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

Gurkirat Wadhwa, Priyank Sinha

TL;DR

This work develops an integrated framework that couples Geometric Brownian Motion price dynamics, Bayesian trust updating, and LOLOG-driven network evolution to analyze the stability of opportunistic supply chains under volatility. It establishes theoretical results on the existence of stable network configurations, a critical volatility threshold, and ergodic long-run behavior, then validates these mechanisms via agent-based simulations across fast fashion, electronics, and perishables. The findings show that volatility, trust, and network structure jointly shape resilience, with industry-specific patterns such as adaptive rewiring in fashion, hub-centric consolidation in electronics, and fragility in perishables. The approach provides actionable insights for managing volatility and trust to sustain OSCs in dynamic, contract-lite environments, and it can be extended to humanitarian, pharmaceutical, and agricultural networks.

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.

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

TL;DR

This work develops an integrated framework that couples Geometric Brownian Motion price dynamics, Bayesian trust updating, and LOLOG-driven network evolution to analyze the stability of opportunistic supply chains under volatility. It establishes theoretical results on the existence of stable network configurations, a critical volatility threshold, and ergodic long-run behavior, then validates these mechanisms via agent-based simulations across fast fashion, electronics, and perishables. The findings show that volatility, trust, and network structure jointly shape resilience, with industry-specific patterns such as adaptive rewiring in fashion, hub-centric consolidation in electronics, and fragility in perishables. The approach provides actionable insights for managing volatility and trust to sustain OSCs in dynamic, contract-lite environments, and it can be extended to humanitarian, pharmaceutical, and agricultural networks.

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.
Paper Structure (25 sections, 7 theorems, 51 equations, 7 figures, 3 tables)

This paper contains 25 sections, 7 theorems, 51 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Model Formulation
  3. Network Representation
  4. Stochastic Pricing of Contracts: Geometric Brownian Motion (GBM)
  5. Contract Structure and Expected Profit Computation
  6. Bayesian Belief Updating in Opportunistic Supply Chains
  7. Network Evolution via Latent-Order-Logistic (LOLOG) Model
  8. Remarks on the Integrated GBM-Bayesian-LOLOG Framework
  9. Analysis
  10. Existence of Stable Network Configurations
  11. Critical Volatility Threshold for Network Stability
  12. Node Importance and Structural Influence
  13. Profit Sensitivity to Trust Beliefs
  14. Optimal Procurement Behavior
  15. Remarks:
  16. ...and 10 more sections

Key Result

Theorem 1

Under Assumptions A.1--A.4 and S.1--S.2, there exists at least one stable network configuration $G^* \in \mathcal{G}$ such that: Consequently, the OSC admits at least one self-consistent configuration that remains stable even in the presence of stochastic pricing, decentralized decisions, and boundedly rational belief updates.

Figures (7)

  • Figure 1: Integrated GBM--Bayesian--LOLOG framework and behavioural feedback process.
  • Figure 2: Fast-fashion apparel: MLSP and NCR across 100 periods with and without shocks.
  • Figure 3: Fast-fashion apparel: final network structures under both scenarios.
  • Figure 4: Electronics spot market: MLSP and NCR across 100 periods.
  • Figure 5: Electronics spot market: final networks under both scenarios.
  • ...and 2 more figures

Theorems & Definitions (9)

  • Theorem 1: Existence of stable network configurations
  • Definition 1: Candidate link set
  • Definition 2: Link utility
  • Theorem 2: Critical volatility threshold for network stability
  • Theorem 3: Node Importance in OSCs
  • Lemma 1: Profit monotonicity in beliefs
  • Theorem 4: Existence and uniqueness of optimal procurement
  • Theorem 5: Monotone comparative statics of the optimal procurement quantity
  • Theorem 6: Ergodicity of LOLOG Network Dynamics