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Mathematics
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7 December 2025

Mathematical Modeling and Optimization of Sustainable Production–Inventory Systems Using Particle Swarm Algorithms

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1
Graduate Institute of Business Administration, Fu Jen Catholic University, New Taipei City 242, Taiwan
2
Department of Information Management, Fu Jen Catholic University, New Taipei City 242, Taiwan
3
Department of Business Administration, Tamkang University, New Taipei City 251, Taiwan
4
Department of Healthcare Administration, Asia Eastern University of Science and Technology, New Taipei City 220, Taiwan
Mathematics2025, 13(24), 3912;https://doi.org/10.3390/math13243912 
(registering DOI)
This article belongs to the Special Issue Modeling and Optimization in Supply Chain Management

Abstract

This research examines a multinational supply chain inventory problem involving one manufacturer and multiple retailers across a range of carbon emission combinations and an incomplete production system. It aims to identify the optimal strategies for material use, production, delivery, replenishment, and pricing to maximize the integrated total profits under various situations. Three particle swarm optimization techniques are used to solve all the models. Numerical examples and sensitivity analyses on parameter changes are provided. The findings indicate that in a multinational supply chain, currency appreciation in individual retailers’ countries decreases their optimal order quantities and the manufacturer’s optimal material purchase quantity, but increases the optimal quantity for other retailers. In summary, this study offers valuable guidance to enterprises and supply chain decision-makers, especially those operating in a multinational framework, aiming to effectively balance carbon reduction and profitability within the context of global trends in carbon emission reduction.

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