Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Inventory Consensus Control in Supply Chain Networks using Dissipativity-Based Control and Topology Co-Design

Shirantha Welikala, Hai Lin, Panos J. Antsaklis

Abstract

Recent global and local phenomena have exposed vulnerabilities in critical supply chain networks (SCNs), drawing significant attention from researchers across various fields. Typically, SCNs are viewed as static entities regularly optimized to maintain their optimal operation. However, the dynamic nature of SCNs and their associated uncertainties have motivated researchers to treat SCNs as dynamic networked systems requiring robust control techniques. In this paper, we address the SCN inventory consensus problem, which aims to synchronize multiple parallel supply chains, enhancing coordination and robustness of the overall SCN. To achieve this, we take a novel approach exploiting dissipativity theory. In particular, we propose a dissipativity-based co-design strategy for distributed consensus controllers and communication topology in SCNs. It requires only the dissipativity information of the individual supply chains and involves solving a set of convex optimization problems, thus contributing to scalability, compositionality, and computational efficiency. Moreover, it optimizes the robustness of the SCN to various associated uncertainties, mitigating both bullwhip and ripple effects. We demonstrate our contributions using numerical examples, mainly by comparing the consensus performance with respect to standard steady-state control, feedback control, and consensus control strategies.

Inventory Consensus Control in Supply Chain Networks using Dissipativity-Based Control and Topology Co-Design

Abstract

Recent global and local phenomena have exposed vulnerabilities in critical supply chain networks (SCNs), drawing significant attention from researchers across various fields. Typically, SCNs are viewed as static entities regularly optimized to maintain their optimal operation. However, the dynamic nature of SCNs and their associated uncertainties have motivated researchers to treat SCNs as dynamic networked systems requiring robust control techniques. In this paper, we address the SCN inventory consensus problem, which aims to synchronize multiple parallel supply chains, enhancing coordination and robustness of the overall SCN. To achieve this, we take a novel approach exploiting dissipativity theory. In particular, we propose a dissipativity-based co-design strategy for distributed consensus controllers and communication topology in SCNs. It requires only the dissipativity information of the individual supply chains and involves solving a set of convex optimization problems, thus contributing to scalability, compositionality, and computational efficiency. Moreover, it optimizes the robustness of the SCN to various associated uncertainties, mitigating both bullwhip and ripple effects. We demonstrate our contributions using numerical examples, mainly by comparing the consensus performance with respect to standard steady-state control, feedback control, and consensus control strategies.

Paper Structure

This paper contains 23 sections, 6 theorems, 75 equations, 14 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Dissipativity
  4. Networked Systems
  5. Inventory Consensus Control Problem Formulation
  6. Supply Chain Dynamics
  7. Steady-State Control
  8. Error Dynamics
  9. Inventory Consensus Control
  10. Networked System View
  11. Dissipativity-Based Control and Topology Co-Design Solution
  12. Local Controller Design
  13. Global Control and Topology Co-Design
  14. Improved Local Controller Design
  15. Simulation Results
  16. ...and 8 more sections

Key Result

Proposition 1

The linear time-invariant (LTI) system is $X$-EID (from input $u$ to output $y$) if there exists a matrix $P\in\mathbb{R}^{n_x\times n_x}$ such that $P>0$ and

Figures (14)

  • Figure 1: The networked system $\Sigma$.
  • Figure 2: The composition of the supply chain network.
  • Figure 3: Closed-loop error dynamics of the SCN as a networked system.
  • Figure 4: Initial state of the considered SCN: Suppliers (red), inventories (green), demands (blue), links (black).
  • Figure 5: The daily mean customer demand values in a week used for simulating the customer demands (straight lines), and the overall mean customer demand values $\{\overline{d}_{in}: i\in\mathbb{N}_N\}$ used in steady-state controllers \ref{['Eq:SteadyStateControlLink']} (dashed lines).
  • ...and 9 more figures

Theorems & Definitions (23)

  • Definition 1
  • Definition 2
  • Remark 1
  • Proposition 1
  • proof
  • Corollary 1
  • proof
  • Remark 2
  • Remark 3
  • Proposition 2
  • ...and 13 more