A decomposition-based matheuristic for supply chain network design with assembly line balancing

This paper addresses a supply chain network design problem with assembly line balancing, which considers a three-layer supply chain including manufacturers, assemblers, and customers. By analyzing the characteristics and complexities of the problem, we decompose it into an upper-level problem and two lower-level problems. The upper level problem is to determine the assignment amount of each assembler. The two lower-level problems include the assembly line balancing problem (ALBP) inside each assembler and the transportation problem (TP) between different layers. To solve the problem effectively, a decomposition-based matheuristic (DMAT) is proposed by fusing metaheuristic and model-based approaches. The ALBP is solved by using branch and bound, and a lookup table method is proposed to speed up the computation time. The TP is solved by using mathematical programming. By solving the lower-level problems, the cost function of the upper-level problem can be evaluated. To optimize the upper-level problem, a metaheuristic based on the differential evolution is presented. In population initialization, the problem specific heuristics are designed. To repair and improve the infeasible solutions, reassignment with local intensification is designed. Numerical tests with extensive instances demonstrate the effectiveness of the proposed DMAT.