Single machine stochastic scheduling to minimize the expected number of tardy jobs using mathematical programming models

This paper studies the single machine scheduling problem for the objective of minimizing the expected number of tardy jobs. Jobs have normally distributed processing times and a common deterministic due date. We develop new approaches for this problem that generate near optimal solutions. The original stochastic problem is transformed into a non-linear integer programming model and its relaxations. Computational study validates their effectiveness by comparison with optimal solutions.