A graph-theoretic approach to interval scheduling on dedicated unrelated parallel machines

Chi To Ng, Tai Chiu Edwin Cheng, Andrei M Bandalouski, Mikhail Y Kovalyov and Sze Sing Lam
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Chi To Ng: The Hong Kong Polytechnic University, Kowloon, Hong Kong
Tai Chiu Edwin Cheng: The Hong Kong Polytechnic University, Kowloon, Hong Kong
Andrei M Bandalouski: National Academy of Sciences of Belarus, Minsk, Belarus
Mikhail Y Kovalyov: National Academy of Sciences of Belarus, Minsk, Belarus
Sze Sing Lam: The Open University of Hong Kong, Kowloon, Hong Kong

Journal of the Operational Research Society, 2014, vol. 65, issue 10, 1571-1579

Abstract: We study the problem of scheduling n non-preemptive jobs on m unrelated parallel machines. Each machine can process a specified subset of the jobs. If a job is assigned to a machine, then it occupies a specified time interval on the machine. Each assignment of a job to a machine yields a value. The objective is to find a subset of the jobs and their feasible assignments to the machines such that the total value is maximized. The problem is NP-hard in the strong sense. We reduce the problem to finding a maximum weight clique in a graph and survey available solution methods. Furthermore, based on the peculiar properties of graphs, we propose an exact solution algorithm and five heuristics. We conduct computer experiments to assess the performance of our and other existing heuristics. The computational results show that our heuristics outperform the existing heuristics.

Date: 2014
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