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

Lina Johansson () and Fredrik Olsson ()
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Lina Johansson: Lund University
Fredrik Olsson: Lund University

Annals of Operations Research, 2017, vol. 259, issue 1, No 10, 217-239

Abstract: 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.

Keywords: Inventory; Multi-echelon; Non-linear backorder cost; Time window service constraint; Sustainability (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10479-017-2542-z

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