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

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.

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

Advances in Applied Probability ◽

10.2307/1427684 ◽

1991 ◽

Vol 23 (4) ◽

pp. 925-944 ◽

Cited By ~ 6

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.

Download Full-text

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

Advances in Applied Probability ◽

10.1017/s0001867800024022 ◽

1991 ◽

Vol 23 (04) ◽

pp. 925-944 ◽

Cited By ~ 2

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.

Download Full-text