Solving the single-machine sequencing problem using integer programming

Various integer programming models have been proposed for sequencing problems. However, little is known about the practical value of these models. This paper reports a comparison of six different integer programming formulations of the single-machine total tardiness problem. We created a set of especially difficult test problems and attempted to solve them with each of the formulations, using CPLEX software. We found that one formulation performs much more effectively than the others. A generic integer programming approach is still not capable of solving problems with hundreds of jobs, so in that respect, it does not compete with state-of-the-art tardiness algorithms. However, the integer programming approach remains viable for problems containing as many as 40 or 50 jobs and may be the better algorithmic choice when convenience in implementation is considered.