Stability radius of the optimal assembly line balance with fixed cycle time

We address the simple assembly line balancing problem: Minimize the number of stations in for processing n partially ordered operations V={1, 2,..., n} within the given cycle time c. The processing time t/sub i/ is given for each operation i/spl isin/V but cannot be changed only for the operations from the subset of automated and semi-automated operations V/spl bsol/V/spl tilde/. If i/spl isin/V/spl bsol/V/spl tilde/, then operation time t/sub i/ is strictly positive real number, which is fixed during the life cycle of the assembly line. Subset V/spl tilde/ of set V includes manual operations, for which it is hard or even impossible to fix processing time for the whole life cycle of the assembly line. We assume that if j/spl isin/V/spl tilde/, then given operation time t/sub j/ can be different for different cycles of production process. For the optimal line balance b of passed assembly line, we investigate its stability radius. In particular, we derive necessary and sufficient conditions when optimal line balance b is stable (in other words, when b has strictly positive stability radius).