A stochastic program based lower bound for assemble-to-order inventory systems.

*(English)*Zbl 1270.90040Summary: We introduce a multi-stage stochastic program that provides a lower bound on the long-run average inventory cost of a general class of assemble-to-order (ATO) inventory systems. The stochastic program also motivates a replenishment policy for these systems. Our lower bound generalizes a previous result of M. K. Doğru et al. [Oper. Res. 58, No. 4, Part 1, 849–864 (2010; Zbl 1231.90026)] for systems with identical component replenishment lead times to those with general deterministic lead times. We provide a set of sufficient conditions under which our replenishment policy, coupled with an allocation policy, attains the lower bound (and is hence optimal). We show that these sufficient conditions hold for two examples, a single product system and a special case of the generalized \(W\) model.

##### Keywords:

assemble-to-order (ATO); inventory; stochastic program; optimal policy; multi-dimensional newsvendor model##### Citations:

Zbl 1231.90026
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\textit{M. I. Reiman} and \textit{Q. Wang}, Oper. Res. Lett. 40, No. 2, 89--95 (2012; Zbl 1270.90040)

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##### References:

[1] | Billingsley, P., Probability and measure, (1979), John Wiley and Sons New York · Zbl 0411.60001 |

[2] | Clark, A.J.; Scarf, H., Optimal policies for a multiechelon inventory problem, Management science, 6, 475-490, (1960) |

[3] | Doğru, M.K.; Reiman, M.I.; Wang, Q., A stochastic programming based inventory policy for assemble-to-order systems with applications to the \(W\) model, Operations research, 58, 849-864, (2010) · Zbl 1231.90026 |

[4] | Harrison, J.M.; van Mieghem, J.A., Multi-resource investment strategies: operational hedging under demand uncertainty, European journal of operational research, 113, 17-29, (1999) · Zbl 0933.91011 |

[5] | Rosling, K., Optimal inventory policies for assembly systems under random demands, Operations research, 37, 565-579, (1989) · Zbl 0677.90025 |

[6] | Song, J.-S.; Zipkin, P., Supply chain operations: assemble-to-order systems, () |

[7] | van Mieghem, J.A.; Rudi, N., Newsvendor networks: inventory management and capacity investment with discretionary activities, Manufacturing & service operations management, 4, 313-335, (2002) |

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