in this paper, we study properties of dense schedules for the open-shop problems and their average performance ratio. after using two sets of test problems, we show that the average performance ratio of dense schedules is actually much better than ( ), the worst-case performance ratio in the conjecture. the results from randomly generated problems which have large sizes show that when the dimension of open-shop problems become larger, the average performance ratio is getting even smaller. twelve heuristic algorithms to generate dense schedules are presented in chapter 3 and the computational results of two sets of test problems are also provided.