A simple assembly line balancing problem is considered provided that number m of working stations is fixed. In such a problem, denoted as SALBP-2, it is necessary to minimize a cycle time for processing a partially ordered set of operations V = {1, 2, ..., n} on a set of m linearly ordered (working) stations. An initial vector of the processing times t of the operations V is given. And for each automated operation, the processing time cannot vary during a life cycle of the assembly line. For each manual operation, the processing times may vary, since different workers may have different skill, experience, etc. We investigate a stability of the optimal line balance of the simple assembly line with respect to simultaneous variations of the processing times of the manual operations. An optimal line balance is stable if it remains optimal for any sufficiently small variations of the processing times of the manual operations. We propose an algorithm and a program in C++ for constructing all the stable optimal line balances for the problem SALBP-2. Computational results for the modified benchmark instances have been presented.