An intelligent physarum solver for supply chain network design under profit maximization and oligopolistic competition

Xiaoge Zhang, Felix T.S. Chan, Andrew Adamatzky, Sankaran Mahadevan, Hai Yang, Zili Zhang, Yong Deng (Corresponding Author)

Research output: Journal article publicationJournal articleAcademic researchpeer-review

44 Citations (Scopus)


We propose an efficient bio-inspired algorithm for design of optimal supply chain networks in a competitive oligopoly markets. The firms compete in manufacture, storage and distribution of a product to several markets. Each firm aims at maximisation of its own profit by optimising the design capacity and product flow in the supply chain. We model the supply chain network as a multi-layer graph of manufacturing nodes, distribution nodes and storage centres. To optimise the network, we adopt the mechanisms of a foraging behaviour of slime mould Physarum polycephalym. First, we extend the original Physarum model to deal with networks with multiple sources and sinks. Second, we develop a novel method to solve the user equilibrium (UE) problem by exploiting the adaptivity of the Physarum model: we update the link costs according to the product flow. Third, we refer to an equivalent transformation between system optimum problem and UE problem to determine the optimal product flows and design capacities of a supply chain. At last, we present an approach to update the amount of product supplied by each firm. By comparing our solutions with that in Nagurney (2010b) on several numerical examples, we demonstrate the efficiency and practicality of the proposed method.

Original languageEnglish
Pages (from-to)244-263
Number of pages20
JournalInternational Journal of Production Research
Issue number1
Publication statusPublished - 2 Jan 2017


  • artificial intelligence
  • decision support systems
  • network oligopolies
  • Physarum
  • supply chain design

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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