Minimizing the sum of weighted completion times in a concurrent open shop

• We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primal-dual 2-approximation algorithm for this problem. We also show that several natural linear programming relaxations for this problem have an integrality gap of 2. Finally, we show that this problem is inapproximable within a factor strictly less than 6/5 if not equal NP, or strictly less than 4/3 if the Unique Games Conjecture also holds. (C) 2010 Elsevier B.V. All rights reserved.

Nyckelord

Scheduling

Integrality gap

Approximation algorithm

Hardness of approximation

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