Semi-Markov decision models for real-time scheduling

Abstract

Abstract We first present a class of real-time scheduling problems and show that these can be formulated as semi-Markov decision problems. Then we discuss two practical difficulties in solving such problems. The first is that the resulting model requires a large amount of data that is difficult to obtain; the second is that the resulting model usually has a state space that is too large for analytic consideration. Finally, we present a non-intrusive ‘knowledge acquisition’ method that identifies the states and transition probabilities that an expert uses in solving these problems. This information is then used in the semi-Markov optimization problem. A circuit board production line is used to demonstrate the feasibility of this method. The size of the state space is reduced from 2035 states to 308 by an empirical procedure. An ‘optimal’ solution is derived based on the model with the reduced state space and estimated transition probabilities. The resulting schedule is significantly better than the one used by the observed expert.