## Abstract

The following problem is treated: there are n jobs with given processing times and an interval for each job's starting time. Each job must be processed, without interruption, on any one of an unlimited set of identical machines. A machine may process any job, but no more than one job at any point in time. The authors' objective is to find the starting time of each job such that the number of machines required to process all jobs is minimal. In addition, the assignment of jobs to each machine must be found. An approximate solution procedure for solving the variable job schedule problem (VSP) based on the entropy principle of informational smoothing is given. Also formulated is VSP as a pure integer programming problem and an exact algorithm is provided. This algorithm examines a sequence of feasibility capacitated transportation problems with job splitting elimination side constraints. Computational experience demonstrates the utility of the entropy approach.

Original language | English |
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Pages (from-to) | 68-85 |

Number of pages | 18 |

Journal | Operations Research |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - 1 Jan 1978 |

## ASJC Scopus subject areas

- Computer Science Applications
- Management Science and Operations Research