Enhanced arc-flow formulations to minimize weighted completion time on identical parallel machines

Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time

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...

Move-Optimal Schedules for Parallel Machines to Minimize Total Weighted Completion Time

We study the minimum total weighted completion time problem P | | wjCj , which is known to be stronglyNP-hard. We analyze a simple local search heuristic, moving jobs from one machine to another. The local optima can be shown to be approximately optimal with approximation ratio 32 . In case all jobs have equal weight to processing time ratios, the approximation ratio is at most 3 2 − 1 6 .

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...

Scheduling on parallel identical machines to minimize total tardiness

This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on r...