### Abstract

Quadratic approximations to the differential cost-to-go function, which yield linear switching curves, have been extensively studied. In this paper, we provide the solution to the partial differential equations associated with the steady-state joint probability density function of the buffer levels for two part-type, single machine flexible manufacturing systems under a linear switching curve (LSC) policy. When there are more than two part-types, we derive the density functions under a prioritized hedging point (PHP) policy by decomposing the multiple part-type problem into a sequence of single part-type problems. The expressions for the steady-state density functions are independent of the cost function. Therefore, for additive cost functions that are non-linear in the buffer levels, we can compute the optimal PHP policy, or the more general optimal LSC policy for two part-type problems.

Original language | English (US) |
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Pages (from-to) | 3627-3631 |

Number of pages | 5 |

Journal | Proceedings of the American Control Conference |

Volume | 5 |

State | Published - Jan 1 1995 |

Externally published | Yes |

Event | Proceedings of the 1995 American Control Conference. Part 1 (of 6) - Seattle, WA, USA Duration: Jun 21 1995 → Jun 23 1995 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

*Proceedings of the American Control Conference*,

*5*, 3627-3631.