## Abstract

We study a single-machine stochastic scheduling problem with n jobs in which each job has a random processing time and a general stochastic cost function which may include a random due date and weight. The processing times are exponentially distributed whereas the stochastic cost functions and the due dates may follow any distributions. The objective is to minimize the expected sum of the cost functions. We prove that a sequence in an order based on the product of the rate of processing time with the expected cost function is optimal and under certain conditions a sequence with the weighted shortest expected processing time first (WSEPT) structure is optimal. We show that this generalizes previous known results to more general situations. Examples of applications to practical problems are also discussed.

Original language | English |
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Pages (from-to) | 317-332 |

Number of pages | 16 |

Journal | Journal of Global Optimization |

Volume | 31 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 2005 |

Externally published | Yes |

## Keywords

- Due dates
- Exponential processing times
- Single machine
- Stochastic cost functions
- Stochastic scheduling