An Inventory Service-Level Optimization Problem for a Multi-Warehouse Supply Chain Network with Stochastic Demands

Roberto León, Pablo A. Miranda-Gonzalez (), Francisco J. Tapia-Ubeda and Elias Olivares-Benitez
Additional contact information
Roberto León: Departamento de Informática, Universidad Técnica Federico Santa María, Santiago 8940897, Chile
Pablo A. Miranda-Gonzalez: Departamento de Ingeniería Industrial, Universidad Católica del Norte, Antofagasta 1270709, Chile
Francisco J. Tapia-Ubeda: Departamento de Ingeniería Industrial, Universidad Católica del Norte, Antofagasta 1270709, Chile
Elias Olivares-Benitez: Facultad de Ingeniería, Universidad Panamericana, Zapopan 45010, Jalisco, Mexico

Mathematics, 2024, vol. 12, issue 16, 1-20

Abstract: This research aims to develop a mathematical model and a solution approach for jointly optimizing a global inventory service level and order sizes for a single-commodity supply chain network with multiple warehouses or distribution centers. The latter face stochastic demands, such as most real-world supply chains do nowadays, yielding significant model complexity. The studied problem is of high relevance for inventory management, inventory location, and supply chain network design-related literature, as well as for logistics and supply chain managers. The proposed optimization model minimizes the total costs associated with cycle inventory, safety stock, and stock-out-related events, considering a global inventory service level and differentiated order sizes for a fixed and known set of warehouses. Subsequently, the model is solved by employing the Newton–Raphson algorithm, which is developed and implemented assuming stochastic demands with a normal approximation. The algorithm reached optimality conditions and the convergence criterion in a few iterations, within less than a second, for a variety of real-world sized instances involving up to 200 warehouses. The model solutions are contrasted with those obtained with a previous widely employed approximation, where safety stock costs were further approximated and order sizes were optimized without considering stock-out-related costs. This comparison denotes valuable benefits without significant additional computational efforts. Thus, the proposed approach is suitable for managers of real-world supply chains, since they would be able to attain system performance improvements by simultaneously optimizing the global inventory service level and order sizes, thereby providing a better system cost equilibrium.

Keywords: supply chain networks; supply chain inventory planning; system inventory service-level optimization; Newton–Raphson (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/16/2544/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/16/2544/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:16:p:2544-:d:1458415

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().