Approximation Schemes for Scheduling Jobs with Common Due Date on Parallel Machines to Minimize Total Tardiness - Kovalyov, Mikhail Y.; Werner, Frank (Journal of heuristics, 2002)
The problem of scheduling n nonpreemptive jobs having a common due date d on m, m > or = 2, parallel identical machines to minimize total tardiness is studied. Approximability issues are discussed and two families of algorithms {A[varepsilon]} and {B[varepsilon]} are presented such that (T0 - T*)/(T* + d) < or = [varepsilon] holds for any problem instance and any given [varepsilon] > 0, where T* is the optimal solution value and T0 is the value of the solution delivered by A[varepsilon] or B[varepsilon]. Algorithms A[varepsilon] and B[varepsilon] run in O(n2m/[varepsilon]m-1) and O(nm+1/[varepsilon]m) time, respectively, if m is a constant. For m = 2, algorithm A[varepsilon] can be improved to run in O(n3/[varepsilon]) time.