This paper deals with the problem of controlling the selection rates of the pooled customer of a single commodity inventory system with postponed demands. The demands arrive according to a Poisson process. The maximum inventory level is fixed at . The ordering policy is policy that is as and when the inventory level drops to an order for items is placed. The ordered items are received after a random time, which is distributed as exponential. We assume that the demands that occur during stock out period either enter a pool of finite size or leave the system according to a Bernoulli distribution. Whenever the on-hand inventory level is positive, customers are selected one-by-one and the selection rate can be chosen from a given set. The problem is to determine a decision rule that specifies the rate of these selections as a function of the on-hand inventory level and the number of customers waiting in the pool at each instant of time to minimise the long-run total expected cost rate. The problem is modelled as a semi-Markov decision problem. The optimal policy is computed using Linear Programming algorithm and the results are illustrated numerically.
Accepté le :
DOI : 10.1051/ro/2015021
Mots-clés : Inventory control, semi-Markov decision process, Postponed demands
@article{RO_2016__50_1_145_0,
author = {Chitra Devi, P. and Sivakumar, B. and Krishnamoorthy, A.},
title = {Optimal {Control} {Policy} of an {Inventory} {System} with {Postponed} {Demand}},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {145--155},
publisher = {EDP-Sciences},
volume = {50},
number = {1},
year = {2016},
doi = {10.1051/ro/2015021},
zbl = {1333.90007},
mrnumber = {3460668},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ro/2015021/}
}
TY - JOUR AU - Chitra Devi, P. AU - Sivakumar, B. AU - Krishnamoorthy, A. TI - Optimal Control Policy of an Inventory System with Postponed Demand JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 145 EP - 155 VL - 50 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2015021/ DO - 10.1051/ro/2015021 LA - en ID - RO_2016__50_1_145_0 ER -
%0 Journal Article %A Chitra Devi, P. %A Sivakumar, B. %A Krishnamoorthy, A. %T Optimal Control Policy of an Inventory System with Postponed Demand %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 145-155 %V 50 %N 1 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2015021/ %R 10.1051/ro/2015021 %G en %F RO_2016__50_1_145_0
Chitra Devi, P.; Sivakumar, B.; Krishnamoorthy, A. Optimal Control Policy of an Inventory System with Postponed Demand. RAIRO - Operations Research - Recherche Opérationnelle, Tome 50 (2016) no. 1, pp. 145-155. doi : 10.1051/ro/2015021. http://www.numdam.org/articles/10.1051/ro/2015021/
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