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

Johansson, Lina LU and Olsson, Fredrik LU (2017) In Annals of Operations Research 259(1-2). p.217-239
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... (More)

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.

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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Inventory, Multi-echelon, Non-linear backorder cost, Sustainability, Time window service constraint
in
Annals of Operations Research
volume
259
issue
1-2
pages
217 - 239
publisher
Kluwer
external identifiers
  • scopus:85019688860
  • wos:000415729500010
ISSN
0254-5330
DOI
10.1007/s10479-017-2542-z
language
English
LU publication?
yes
id
e12b33bd-33d5-4391-8cd7-5a792fff8871
date added to LUP
2017-06-08 13:33:03
date last changed
2018-02-19 02:41:52
@article{e12b33bd-33d5-4391-8cd7-5a792fff8871,
  abstract     = {<p>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.</p>},
  author       = {Johansson, Lina and Olsson, Fredrik},
  issn         = {0254-5330},
  keyword      = {Inventory,Multi-echelon,Non-linear backorder cost,Sustainability,Time window service constraint},
  language     = {eng},
  number       = {1-2},
  pages        = {217--239},
  publisher    = {Kluwer},
  series       = {Annals of Operations Research},
  title        = {Quantifying sustainable control of inventory systems with non-linear backorder costs},
  url          = {http://dx.doi.org/10.1007/s10479-017-2542-z},
  volume       = {259},
  year         = {2017},
}