This paper considers the problems of scheduling n independent jobs on a single-machine to minimize total tardiness and weighted total tardiness of all jobs. Both the problems possess exponential time complexity function to solve optimally. In this paper, some working models are discussed. These may be of great use to solve the problems of moderate size optimally with the help of some recent integer programming softwares and hightech computers. Also, these may be used to compare emerging heuristics against optimal solution. Application of these models to some numerical problems are also discussed.
