Approximate Solution of a Time-dependent Scheduling Problem for lp-norm-based Criteria

In the paper we consider an approximate O(n log n) time solution of theproblem of a single machine scheduling with time dependentprocessing times, where α j ≥ 0.The main result of the paper is that in view of the inequality‖C‖1 ≤ ω(n,r)‖C‖ r , where‖C‖ r = (n + l)1-1/r and1 ≤ r ≤ +∞, the solution of the ‖C‖1— problem with the actuallyrecognized O(2 n ) complexity ((1991)) can beapproximated in terms of the l p —norm-based criteria ‖C‖ r merely with the complexity O(n log n), where 1 < r 1 ≤r ≤ +∞and r 1 is large enough. Relations to some more general problems are also indicated.