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

Authors:
Monaldo Mastrolilli;Maurice Queyranne;Andreas S. Schulz;Ola Svensson;Nelson A. Uhan
Affiliations:
IDSIA, Manno, Switzerland;Sauder School of Business, University of British Columbia, Vancouver, BC, Canada;Sloan School of Management and Operations Research Center, Massachusetts Institute of Technology, Cambridge, MA, USA;KTH Computer Science and Communication, Stockholm, Sweden;School of Industrial Engineering, Purdue University, West Lafayette, IN, USA
Venue:
Operations Research Letters
Year:
2010

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Abstract

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 PNP, or strictly less than 4/3 if the Unique Games Conjecture also holds.