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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
Publisher : Department Industrial Engineering, University of Muhammadiyah Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22219/JTIUMM.Vol27.No1.63-82

Abstract

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.