## Abstract

We analyze a two-machine flow-shop scheduling problem in which the job processing times are controllable by the allocation of resources to the job operations and the resources can be used in discrete quantities. We provide a bicriteria analysis of the problem where the first criterion is to maximize the weighted number of just-in-time jobs and the second criterion is to minimize the total resource consumption cost. We prove that although the problem is known to be NP-hard even for constant processing times, a pseudo-polynomial time algorithm for its solution exists. In addition, we show how the pseudo-polynomial time algorithm can be converted into a two-dimensional fully polynomial approximation scheme for finding an approximate Pareto solution.

Original language | English |
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Pages (from-to) | 67-74 |

Number of pages | 8 |

Journal | International Journal of Production Economics |

Volume | 136 |

Issue number | 1 |

DOIs | |

State | Published - 1 Mar 2012 |

## Keywords

- Controllable processing times
- FPTAS
- Flow shop
- Just-in-time scheduling
- Pseudo-polynomial time algorithm
- Resource allocation

## ASJC Scopus subject areas

- Business, Management and Accounting (all)
- Economics and Econometrics
- Management Science and Operations Research
- Industrial and Manufacturing Engineering