Analysis of antithetic sequences in flowshop scheduling to minimize makespan

The antithetic properties of flowshop sequences are investigated to improve the classical Monte Carlo method for solving the n-job, m-machine problem with minimization of makespan. The major issues considered are (1) establishing a negative correlation of the makespan values of forward and reverse sequences; (2) developing the Antithetical Monte Carlo (AMC) method, which can be used to quickly estimate the mean of the makespan distribution by exploiting the antithetic property of sequences; (3) using AMC to find low makespan values; (4) determining a threshold value of makespan beyond which it would be likely to find an optimal or near optimal makespan when reversing a sequence. Statistical tests indicate that the performance of AMC is superior to that of the classical Monte Carlo method. Possible applications of this concept are discussed including extensions to other mathematical problems with antithetic properties.