## Abstract

Consideration is given to the problem of minimizing the expected makespan of n jobs with independent exponentially distributed processing times on two parallel machines, under resource constraints. Job j has expected processing time 1/ mu //j and requires throughout its processing an amount r//j of a resource; the total amount of resource available is r. In the case where 1/ mu //1 less than . . . less than 1/ mu //n and r//1 less than . . . less than r//n, authors characterize all the optimal policies in the class of preemptive schedules, and show that the following nonpreemptive policy is optimal: Find the largest k for which r//k plus r//k// minus //1 less than r, and start processing jobs k minus 1,k. Thereafter, at any job completion, start processing on the machine that is freed, the longest job compatible with the job running on the other machine.

Original language | English |
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Pages (from-to) | 883-889 |

Number of pages | 7 |

Journal | Management Science |

Volume | 30 |

Issue number | 7 |

DOIs | |

State | Published - 1984 |

## ASJC Scopus subject areas

- Strategy and Management
- Management Science and Operations Research