  The parallel machine scheduling problem has been a popular topic for many
years due to its theoretical and practical importance. This paper addresses the
robust makespan optimization problem on unrelated parallel machine scheduling
with sequence-dependent setup times, where the processing times are uncertain,
and the only knowledge is the intervals they take values from. We propose a
robust optimization model with min-max regret criterion to formulate this
problem. To solve this problem, we prove that the worst-case scenario with the
maximum regret for a given solution belongs to a finite set of extreme
scenarios. Based on this theoretical analysis, the procedure to obtain the
maximum regret is proposed and an enhanced regret evaluation method (ERE) is
designed to accelerate this process. A multi-start decomposition-based
heuristic algorithm (MDH) is proposed to solve this problem. High-quality
initial solutions and an upper bound are examined to help better solve the
problem. Computational experiments are conducted to justify the performance of
these methods.
