We consider the problem of schedulingnjobs on a single machine that is continuously available from time zero onward and that can handle no more than one job at a time. Each job requires processing during a given positive uninterrupted time. The cost of each job is measured byK(K=2, 3) nondecreasing penalty functions; the quality of a schedule is computed on the basis ofKperformance criteria, thekth one being given by the maximum value of thekth penalty function over all jobs. We wish to minimize an objective function that is a nondecreasing function of theseKperformance criteria. We present a polynomial algorithm for both problems and we show that these can also be used if precedence constraints exist between the jobs or if all penalty functions are nonincreasing in the job completion times.