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Modeling and solving the periodic maintenance problem

Modeling and solving the periodic maintenance problem. 指導教授：童超塵 老師 作者： Alexander Grigoriev, Joris van de Klundert, and Frits C.R. Spieksma 出處： European Journal of Operation Research, Vol. 172, pp.783-797, 2006 報告人：陳建旻. Outline. Introduction Modeling PMP Computational results

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Modeling and solving the periodic maintenance problem

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  1. Modeling and solving the periodic maintenance problem 指導教授：童超塵 老師 作者：Alexander Grigoriev, Joris van de Klundert, and Frits C.R. Spieksma 出處：European Journal of Operation Research, Vol. 172, pp.783-797, 2006 報告人：陳建旻

  2. Outline • Introduction • Modeling PMP • Computational results • Conclusions

  3. Introduction 以實務觀點而言，週期性維護間隔時間不宜過長，一般為每年中數天、每年中數星期或每星期中數天。

  4. Modeling PMP (1/5) • 二次規畫(quadratic programming)方程式 變數xi,t與xi,t-1相加為1，當機器i在週期t進行維修時， 將xi,t設為0，PMP以下列方程式呈現： 表示兩台機器不會 同時進行維修

  5. Modeling PMP (2/5) • 將維修成本bi納入考量後，方程式(1)-(5)以下列方程式呈現： 第i台機器在週期t進行維修 yi,t設為1；0 otherwise 單一週期內不會超過 1台機 器進行維修

  6. Modeling PMP (3/5) • 整數規劃(integer programming)方程式 (14)、(15)表示下個週期將有1台機器進行維修

  7. Modeling PMP (4/5) • 方程式(16)以下列方程式替代：

  8. Modeling PMP (5/5) • 集合分割(set-partitioning; SP)方程式 S：維護間隔時間T下的非空子集合 s：維修策略 Cis：實施維修策略s下機器i的總操作成本與維修成本

  9. Computational results (1/5) 資料來源：Anily et al. (1998)

  10. Computational results (2/5)

  11. Computational results (3/5)

  12. Computational results (4/5)

  13. Computational results (5/5)

  14. Conclusions • 本研究主要係以整數線性方程式建構週期性維護問題(PMP)模型。 • 本研究固定維護間隔時間T，以LP為基礎求解方程式。

  15. 報告完畢

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