Minimizing the sum of weighted completion times with unrestricted weights

Minimizing the Sum of Weighted Completion Times with Unrestricted Weights

Given a set of tasks with associated processing times, deadlines and weights unrestricted in sign, we consider the problem of determining a task schedule on one machine by minimizing the sum of weighted completion times. The problem is NP-hard in the strong sense. We present a lower bound based on task splitting, an approximation algorithm, and two exact approaches, one based on branch-and-boun...

Weighted sum of completion times

4. Weighted sum of completion times 1 Eugene L. Lawler, Maurice Queyranne, Andreas S. Schulz, David B. Shmoys 4.1. Smith’s ratio rule 2 4.2. Preference orders on jobs 5 4.3. Preference orders on sequences and series-parallel precedence constraints 8 4.4. NP-hardness of further constrained min-sum problems 14 4.5. The ratio rule via linear programming 18 4.6. Approximation algorithms for 1|prec|...

The Stability Box in Interval Data for Minimizing the Sum of Weighted Completion Times

We consider a single-machine scheduling problem, in which the processing time of a job can take any value from a given segment. The criterion is to minimize the sum of weighted completion times of the n jobs, a positive weight being associated with a job. For a job permutation, we study the stability box, which is a subset of the stability region. We derive an O(n logn) algorithm for constructi...

Approximating the Con guration-LP for Minimizing Weighted Sum of Completion Times on Unrelated Ma hines

Combinatorial algorithms for minimizing the weighted sum of completion times on a single machine

In this paper we study the problem of minimizing the weighted sum of completion times of jobs with release dates on a single machine. We develop two algorithms that rely on “the simplest [linear program] relaxation” [8]. For the first algorithm we consider the online setting where we gain knowledge of a job on its release date and produce a schedule as the machine processes jobs. We develop an ...