Continuation of Shifting Bottleneck Heuristic applies the single-machine sub-problem optimization iteratively across all machines to minimize job shop makespan. Line Balancing problem assigns assembly tasks to workstations, minimizing the number of stations while respecting task precedence constraints and cycle time limits. Table of Contents: • Shifting Bottleneck continuation: sequential machine optimization, makespan update after each machine • Single-machine sub-problem parameters: release times from predecessor operations, due dates derived from current makespan estimate • Dominance conditions: eliminate inferior node sequences in branch-and-bound on sub-problems • Line Balancing formulation: workstation assignment problem with binary variables for station selection and task allocation • Cycle time definition: desired output rate constraint on workstation time • Precedence constraint modeling: task i must complete before task j if i precedes j • Workload balance: minimize idle time and uneven station loads
Continuation of Shifting Bottleneck Heuristic applies the single-machine sub-problem optimization iteratively across all machines to minimize job shop makespan. Line Balancing problem assigns assembl…