We study minimizing the sum of weighted completion times in a concurrent open shop. We give a primaldual 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 65 if P≠NP, or strictly less than 43 if the Unique Games Conjecture also holds. © 2010 Elsevier B.V. All rights reserved.