A Physarum-Inspired Approach to Optimal Supply Chain Network Design at Minimum Total Cost with Demand Satisfaction

TL;DR

This paper introduces a novel Physarum-inspired algorithm for designing cost-effective supply chain networks that adapt to demand and cost changes, ensuring demand satisfaction and minimizing total costs.

Contribution

The paper presents a new biologically inspired algorithm for supply chain design that incorporates capacity, flow, and demand constraints, with real-time cost updates and adaptivity.

Findings

Algorithm effectively minimizes total costs.

Network converges to equilibrium under cost changes.

Numerical examples demonstrate practicality and flexibility.

Abstract

A supply chain is a system which moves products from a supplier to customers. The supply chains are ubiquitous. They play a key role in all economic activities. Inspired by biological principles of nutrients' distribution in protoplasmic networks of slime mould Physarum polycephalum we propose a novel algorithm for a supply chain design. The algorithm handles the supply networks where capacity investments and product flows are variables. The networks are constrained by a need to satisfy product demands. Two features of the slime mould are adopted in our algorithm. The first is the continuity of a flux during the iterative process, which is used in real-time update of the costs associated with the supply links. The second feature is adaptivity. The supply chain can converge to an equilibrium state when costs are changed. Practicality and flexibility of our algorithm is illustrated on numerical examples.