Stability in Supply Chain Networks

TLDR

Supply chain networks involve many specialized workers collaborating to produce finished goods, as illustrated by the woollen coat example. The study investigates matching in vertical supply chain networks, extending two‑sided market theory. The authors analyze stable network properties and propose an algorithm to identify two stable configurations, applying the framework to multi‑type matching markets and empirical supply‑chain studies. They prove sufficient conditions for stable network existence, present an algorithm that finds two stable networks—one optimal for upstream agents and the other for downstream agents. —Adam Smith (1776).

Abstract

This paper studies matching in vertical networks, generalizing the theory of matching in two-sided markets. It gives sufficient conditions for the existence of stable networks and presents an algorithm for finding two of them. One is the best stable network for the agents on the “upstream” end of an industry. The other is best for the agents on the “downstream” end. The paper describes several properties of the set of stable networks and discusses applications of the theory to the design of matching markets with more than two types of agents and to the empirical analysis of supply chains. (JEL C78, D85, L14) The woollen coat, for example, which covers the day-labourer, as coarse and rough as it may appear, is the produce of the joint labour of a great multitude of workmen. The shepherd, the sorter of the wool, the wool-comber or carder, the dyer, the scribbler, the spinner, the weaver, the fuller, the dresser, with many others, must all join their different arts in order to complete even this homely production. —Adam Smith (1776)