A Stochastically Optimized Two-Echelon Supply Chain Model: An Entropy Approach for Operational Risk Assessment

Konstantinos Petridis, Prasanta Dey, Amit Chattopadhyay, Paraskevi Boufounou*, Kanellos Toudas, Chrisovalantis Malesios

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Minimizing a company’s operational risk by optimizing the performance of the manufacturing and distribution supply chain is a complex task that involves multiple elements, each with their own supply line constraints. Traditional approaches to optimization often assume determinism as the underlying principle. However, this paper, adopting an entropy approach, emphasizes the
significance of subjective and objective uncertainty in achieving optimized decisions by incorporating stochastic fluctuations into the supply chain structure. Stochasticity, representing randomness, quantifies the level of uncertainty or risk involved. In this study, we focus on a processing production plant as a model for a chain of operations and supply chain actions. We consider the stochastically
varying production and transportation costs from the site to the plant, as well as from the plant to the customer base. Through stochastic optimization, we demonstrate that the plant producer can benefit from improved financial outcomes by setting higher sale prices while simultaneously lowering optimized production costs. This can be accomplished by selectively choosing producers
whose production cost probability density function follows a Pareto distribution. Notably, a lower Pareto exponent yields better supply chain cost optimization predictions. Alternatively, a Gaussian stochastic fluctuation may be proposed as a more suitable choice when trading off optimization and simplicity. Although this may result in slightly less optimal performance, it offers advantages in
terms of ease of implementation and computational efficiency.
Original languageEnglish
Article number1245
Number of pages21
Issue number9
Early online date22 Aug 2023
Publication statusPublished - 22 Aug 2023

Bibliographical note

Copyright © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).


  • green supply chain management
  • noise
  • stochastic models
  • supply chain risk model


Dive into the research topics of 'A Stochastically Optimized Two-Echelon Supply Chain Model: An Entropy Approach for Operational Risk Assessment'. Together they form a unique fingerprint.

Cite this