Robert F. Gordon, Edward A. MacNair, et al.
WSC 1985
We present a new linear programming relaxation for the problem of minimizing the sum of weighted completion times of precedence-constrained jobs. Given a set of n jobs, each job j has processing time pj and weight wj. There is also a partial order<on the execution of the jobs: if j<k, job k may not start processing before job j has been completed. For Cj representing the completion time of job j, the objective is to minimize the weighted sum of completion times, ΣjwjCj. The new relaxation is simple and compact, has exactly two variables per inequality and half-integral extreme points. An optimal solution can be found via a minimum cut computation, which provides a new 2-approximation algorithm in the complexity of a minimum cut on a graph. As a by-product, we also introduce another new 2-approximation algorithm for the problem.
Robert F. Gordon, Edward A. MacNair, et al.
WSC 1985
Trang H. Tran, Lam Nguyen, et al.
INFORMS 2022
Harpreet S. Sawhney
IS&T/SPIE Electronic Imaging 1994
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ