SINGLE-MACHINE SCHEDULING TO MINIMIZE A FUNCTION OF 2 OR 3 MAXIMUM COST CRITERIA

We consider the problem of scheduling n jobs 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 gi ven positive uninterrupted time. The cost of each job is measured by K (K = 2,3) nondecreasing penalty functions; the quality of a schedule is computed on the basis of K performance criteria, the kth one being given by the maximum value of the kth penalty function over all jobs. We wish to minimize an objective function that is a nondecreasing func tion of these K performance criteria. We present a polynomial algorith m for both problems and we show that these can also be used if precede nce constraints exist between the jobs or if all penalty functions are nonincreasing in the job completion times. (C) 1996 Academic Press, I nc.