Integrated optimization model for three-layer distribution network design and its solution algorithm

A particular three-layer capacitated location-routing problem is investigated in which there exist two echelons of facilities to be located. A Lagrangian relaxation is used to separate the problem and obtain lower bound. Subgradient optimization is used to improve the lower bound and feedback information among the sub problems. Genetic algorithm and other heuristics are used to solve subproblems. Two level chromosome coding method composed of binary code and real code and corresponding crossover operator and mutation operator is used. The numerical results indicate that the method is efficient for solving small scale problem.