-manufacturing applications. We propose a method to iteratively schedule the jobs in polynomial time, ensuring the optimal insertion of each job relative to the already scheduled ones. We also present a comprehensive computational evaluation of the proposed method.