Stability radii of optimal assembly line balances with a fixed workstation set

For an assembly line, it is required to minimize the line's cycle time for processing a partially ordered set of the assembly operations on a linearly ordered set of the workstations. The operation set is partitioned into two subsets, manual and automated. The durations of the manual operations are variable and those of the automated operations are fixed. We conduct a stability analysis for this problem. First, we derive a sufficient and necessary condition for the optimal line balance to have an infinitely large stability radius. Second, we derive formulas and an algorithm for calculating the stability radii for the optimal line balances. Third, we report computational results for the stability analysis of the benchmark instances. Finally, we outline managerial implications of the stability results for choosing most stable line balances, which save their optimality in spite of the variations of the operation durations, and for identifying the right time for the re-balancing of the assembly line.