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Inventory policies for two products under Poisson demand: Interaction between demand substitution, limited storage capacity and replenishment time uncertainty

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  • Apostolos Burnetas
  • Odysseas Kanavetas

Abstract

We consider a two‐product inventory system with independent Poisson demands, limited joint storage capacity and partial demand substitution. Replenishment is performed simultaneously for both products and the replenishment time may be fixed or exponentially distributed. For both cases we develop a Continuous Time Markov Chain model for the inventory levels and derive expressions for the expected profit per unit time. We establish analytic expressions for the profit function and show that it satisfies decreasing differences properties in the order quantities, which allows for a more efficient algorithm to determine the optimal ordering policy. Using computational experiments, we assess the effect of substitution and replenishment time uncertainty on the order quantities and the profit as a function of the storage capacity.

Suggested Citation

  • Apostolos Burnetas & Odysseas Kanavetas, 2018. "Inventory policies for two products under Poisson demand: Interaction between demand substitution, limited storage capacity and replenishment time uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 676-698, December.
    • Handle: RePEc:wly:navres:v:65:y:2018:i:8:p:676-698
    DOI: 10.1002/nav.21788
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    References listed on IDEAS

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    Cited by:

    1. Jian Zhang & Shuang He & Juliang Zhang & T. C. Edwin Cheng, 2020. "Purchase and retrieval competition for seasonal produce," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(3), pages 161-184, April.
    2. Liu, Baolong & Papier, Felix, 2022. "Remanufacturing of multi-component systems with product substitution," European Journal of Operational Research, Elsevier, vol. 301(3), pages 896-911.
    3. He, Shuang & Zhang, Jian & Zhang, Juliang & Cheng, T.C.E., 2022. "Production/inventory competition between firms with fixed-proportions co-production systems," European Journal of Operational Research, Elsevier, vol. 299(2), pages 497-509.

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