This paper examines the nonpreemptive assignment of independent jobs to a system of uniform processors with the objective of reducing makespan, or the time required from the start of execution until all jobs are completed. We consider a set of n jobs, each having an execution time and a set of m > or = 2 processors which are assumed to have different speeds (say sigma1 = 1<FONT FACE=Symbol>£s</FONT>2<= ... <FONT FACE=Symbol>£s</FONT>m). Since the problem of finding a minimal makespan has been show to be NP-hard, we develop a powerful interchange heuristic. The heuristic proposed is composed by three phases: initial assignment, job reassignment and job interchange. The main feature of this method is not perform a pre-classification of the tasks. Some comparison are made with other heuristic schemes and a lower bound that validates the results obtained. The heuristic achieve optimal solutions for several instances in a short computational time.
scheduling problems; combinatorial optimization; heuristics
