Qualitative stability analysis of an optimal balance for an assembly line with fixed stations number

We focus on one of the simple assembly line balancing problems known as SALBP-2 which consists in assigning a set of elementary operations V = {1, 2, ... , n} to the m linearly ordered stations with respect to the precedence constraints and aims in minimizing the line cycle time c. The processing times of operations t_j , j ¿ V may vary during the life cycle of assembly line for manual operations (represented by set V¿ ) and be fixed for automated operations (set V V¿ ). The goal of this paper is to derive necessary and sufficient condition (so-called qualitative analysis) of the stability of an optimal balance found for a given vector of operations times t = (t₁, t₂, ... , t_n) with regard to possible independent perturbations of the processing times of the operations from set .