Minimizing the number of late jobs when the start time of the machine is variable

Abstract We consider the bicriteria single-machine scheduling problem of minimizing the number of tardy jobs and the cost of starting the machine at time − A . We show that we can find all Pareto optimal points by considering at most O ( n 2 ) values of A , where for a given A value, we use an SPT-based algorithm to find the optimal solution instead of Moore–Hodgson.