  A single machine total weighted tardiness minimization (TWTM) problem in
operational planning is considered. The problem is formulated as an NP-hard
constrained combinatorial problem, which has no known deterministic polynomial
complexity solution using classical computing. Based on efficient Grover's
quantum search and Trugenberger's quantum optimization algorithms, a novel
efficient quantum optimization algorithm is proposed to solve the NP-hard
single machine TWTM problem, which makes the desired solution satisfying the
searching constraints and showing the minimal TWT value be measured with the
highest probability.
