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

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6 Citations (SciVal)


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 (Formula presented.) 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.

Original languageEnglish
Pages (from-to)217-239
JournalAnnals of Operations Research
Issue number1-2
Early online date2017 May 30
Publication statusPublished - 2017 Dec

Subject classification (UKÄ)

  • Transport Systems and Logistics
  • Probability Theory and Statistics


  • Inventory
  • Multi-echelon
  • Non-linear backorder cost
  • Sustainability
  • Time window service constraint


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