Proactive Algorithms for Job Shop Scheduling with Probabilistic
  Durations
  Most classical scheduling formulations assume a fixed and known duration for
each activity. In this paper, we weaken this assumption, requiring instead that
each duration can be represented by an independent random variable with a known
mean and variance. The best solutions are ones which have a high probability of
achieving a good makespan. We first create a theoretical framework, formally
showing how Monte Carlo simulation can be combined with deterministic
scheduling algorithms to solve this problem. We propose an associated
deterministic scheduling problem whose solution is proved, under certain
conditions, to be a lower bound for the probabilistic problem. We then propose
and investigate a number of techniques for solving such problems based on
combinations of Monte Carlo simulation, solutions to the associated
deterministic problem, and either constraint programming or tabu search. Our
empirical results demonstrate that a combination of the use of the associated
deterministic problem and Monte Carlo simulation results in algorithms that
scale best both in terms of problem size and uncertainty. Further experiments
point to the correlation between the quality of the deterministic solution and
the quality of the probabilistic solution as a major factor responsible for
this success.
