Stability Analysis and Stabilization Strategies for Linear Supply Chains

TL;DR

This paper analyzes how different production control strategies, including anticipation of future stock levels, can stabilize linear supply chains and mitigate the bull-whip effect, using stability conditions and simulations.

Contribution

It introduces a linear stability analysis framework for supply chain control strategies and explores the stabilizing effects of reaction and anticipation mechanisms.

Findings

Reaction to stock levels can stabilize supply chains.

Anticipating future stock levels enhances stability.

Linear stability analysis aids in evaluating control strategies.

Abstract

Due to delays in the adaptation of production or delivery rates, supply chains can be dynamically unstable with respect to perturbations in the consumption rate, which is known as "bull-whip effect". Here, we study several conceivable production strategies to stabilize supply chains, which is expressed by different specifications of the management function controlling the production speed in dependence of the stock levels. In particular, we will investigate, whether the reaction to stock levels of other producers or suppliers has a stabilizing effect. We will also demonstrate that the anticipation of future stock levels can stabilize the supply system, given the forecast horizon is long enough. To show this, we derive linear stability conditions and carry out simulations for different control strategies. The results indicate that the linear stability analysis is a helpful tool for the judgement of the stabilization effect, although unexpected deviations can occur in the non-linear regime. There are also signs of phase transitions and chaotic behavior, but this remains to be investigated more thoroughly in the future.