On Analyzing the Conditions for Stability of Opportunistic Supply Chains Under Network Growth

TL;DR

This paper develops an integrated mathematical framework combining stochastic volatility, Bayesian learning, and network modeling to analyze the stability and phase transitions of opportunistic supply chains under network growth.

Contribution

It introduces a novel combined modeling approach to understand the conditions leading to stability or fragmentation in opportunistic supply chains.

Findings

Identifies a critical volatility threshold causing network fragmentation.

Establishes formal stability conditions and phase transition mechanisms.

Demonstrates the model's applicability to various industry supply chains.

Abstract

Even large firms such as Walmart, Apple, and Coca-Cola face persistent fluctuations in costs, demand, and raw material availability. These are not \textit{rare events} and cannot be evaluated using traditional disruption models focused on infrequent events. Instead, sustained volatility induces opportunistic behavior, as firms repeatedly reconfigure partners in absence of long-term contracts, often due to trust deficits. The resulting web of transient relationships forms opportunistic supply chains (OSCs). To capture OSC evolution, we develop an integrated mathematical framework combining a Geometric Brownian Motion (GBM) model to represent stochastic price volatility, a Bayesian learning model to describe adaptive belief updates regarding partner reliability, and a Latent Order Logistic (LOLOG) network model for endogenous changes in network structure. This framework is implemented in an agent-based simulation to examine how volatility, trust, and network structure jointly shape SC resilience. Our modeling approach identifies critical volatility threshold; a tipping point beyond which the network shifts from a stable, link-preserving regime to a fragmented regime marked by rapid relationship dissolution. We analytically establish monotonic effects of volatility on profitability, trust, and link activation; derive formal stability conditions and volatility-driven phase transitions, and show how these mechanisms shape node importance and procurement behavior. These theoretical mechanisms are illustrated through computational experiments reflecting industry behaviors in fast fashion, electronics, and perishables. Overall, our contribution is to develop an integrated GBM-Bayesian-LOLOG framework to analyze OSC stability and our model can be extended to other OSCs including humanitarian, pharmaceutical, and poultry networks.