Time Evolution of a Supply Chain Network: Kinetic Modeling

Biswajit Debnath, Rihab El-Hassani, Amit Chattopadhyay, T Krishna Kumar, Sadhan K. Ghosh, Rahul Baidya

Research output: Contribution to journalArticlepeer-review


Resilient supply chains are often inherently dependent on the nature of their complex interconnected networks that are simultaneously multi-dimensional and multi-layered. This article presents a Supply Chain Network (SCN) model that can be used to regulate downstream relationships towards a sustainable SME using a 4-component cost function structure - Environmental (E), Demand (D), Economic (E), and Social (S). As a major generalization to the existing practice of using phenomenological interrelationships between the EDES cost kernels, we propose a complementary time varying model of a cost function, based on Lagrangian mechanics (incorporating SCN constraints through Lagrange multipliers), to analyze the time evolution of the SCN variables to interpret the competition between economic inertia and market potential. Multicriteria decision making, based on an Analytic Hierarchy Process (AHP), ranks performance quality, identifying key business decision makers. The model is first solved numerically and then validated against real data pertaining to two Small and Medium Enterprises (SMEs) from diverse domains, establishing the domain-independent nature of the model. The results quantify how increases in a production line without appropriate consideration of market volatility can lead to bankruptcy, and how high transportation cost together with increased production may lead to a break-even state. The model also predicts the time it takes a policy change to reinvigorate sales, thereby forecasting best practice operational procedure that ensures holistic sustainability on all four sustainability fronts.
Original languageEnglish
Article number128085
Number of pages16
JournalPhysica A
Early online date1 Sept 2022
Publication statusPublished - 1 Dec 2022

Bibliographical note

© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (https://creativecommons.org/licenses/by/4.0/).

The authors acknowledge partial financial supports from the Commonwealth Scholarships Commission (Reference: INCN-2018-52) and Aston University . Dr. Prasanta Kumar Dey, Aston Business School is acknowledged for his general advice on supply chain literature.


  • Sustainable Production
  • Supply chain management
  • Multiple criteria analysis
  • Optimization
  • Lagrangian mechanics
  • Analytic hierarchy process (AHP)


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