Logic-based benders decomposition for a novel disassembly line balancing and sequencing problem with parallel branch lines

Disassembly line balancing and sequencing (DLBS) problem has received considerable attention from both enterprises and researchers, driven by its significant impact on end-of-life (EOL) product processing efficiency. Most existing studies focus on parallel lines with shared workstations, handling different products simultaneously. However, the consecutive connected lines, implemented in practice for processing complex EOL products, remain unexplored in the existing literature. This study addresses the parallel DLBS problem considering line consecutive connectivity, where products undergo initial disassembly on the main line before being transferred to branch lines for further processing, aiming to minimize the overall system cost. We propose a mixed-integer linear programming (MILP) model and then develop a customized logic-based Benders decomposition (LBBD) approach to improve computational efficiency. The LBBD method divides the problem into a master task assignment problem, which is enhanced by some valid inequalities and solved in the branch-and-cut framework, and a task sequencing subproblem, tackled via the dynamic programming approach. Numerical results demonstrate the effectiveness and efficiency of our proposed LBBD algorithm.