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Quantifying sustainable control of inventory systems with non-linear backorder costs

Author

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  • Lina Johansson

    (Lund University)

  • Fredrik Olsson

    (Lund University)

Abstract

Traditionally, when optimizing base-stock levels in spare parts inventory systems, it is common to base the decisions either on a linear shortage cost or on a certain target fill rate. However, in many practical settings the shortage cost is a non-linear function of the customer waiting time. In particular, there may exist contracts between the spare parts provider and the customer, where the provider is obliged to pay a fixed penalty fee if the spare part is not delivered within a certain time window. We consider a two-echelon inventory system with one central warehouse and multiple local sites. Focusing on spare parts products, we assume continuous review base stock policies. We first consider a fixed backorder cost whenever a customer’s time in backorder exceeds a prescribed time limit, second a general non-linear backorder cost as a function of the customer waiting time, and third a time window service constraint. We show from a sustainability perspective how our model may be used for evaluating the expected $$\hbox {CO}_2$$ CO 2 emissions associated with not satisfying the customer demands on time. Finally, we generalize some known inventory models by deriving exact closed form expressions of inventory level distributions.

Suggested Citation

  • Lina Johansson & Fredrik Olsson, 2017. "Quantifying sustainable control of inventory systems with non-linear backorder costs," Annals of Operations Research, Springer, vol. 259(1), pages 217-239, December.
  • Handle: RePEc:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2542-z
    DOI: 10.1007/s10479-017-2542-z
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    References listed on IDEAS

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    Cited by:

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    3. Straubert, Christian, 2024. "A continuous approximation location-inventory model with exact inventory costs and nonlinear delivery lead time penalties," International Journal of Production Economics, Elsevier, vol. 268(C).
    4. Guanqun Ni, 2023. "An improved online replenishment policy and its competitive ratio analysis for a purchase-to-order seller," Journal of Combinatorial Optimization, Springer, vol. 46(2), pages 1-14, September.
    5. Johansson, Lina & Olsson, Fredrik, 2018. "Age-based inventory control in a multi-echelon system with emergency replenishments," European Journal of Operational Research, Elsevier, vol. 265(3), pages 951-961.
    6. Mahmud Akhter Shareef & Yogesh K. Dwivedi & Rafeed Mahmud & Angela Wright & Mohammad Mahboob Rahman & Hatice Kizgin & Nripendra P. Rana, 2019. "Disaster management in Bangladesh: developing an effective emergency supply chain network," Annals of Operations Research, Springer, vol. 283(1), pages 1463-1487, December.

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