Distributed Asynchronous Primal-Dual Optimization for Supply-Chain Networks

TL;DR

This paper introduces DAPD-SCO, an asynchronous primal-dual algorithm for supply-chain network optimization that guarantees convergence despite delays and unreliable communication, outperforming existing methods in speed and robustness.

Contribution

The paper presents a novel fully asynchronous primal-dual scheme for supply-chain networks with provable convergence and rate guarantees under realistic network conditions.

Findings

Achieves almost-sure convergence to a saddle point.

Establishes an ergodic duality gap rate of $O(K^{-1/2})$.

Outperforms synchronous and other asynchronous methods in simulations.

Abstract

Distributed supply-chain optimization demands algorithms that can cope with unreliable communication, unbounded messaging delays, and geographically dispersed agents while still guaranteeing convergence with provable rates. In this work, we introduce DAPD-SCO (Distributed Asynchronous Primal-Dual Optimization for Supply-Chain Networks), a fully asynchronous primal-dual scheme for network flow allocation over directed acyclic supply-chain graphs. Each edge agent independently updates its local flow by projected gradient descent, and each retailer agent independently updates its dual multiplier by projected gradient ascent, using only potentially stale information whose delays can grow sublinearly. Under standard convexity and Slater's conditions and without any global synchronization or bounded-delay assumptions, we prove almost-sure convergence to a saddle point and establish an ergodic duality gap rate of $O(K^{-1/2})$, matching centralized lower bounds. Our analysis uses a Lyapunov-based decomposition that isolates delay-induced errors and handles time-varying communication topologies, bounded noise, and slowly drifting cost or capacity parameters. Extensive simulations on realistic three-tier networks show that DAPD-SCO outperforms synchronous primal-dual methods, Asynchronous Distributed Decision-Making (ADDM), and gradient-push, achieving faster convergence, lower communication overhead, and robust performance under packet loss and high staleness.