Time Evolution of a Supply Chain Network: Kinetic Modeling

TL;DR

This paper introduces a kinetic model for supply chain networks that captures their dynamic evolution over time, integrating multi-dimensional sustainability factors and validated with real SME data.

Contribution

It proposes a novel time-varying cost function model based on Lagrangian mechanics for analyzing supply chain dynamics and sustainability.

Findings

Increases in production without market consideration can cause bankruptcy.

High transportation costs with increased production can lead to break-even points.

The model forecasts the time for policy changes to boost sales.

Abstract

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.