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

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Yang, Ye and Zhang

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 a single
machine, so as to minimize the total weighted
completion time of the jobs. We study a semidefinite
programming (SDP) based approximation algorithm
for solving this problem and prove that the algorithm
has a worst case ratio at most $1.1626$.
Working Paper, Department of Management Sciences,
University of Iowa, IA 52242, USA

Contact: yinyu-ye@uiowa.edu