Supply Chain Management

Supply Chain Management

A Robust MINLP Model for Production-Distribution Planning in Three-Echelon Supply Chain

Document Type : Research/ Original/ Regular Article

Authors
1 Ph.D. Students, Industrial Engineering and Systems Optimization, Imam Hossein University, Tehran, Iran.
2 Associate Professor, Imam Hossein University, Tehran, Iran.
3 Ph.D. in Industrial Management (Production and Operations) Islamic Azad University, Roudehen Branch, Tehran, Iran.
4 M.Sc. in Industrial Management (Production and Operations) Islamic Azad University, Tehran North Branch,Tehran, Iran.
Abstract
This research presents a robust optimization model for integrated production-distribution planning in a three-echelon supply chain network comprising suppliers, manufacturers, and distributors. By employing the Bertsimas-Sim robust optimization approach, uncertainties in demand and transportation costs across four transportation modes (road, rail, maritime, and air) are managed to maximize net profit. The proposed Mixed-Integer Nonlinear Programming (MINLP) model is solved using GAMS/BARON version 12.6 optimization software for four uncertainty levels (ρ=0.2, 0.4, 0.6, 0.8) across five randomly generated scenarios. Comparative analysis of deterministic and robust models indicates that the robust model reduces standard deviation by 62 to 65 percent, while only resulting in a 0.75 to 1.79 percent reduction in average profit. Findings demonstrate that the robust model achieves a superior risk-return ratio and improves the coefficient of variation by over 60 percent across all uncertainty levels, making it highly effective for high-uncertainty business environments.
Keywords
Subjects

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Volume 28, Issue 91 - Serial Number 91
Serial number 91. Summer 2026
Summer 2026
Pages 21-37

  • Receive Date 30 October 2025
  • Revise Date 17 December 2025
  • Accept Date 29 July 2026
  • Publish Date 23 August 2026