Scheduling to minimize the weighted sum of completion times with secondary criteria

1976 ◽  
Vol 23 (1) ◽  
pp. 125-129 ◽  
Author(s):  
Richard N. Burns
Keyword(s):  
Weighted Sum ◽  
Completion Times ◽  
Sum Of Completion Times

scholarly journals Tabu search for a parallel-machine scheduling problem with periodic maintenance, job rejection and weighted sum of completion times

2021 ◽  
Author(s):  
Hanane Krim ◽  
Nicolas Zufferey ◽  
Jean-Yves Potvin ◽  
Rachid Benmansour ◽  
David Duvivier
Keyword(s):  
Tabu Search ◽  
Parallel Machines ◽  
Mixed Integer ◽  
Weighted Sum ◽  
Scheduling Problem ◽  
Maintenance Policy ◽  
Mixed Integer Linear Program ◽  
Job Rejection ◽  
Completion Times ◽  
Sum Of Completion Times

AbstractWe consider in this work a bicriteria scheduling problem on two different parallel machines with a periodic preventive maintenance policy. The two objectives considered involve minimization of job rejection costs and weighted sum of completion times. They are handled through a lexicographic approach, due to a natural hierarchy among the two objectives in the applications considered. The main contributions of this paper are first to present a new problem relevant to practice, second, to develop a mixed-integer-linear-program model for the problem, and third, to introduce two generalizable tabu-search metaheuristics relying on different neighborhood structures and solution spaces. Computational results for 120 instances (generated from a real case) are reported to empirically demonstrate the effectiveness of the proposed metaheuristics.

Scheduling two classes of exponential jobs on parallel processors: structural results and worst-case analysis

1991 ◽  
Vol 23 (4) ◽  
pp. 925-944 ◽  
Author(s):  
Cheng-Shang Chang ◽  
Randolph Nelson ◽  
Michael Pinedo
Keyword(s):  
Case Analysis ◽  
Parallel Processors ◽  
Worst Case Analysis ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Worst Case ◽  
Total Cost ◽  
Class 1 ◽  
Completion Times ◽  
Sum Of Completion Times

In this paper, we consider scheduling problems with m machines in parallel and two classes of job. We assume that all jobs are present at time 0 and there are no further arrivals. The service times of class 1 (2) jobs are independent and exponentially distributed with mean . Each class 1 (2) job incurs a cost c1 (c2) per unit of time until it leaves the system. The objective is to minimize the expected total cost, that is the expected weighted sum of completion times. We show that the optimal policy among all preemptive policies is of threshold type. Based on these structural results, we also show that the ratio of the expected weighted sum of completion times under the cµ-rule to that under the optimal rule is less than 1·71.

Scheduling two classes of exponential jobs on parallel processors: structural results and worst-case analysis

1991 ◽  
Vol 23 (04) ◽  
pp. 925-944 ◽  
Author(s):  
Cheng-Shang Chang ◽  
Randolph Nelson ◽  
Michael Pinedo
Keyword(s):  
Case Analysis ◽  
Parallel Processors ◽  
Worst Case Analysis ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Worst Case ◽  
Total Cost ◽  
Class 1 ◽  
Completion Times ◽  
Sum Of Completion Times

In this paper, we consider scheduling problems with m machines in parallel and two classes of job. We assume that all jobs are present at time 0 and there are no further arrivals. The service times of class 1 (2) jobs are independent and exponentially distributed with mean . Each class 1 (2) job incurs a cost c 1 (c 2) per unit of time until it leaves the system. The objective is to minimize the expected total cost, that is the expected weighted sum of completion times. We show that the optimal policy among all preemptive policies is of threshold type. Based on these structural results, we also show that the ratio of the expected weighted sum of completion times under the cµ-rule to that under the optimal rule is less than 1·71.

Heuristics for the single machine weighted sum of completion times scheduling problem with periodic maintenance

2019 ◽  
Vol 75 (1) ◽  
pp. 291-320 ◽  
Author(s):  
Hanane Krim ◽  
Rachid Benmansour ◽  
David Duvivier ◽  
Daoud Aït-Kadi ◽  
Said Hanafi
Keyword(s):  
Single Machine ◽  
Weighted Sum ◽  
Scheduling Problem ◽  
Periodic Maintenance ◽  
Completion Times ◽  
Sum Of Completion Times
Sign in / Sign up

Export Citation Format

Share Document