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Order-fulfillment performance analysis of an assemble-to-order system with unreliable machines

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  • Gao, Chunyan
  • Shen, Houcai
  • Cheng, T.C.E.

Abstract

We study a multi-item, multiple classes of demand, assemble-to-order system. The inventory of each item is kept at the item level and controlled by the base-stock policy with a finite capacity. Each item is replenished by an independent unreliable machine. Each type of demand arrives according to a Poisson process with an individual rate and requires a subset of the items. When the item requirements of an arriving demand cannot be satisfied entirely, two kinds of stockout may occur, namely total-order-service and partial-order-service. We formulate the system as a queuing network and deduce that it is a quasi-birth-death process. Applying the matrix-geometric solution approach, we derive the exact joint steady-state distribution of on-order inventories, based on which we compute the order-based and item-based the fill rate within a time window and the service level. We present numerical examples to show how system performance varies with changes in system parameters to show the importance of taking machine failures into consideration.

Suggested Citation

  • Gao, Chunyan & Shen, Houcai & Cheng, T.C.E., 2010. "Order-fulfillment performance analysis of an assemble-to-order system with unreliable machines," International Journal of Production Economics, Elsevier, vol. 126(2), pages 341-349, August.
    • Handle: RePEc:eee:proeco:v:126:y:2010:i:2:p:341-349
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    References listed on IDEAS

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    Cited by:

    1. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    2. Atan, Zümbül & Ahmadi, Taher & Stegehuis, Clara & Kok, Ton de & Adan, Ivo, 2017. "Assemble-to-order systems: A review," European Journal of Operational Research, Elsevier, vol. 261(3), pages 866-879.
    3. Cheng, T.C.E. & Gao, Chunyan & Shen, Houcai, 2011. "Production planning and inventory allocation of a single-product assemble-to-order system with failure-prone machines," International Journal of Production Economics, Elsevier, vol. 131(2), pages 604-617, June.
    4. ElHafsi, Mohsen & Fang, Jianxin & Hamouda, Essia, 2020. "A novel decomposition-based method for solving general-product structure assemble-to-order systems," European Journal of Operational Research, Elsevier, vol. 286(1), pages 233-249.
    5. ElHafsi, Mohsen & Fang, Jianxin & Camus, Herve, 2018. "Optimal control of a continuous-time W-configuration assemble-to-order system," European Journal of Operational Research, Elsevier, vol. 267(3), pages 917-932.

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