Job shop scheduling with probabilistic durations

Proactive approaches to scheduling take into account information about the execution time uncertainty in forming a schedule. In this paper, we investigate proactive approaches for the job shop scheduling problem where activity durations are random variables. The main contributions are (i) the introduction of the problem of finding probabilistic execution guarantees for difficult scheduling problems; (ii) a method for generating a lower bound on the minimal makespan; (iii) the development of the Monte Carlo approach for evaluating solutions; and (iv) the design and empirical analysis of three solution techniques: An approximately complete technique, found to be computationally feasible only for very small problems, and two techniques based on finding good solutions to a deterministic scheduling problem, which scale to much larger problems.