The urgency indices which are used to schedule multiclass production systems are calculated for production flows characterized by M/G/1 dynamics. The calculation of the indices is based on a myopic policy for which the time look-ahead distribution is chosen to be a Gamma distribution with its first two moments matching either those of the waiting time or the busy period distributions of the M/G/1 queue. For a single item, the priority index can also be used to determine the position of an optimal hedging stock. It is shown that only the priority indices obtained from waiting time look-ahead produce consistent results with the optimal values of the hedging obtained in solving directly the optimal control problem for a Markovian dynamics. Additionally, consistency is also guaranteed when the diffusive approximation is used to discuss the heavy traffic regimes.
