Two types of flexibility are important in manufacturing scheduling in general and in real-time scheduling in particular. The first is flexibility with respect to the criteria that can be considered in the scheduling decisions. The second is flexibility with respect to the trade-off between decision quality and computational burden: that is, the ability to arrive at a solution that makes maximum use of theavailable computational capacity and computation time. This paper describes a procedure which meets the above requirements. The procedure is justified using a theoretical analysis based on probability. Experimental results of the procedure's performance are also presented. The results show that random selection (which is used in the procedure) can play a useful role in the real-time scheduling problem.