Volume 55, Number 3, May-June 2021
|Page(s)||1841 - 1863|
|Published online||22 June 2021|
Optimal policies for a deterministic continuous-time inventory model with several suppliers: a hyper-generalized (s, S) policy
Department of Statistics and Operations Research, College of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
2 Department of Mathematics, College of Science, Kuwait University (Retired), P.O. Box 5969, Safat 13060, Kuwait.
* Corresponding author: email@example.com
Accepted: 9 May 2021
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.
Mathematics Subject Classification: 90B05
Key words: Optimal inventory policy / quasi-variational inequality (s, S) policy / generalized (s, S) policy / hyper-generalized (s, S) policy
© The authors. Published by EDP Sciences, ROADEF, SMAI 2021
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