Abstract
We study the situation where a set of n jobs with release dates and equal processing times have to be scheduled on m identical parallel machines. We show that, if the objective function can be expressed as the sum of n functions f i of the completion time C i of each job J i , the problem can be solved in polynomial time for any fixed value of m. The only restriction is that functions f i have to be non-decreasing and that for any pair of jobs ( J i , J j ), the function f i − f j has to be monotonous. This assumption holds for several standard scheduling objectives, such as the weighted sum of completion times or the total tardiness. Hence, the problems ( Pm| p i = p, r i |∑ w i C i ) and ( Pm| p i = p, r i |∑ T i ) are polynomially solvable.
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