The Constrained Minimum Weighted Sum of Job Completion Times Problem

We consider the problem of minimizing the weighted sum of job completion times on a single machine (subject to certain job weights) with an additional side constraint on the weighted sum of job completion times (with respect to different job weights). This problem is NP-hard, and we provide a polynomial time approximation scheme for this problem. Our method is based on Lagrangian relaxation mixed with carefully guessing the positions of certain jobs in the schedule.

• Type: Conference
• Year: 2004
• Where: IPCO
• Authors: Asaf Levin, Gerhard J. Woeginger
• Keywords: IPCO 2004, IPCO 2007, Job Completion Times, Job Weights, Weighted Sum