Volume 56, Number 3, May-June 2022
|Page(s)||1453 - 1490|
|Published online||13 June 2022|
Optimal policies for a deterministic continuous-time inventory model with several suppliers: when a supplier incurs no set-up cost
Department of Mathematics, College of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait (Retired)
* Corresponding author: email@example.com
Accepted: 23 April 2022
The subject is a deterministic continuous-time continuous-state inventory control model. Stock is replenished by ordering from one of a number of suppliers incurring a different cost per item and a different set-up cost. Taking the cost of procurement into account, the objective is to minimize the total discounted cost over an infinite planning horizon. The size of the order that is to be placed and the supplier with which it is to be placed are to be decided. Earlier studies of the problem have relied substantially on the assumption that the set-up cost of every supplier is strictly positive. Removing this restriction calls for a significant modification of the adopted approach. This is realized in the present study. It is shown that there is a stable unique optimal policy of a type that encompasses (s, S) and generalized (s, S) policies. Conditions that are necessary and sufficient for it to reduce to each of these types are established. The case of two suppliers is studied in detail, properties of the solution are investigated, numerical examples illustrating various aspects are included, and the connection with antecedent results is assessed.
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 2022
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