Maximizing the minimum completion time on parallel machines

Maximizing the minimum completion time on parallel machines

We propose an exact branch-and-bound algorithm for the problem of maximizing the minimum machine completion time on identical parallel machines. The proposed algorithm is based on tight lower and upper bounds aswell as an effective symmetry-breaking branching strategy. Computational results performed on a large set of randomly generated instances attest to the efficacy of the proposed algorithm.

Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time

A PTAS for Minimizing the Total Weighted Completion Time on Identical Parallel Machines

We consider the problem of scheduling a set of n jobs on m identical parallel machines so as to minimize the weighted sum of job completion times. This problem is NP-hard in the strong sense. The best approximation result known so far was a 2 (1 + √ 2)-approximation algorithm that has been derived by Kawaguchi and Kyan back in 1986. The contribution of this paper is a polynomial time approximat...

Minimum Weighted Completion Time ( 1999

The minimum weighted completion time problem involves (i) a set J of n jobs, a positive weight wj for each job j ∈ J , and a release date rj before which it cannot be scheduled; (ii) a set of m machines, each of which can process at most one job at any time, and (iii) an arbitrary set of positive values {pi,j}, where pi,j denotes the time to process job j on machine i. A schedule involves assig...

Scheduling Multiple Families of Jobs on Parallel Machines to Minimize Total Weighted Completion Time

We consider the problem of scheduling multiple families of jobs on identical parallel machines to minimize the total weighted completion time of the jobs. In this problem, a setup time is necessary whenever a job from one family is processed immediately after another job from a di erent family. The setup time could be sequence independent or sequence dependent. We propose a column generation ba...