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RESEARCH ARTICLE

A two-stage stochastic model considering conditional risk in a multi-level multi-product supply chain

Sayyed Mohammad Reza Davoodi1† ,  Elham Gholamian1† ,  Thomas Hanne2*
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1 Department of Management, Deh.C., Islamic Azad University, Isfahan, Iran
2 Institute for Information Systems, University of Applied Sciences and Arts Northwestern Switzerland, Olten, Switzerland
†These authors contributed equally to this work.
IJOCTA, 025300131 https://doi.org/10.36922/IJOCTA025300131
Received: 24 July 2025 | Revised: 24 September 2025 | Accepted: 9 October 2025 | Published online: 4 November 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This study introduces a novel two-stage stochastic model of mean value exposed to conditional risk to allocate locations and to calculate the flow of materials and manufactured goods in a multi-level, multi-product supply chain. In this model, distributors and suppliers face potential disruptions and could spend money to prevent them. The suggested model considered several sources of uncertainty, such as transportation costs, final customer demand, and the possibility of disruptions at distribution centers and suppliers. The model used the conditional risk-exposed value and the risk-aversion coefficient to control for the risk caused by significant deviations from expected values. The designed model was transformed into a single-level linear programming model using a Monte Carlo simulation. Finally, the model was implemented through a numerical example, and its sensitivity analysis was conducted. The results of the model show that increasing the risk-aversion coefficient led to a decrease of more than 20% in the objective function across all confidence levels for the test problem, indicating the effectiveness of the proposed two-stage stochastic model in proactively mitigating disruptions.

Keywords
Conditional value-at-risk
Disruption
Monte Carlo simulation
Multi-level supply chain
Supply chain
Two-stage stochastic programming
Funding
None.
Conflict of interest
The authors declare that they have no competing interests.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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