Game-Theoretic Coordination in a Three-Echelon Vendor Managed Inventory System: A Comparison of Vertical Nash and Stackelberg Games Using the Grey Wolf Optimizer

Abdullah , Fakhrina Fahma
Widodo, Erwin
Maulana, Sri Kurnia Dwi Budi

Jurnal Teknik Industri
Vol. 27 No. 1 (2026): February

This research developed a Vendor Managed Inventory (VMI) model for a three-echelon supply chain consisting of multiple suppliers, one manufacturer, and multiple buyers. The study aimed to optimize total system profit under deterministic demand and industrial constraints. Strategic interactions among actors were modeled using Vertical Nash and Stackelberg game frameworks, and the resulting nonlinear optimization problem was solved using the grey wolf optimizer algorithm. The results indicated that the Vertical Nash game produced higher total profit than the Stackelberg game. Profit distribution reached 6.78% for suppliers, 39.60% for the manufacturer, and 53.62% for buyers under the Vertical Nash game, while the Stackelberg game produced shares of 11.50%, 24.37%, and 64.14%, respectively. These findings demonstrated that decision structure significantly affected system performance and profit allocation in integrated supply chains.