## Abstract

We study a problem of scheduling a set of n jobs with unit processing times on a set of m multipurpose machines in which the objective is to minimize the makespan. It is assumed that there are two different job types, where each job type can be processed on a unique subset of machines. We provide an optimal offline algorithm to solve the problem in constant time and an online algorithm with a competitive ratio that equals the lower bound. We show that the worst competitive ratio is obtained for an inclusive job-machine structure in which the first job type can be processed on any of the m machines while the second job type can be processed only on a subset of m/2 machines. Moreover, we show that our online algorithm is 1-competitive if the machines are not flexible, i.e., each machine can process only a single job type.

Original language | English |
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Pages (from-to) | 405-412 |

Number of pages | 8 |

Journal | Computers and Operations Research |

Volume | 39 |

Issue number | 2 |

DOIs | |

State | Published - 1 Feb 2012 |

## Keywords

- Competitive ratio
- Eligibility constraint
- Multipurpose machine scheduling
- Online scheduling

## ASJC Scopus subject areas

- Computer Science (all)
- Modeling and Simulation
- Management Science and Operations Research