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

We propose an efficient bio-inspired algorithm for design of optimal supply chain networks in a competitive oligopolymarkets. 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 Nagurney's on several numerical examples, we demonstrate the efficiency and practicality of the proposed method.