Balancing profits and planet: a game-theoretic particle swarm optimization for green inventory routing

Abstract

In an era of heightened environmental awareness and increasing energy costs, sustainable logistics has become a critical focus in supply chain management. The Green Inventory Routing Problem (GIRP) extends the classic Inventory Routing Problem (IRP) by integrating environmental objectives—such as minimizing greenhouse gas (GHG) emissions— alongside traditional economic costs. This study proposes a novel Game-Theoretic Particle Swarm Optimization (GT-PSO) algorithm to address the GIRP, conceptualizing the discretization process as a strategic game to transform continuous swarm behavior into discrete logistics decisions. The objective minimizes a weighted cost function of transportation, inventory holding, and carbon emissions, supporting efficient management of material and transport flows. Thirteen benchmark instances representing different logistics network scales were used to evaluate performance against Genetic Algorithm (GA), Simulated Annealing (SA), and the commercial solver Gurobi. Results show that GT-PSO achieves the best-known solutions for medium-and large-sized problems with an average gap below 0.97%. ANOVA tests confirm statistically significant superiority, and coefficient of variation analysis highlights consistent performance. This research contributes an advanced optimization tool for sustainable logistics and distribution systems, helping managers balance economic efficiency with environmental responsibility.