Distributed Optimization for Supply Chain Planning for Multiple Companies Using Subgradient Method and Consensus Control

With recent liberalization and enlarging of trade among companies, it is necessary to generate an optimal supply chain planning by cooperation and coordination of supply chain planning for multiple companies without sharing sensitive information such as costs and profit among competitive companies. A distributed optimization can solve the optimization problems with limited information. A distributed optimization method using subgradient and consensus control methods has been proposed to solve continuous optimization problems. However, conventional distributed optimization methods using subgradient and consensus control methods cannot be applied to the supply chain planning for multiple companies including 0–1 decision variables. In this paper, we propose a new distributed optimization method for solving the supply chain planning problem for multiple companies by subgradient method and consensus control. By branching the cases 0–1 variables, an optimal solution can be obtained by the enumeration. A method to reduce the computational effort has been developed in the proposed method. From numerical experiments, it is confirmed that we can obtain an optimal solution by the reduction of the computation.