An approximation algorithm for scheduling two parallel machines with capacity constraints

An approximation algorithm for scheduling two parallel machines with capacity constraints

We consider the problem of scheduling n independent jobs on two identical parallel machines, with a limit on the number of jobs that can be assigned to each single machine, so as to minimize the total weighted completion time of the jobs. We study a semide3nite programming-based approximation algorithm for solving this problem and prove that the algorithm has a worst case ratio at most 1.1626. ...

An Approximation Algorithm for the Two-Parallel Machines Scheduling Problem with Capacity Constraints

Approximation algorithms for scheduling parallel machines with capacity constraints ∗

In this paper, we consider the classical scheduling problem on parallel machines with capacity constraints. We are given m identical machines, where each machine k can process up to ck jobs. The goal is to assign the n ≤ ∑m k=1 ck independent jobs on the machines subject to the capacity constraints such that the makespan is minimized. This problem is a generalization of the c-partition problem ...

A comment on scheduling two parallel machines with capacity constraints

In a recent paper [Discrete Appl. Math. 130 (2003) 449–467], Yang, Ye, and Zhang investigate the problem of scheduling independent jobs on two identical machines, with a limit on the number of jobs that can be assigned to each single machine, so as to minimize the total weighted completion time of the jobs. They provide a semidefinite programming based, polynomial time approximation algorithm w...

Multi-Objective Unrelated Parallel Machines Scheduling with Sequence-Dependent Setup Times and Precedence Constraints

This paper presents a novel, multi-objective model of a parallel machines scheduling problem that minimizes the number of tardy jobs and total completion time of all jobs. In this model, machines are considered as unrelated parallel units with different speeds. In addition, there is some precedence, relating the jobs with non-identical due dates and their ready times. Sequence-dependent setup t...