A deterministic continuous-time continuous-state inventory model is studied. In the absence of intervention, the level of stock evolves by a process governed by a differential equation. The inventory level is monitored continuously, and can be adjusted upwards at any time. The decision maker can order from several suppliers, each of which charges a different ordering and purchasing cost. The problem of selecting the supplier and the size of the order to minimize the total inventory cost over an infinite planning horizon is formulated as the solution of a quasi-variational inequality (QVI). It is shown that the QVI has a unique solution. This corresponds to a generalized (s, S) policy under amenable conditions, which have been characterized in an earlier work by the present authors. Under the complementary conditions a new type of optimal control policy emerges. This leads to the concept of a hyper-generalized (s, S) policy. The theory behind a policy of this type is exposed.
Keywords: Optimal inventory policy, quasi-variational inequality ($$, $$) policy, generalized ($$, $$) policy, hyper-generalized ($$, $$) policy
@article{RO_2021__55_3_1841_0,
author = {Benkherouf, Lakdere and Gilding, Brian H.},
title = {Optimal policies for a deterministic continuous-time inventory model with several suppliers: a hyper-generalized $(s , S)$\protect\emph{}\protect\emph{} policy},
journal = {RAIRO. Operations Research},
pages = {1841--1863},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {3},
doi = {10.1051/ro/2021080},
mrnumber = {4275485},
zbl = {1468.90009},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021080/}
}
TY - JOUR AU - Benkherouf, Lakdere AU - Gilding, Brian H. TI - Optimal policies for a deterministic continuous-time inventory model with several suppliers: a hyper-generalized $(s , S)$ policy JO - RAIRO. Operations Research PY - 2021 SP - 1841 EP - 1863 VL - 55 IS - 3 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021080/ DO - 10.1051/ro/2021080 LA - en ID - RO_2021__55_3_1841_0 ER -
%0 Journal Article %A Benkherouf, Lakdere %A Gilding, Brian H. %T Optimal policies for a deterministic continuous-time inventory model with several suppliers: a hyper-generalized $(s , S)$ policy %J RAIRO. Operations Research %D 2021 %P 1841-1863 %V 55 %N 3 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021080/ %R 10.1051/ro/2021080 %G en %F RO_2021__55_3_1841_0
Benkherouf, Lakdere; Gilding, Brian H. Optimal policies for a deterministic continuous-time inventory model with several suppliers: a hyper-generalized $(s , S)$ policy. RAIRO. Operations Research, Tome 55 (2021) no. 3, pp. 1841-1863. doi: 10.1051/ro/2021080
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