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

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.