Algorithms for scheduling independent jobs with restricted processing times

Abstract

We describe exact algorithms for R//Cmax' P//Cmax and RM//Cmax. Let k be the maximum cardinality of a subset of jobs, any two of them with different processing times in some machine. If k is fixed the algorithms terminate within polynomial time. In this case, if additionally the maximum processing time can be expressed as a polynomial in the number n of jobs then Pm//Cmax can be solved in 0 (n) time. The proposed algorithms allow the processing times to be real numbers, except that for Pm//max which restricts them to integers.