Formulating the single machine sequencing problem with release dates as a mixed integer program
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Integer Programming Formulation of Traveling Salesman Problems
Journal of the ACM (JACM)
Mathematical Programming: Series A and B
Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints
Operations Research Letters
A decomposition algorithm for the single machine total tardiness problem
Operations Research Letters
A periodic tabular policy for scheduling of a single stage production-inventory system
Computers and Industrial Engineering
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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.