Stochastic programming and robust optimization approaches for the product mix problem under uncertainty (case study: lubricant refinery)

Nemati, Mohammadreza; Kargari, Mehrdad; Nikbakhsh, Ehsan

doi:10.22068/ijiepr.37.2.2578

Volume 37, Issue 2 (IJIEPR- In Progress 2026) IJIEPR 2026, 37(2): 108-122 | Back to browse issues page

‎ 10.22068/ijiepr.37.2.2578

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Nemati M, Kargari M, Nikbakhsh E. Stochastic programming and robust optimization approaches for the product mix problem under uncertainty (case study: lubricant refinery). IJIEPR 2026; 37 (2) :108-122
URL: http://ijiepr.iust.ac.ir/article-1-2578-en.html

Stochastic programming and robust optimization approaches for the product mix problem under uncertainty (case study: lubricant refinery)

Mohammadreza Nemati¹

, Mehrdad Kargari²

, Ehsan Nikbakhsh³

1- PhD candidate in Industrial Engineering
2- Associate Professor of Industrial and Systems Engineering, Tarbiat Modares University , m_kargari@modares.ac.ir
3- Assistant Professor of Industrial and Systems Engineering, Tarbiat Modares University

Abstract: (125 Views)

Determining optimal product mix under uncertain demand and capacity is a critical challenge in the lubricant industry. This study proposes four MILP models: deterministic, robust scenario-based, downside-risk two-stage stochastic, and CVaR two-stage stochastic. All models incorporate real-world constraints including multi-period, multi-product settings, dual-warehouse inventory, backlog/lost-sale shortages, and mandatory production of unprofitable products. Using real data from a major Iranian lubricant refinery, the models improve profit from the company's actual 300 million monetary units (MU) to 535 (deterministic) and 504 million MU (CVaR). Among stochastic models, the robust approach provides the highest worst-case profit and most stable performance. This is the first systematic comparison of these three stochastic approaches in the lubricant industry under identical constraints, demonstrating the value of uncertainty-aware production planning.

Keywords: Product mix, inventory and shortage system, uncertainty, robust model, two-stage stochastic model, lubricant industry

Full-Text [PDF 706 kb] (54 Downloads)

Type of Study: Research | Subject: Production Planning & Control
Received: 2025/10/14 | Accepted: 2026/05/17 | Published: 2026/06/20