  In this work, we present a new iterative exact solution algorithm for the
weighted fair sequences problem, which is a recently introduced NP-hard
sequencing problem with applications in diverse areas such as TV advertisement
scheduling, periodic machine maintenance and real-time scheduling. In the
problem we are given an upper bound on the allowed solution sequence length and
a list of symbols. For each symbols, there is a positive weight and a number,
which gives the minimum times the symbol has to occur in a feasible solution
sequence. The goal is to find a feasible sequence, which minimizes the maximum
weight-distance product, which is calculated for each consecutive appearance of
each symbol in the sequence, including the last and first appearance in the
sequence, i.e., the sequence is considered to be circular for the calculation
of the objective function. Our proposed solution algorithm is based on a new
mixed-integer programming model for the problem for a fixed sequence length.
The model is enhanced with valid inequalities and variable fixings. We also
develop an extended model, which allows the definition of an additional set of
valid inequalities and present additional results which can allow us to skip
the solution of the mixed-integer program for some sequence lengths. We conduct
a computational study on the instances from literature to assess the efficiency
of our newly proposed solution approach. Our approach manages to solve 404 of
440 instances to optimality within the given timelimit, most of them within
five minutes. The previous best existing solution approach for the problem only
managed to solve 229 of these instances, and its exactness depends on an
unproven conjecture. Moreover, our approach is up to two magnitudes faster
compared to this best existing solution approach.
