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Approximation algorithms for optimal purchase/inventory policy when purchase price and demand are stochastic

Berling, Peter LU and Xie, Zhixue (2014) In OR Spectrum: Quantitative Approaches in Management 36(4). p.1077-1095
Abstract
We consider a purchase/inventory control problem in which the purchase price and demand are stochastic, a common situation encountered by firms that replenish in a foreign currency or from commodity markets. More specifically, we assume that the demand follows a Poisson arrival process and that the log-price evolves according to a general Wiener process. Under these circumstances, the optimal policy is a state dependent base-stock policy that can be described as a series of threshold prices. An iterative procedure for determining the optimal thresholds has been derived earlier but, even for the simplest price process, the solution quickly becomes numerically intractable. To deal with this, we propose an approximation that allows us to... (More)
We consider a purchase/inventory control problem in which the purchase price and demand are stochastic, a common situation encountered by firms that replenish in a foreign currency or from commodity markets. More specifically, we assume that the demand follows a Poisson arrival process and that the log-price evolves according to a general Wiener process. Under these circumstances, the optimal policy is a state dependent base-stock policy that can be described as a series of threshold prices. An iterative procedure for determining the optimal thresholds has been derived earlier but, even for the simplest price process, the solution quickly becomes numerically intractable. To deal with this, we propose an approximation that allows us to derive simple heuristics for finding thresholds that are close to optimal. For certain price processes the heuristics are just a series of closed-form expressions. The computational complexity is reduced significantly, and the numerical study shows that the new heuristics perform considerably better than earlier suggested heuristics. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Stochastic purchase price, Inventory control, Approximation algorithms, Base-stock levels
in
OR Spectrum: Quantitative Approaches in Management
volume
36
issue
4
pages
1077 - 1095
publisher
Springer
external identifiers
  • wos:000342206700010
  • scopus:84907686852
ISSN
1436-6304
DOI
10.1007/s00291-014-0369-4
language
English
LU publication?
yes
id
3560f954-ace8-4251-af45-5a11cd115cdd (old id 4699706)
date added to LUP
2014-10-23 07:54:38
date last changed
2017-03-12 03:19:15
@article{3560f954-ace8-4251-af45-5a11cd115cdd,
  abstract     = {We consider a purchase/inventory control problem in which the purchase price and demand are stochastic, a common situation encountered by firms that replenish in a foreign currency or from commodity markets. More specifically, we assume that the demand follows a Poisson arrival process and that the log-price evolves according to a general Wiener process. Under these circumstances, the optimal policy is a state dependent base-stock policy that can be described as a series of threshold prices. An iterative procedure for determining the optimal thresholds has been derived earlier but, even for the simplest price process, the solution quickly becomes numerically intractable. To deal with this, we propose an approximation that allows us to derive simple heuristics for finding thresholds that are close to optimal. For certain price processes the heuristics are just a series of closed-form expressions. The computational complexity is reduced significantly, and the numerical study shows that the new heuristics perform considerably better than earlier suggested heuristics.},
  author       = {Berling, Peter and Xie, Zhixue},
  issn         = {1436-6304},
  keyword      = {Stochastic purchase price,Inventory control,Approximation algorithms,Base-stock levels},
  language     = {eng},
  number       = {4},
  pages        = {1077--1095},
  publisher    = {Springer},
  series       = {OR Spectrum: Quantitative Approaches in Management},
  title        = {Approximation algorithms for optimal purchase/inventory policy when purchase price and demand are stochastic},
  url          = {http://dx.doi.org/10.1007/s00291-014-0369-4},
  volume       = {36},
  year         = {2014},
}