Capacitated two-parallel machines scheduling to minimize sum of job completion times

Parallel Machine Scheduling to Minimize the Sum of Quadratic Completion Times

We consider the parallel machine scheduling problem of minimizing the sum of quadratic job completion times. We first prove that the problem is strongly NP-hard. We then demonstrate by probabilistic analysis that the shortest processing time rule solves the problem asymptotically. The relative error of the rule converges in probability to zero under the assumption that the job processing times ...

Scheduling Identical Parallel Machines to Minimize Total Weighted Completion Time

Single-Machine Group Scheduling Problems with Deterioration to Minimize the Sum of Completion Times

We consider two single-machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing or decreasing functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum...

Precedence Constrained Scheduling to Minimize Sum of Weighted Completion Times on a Single Machine

We consider the problem of scheduling a set of jobs on a single machine with the objective of minimizing sum of weighted completion times. The problem is NP-hard when there are precedence constraints between jobs 15]. We provide an eecient com-binatorial 2-approximation algorithm for this problem. In contrast to our work, earlier approximation algorithms 12] achieving constant factor approximat...

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...