## Abstract

The paper introduces the finite class of set strategies for stochastic scheduling problems. It is shown that the known stable classes of strategies such as ES and MES strategies are of this type, as are list-scheduling strategies such as LEPT and SEPT and other, more complicated priority-type strategies. Roughly speaking, set strategies are characterized by the fact that the decision as to which jobs should be started at time t depends only on the knowledge of the two sets of jobs finished up to time t and being processed at time t. Contrary to list scheduling strategies, set strategies may involve deliberate idleness of machines, i.e. may not be greedy and can therefore not generally be induced by priority rules. It is demonstrated that set strategies have useful properties. They are e.g. λ^{n}-almost everywhere continuous and therefore show satisfactory stability behaviour w.r.t. weak convergence of the joint distribution of job durations. Furthermore, the optimum w.r.t. all strategies is already attained on this class if job durations are independent and exponentially distributed and the performance measure fulfills a certain shift condition. This shift property is a quite natural concept and generalizes aspects of the notion of additivity in semi-Markov decision theory and stochastic dynamic optimization. Its complete analytical characterization is a major object of this paper. Typical additive cost criteria such as makespan and flowtime are of course covered, which yields simultaneously a first step towards generalization of optimality of LEPT and SEPT rules, as known for special cases. In fact, in view of the obtained optimality result, the question of when deliberate idleness of machines can be avoided, gains considerable interest, as it characterizes stochastic environments in which priority strategies are optimal. This provides a major link with current research on the analysis of networks of queues in the context of computer systems.

Original language | English |
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Pages (from-to) | 65-104 |

Number of pages | 40 |

Journal | Mathematical Methods of Operations Research |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1985 |

Externally published | Yes |

## Keywords

- Additive cost criterion
- ES strategy
- MES strategy
- analytic behaviour of strategies
- list schedule
- priority rule
- quasi-stability
- regular measure of performance
- scheduling problems
- set strategy
- shift property
- stability
- stochastic scheduling

## ASJC Scopus subject areas

- Engineering (all)