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

Monaldo Mastrolilli (monaldo***at***idsia.ch)
Maurice Queyranne (maurice.queyranne***at***sauder.ubc.ca)
Andreas S. Schulz (schulz***at***mit.edu)
Ola Svensson (ola***at***idsia.ch)
Nelson A. Uhan (nuhan***at***purdue.edu)

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 P \ne NP, or strictly less than 4/3 if the Unique Games Conjecture also holds.

Keywords: scheduling, integrality gap, approximation algorithms, hardness of approximation

Category 1: Combinatorial Optimization (Approximation Algorithms )

Category 2: Integer Programming ((Mixed) Integer Linear Programming )

Category 3: Applications -- OR and Management Sciences (Scheduling )

Citation: Operations Research Letters, to appear. doi:10.1016/j.orl.2010.04.011

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Entry Submitted: 11/11/2008
Entry Accepted: 11/12/2008
Entry Last Modified: 06/22/2010

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