V-shape property for job sequences that minimize the expected completion time variance |
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| Institution: | 1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China;2. School of Electrical Engineering and Computing, The University of Newcastle, Callaghan NSW 2308, Australia;1. School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China;2. Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong, PR China;1. Heinz-Nixdorf-Institute, Paderborn University, Fuerstenallee 11, Paderborn, 33102, Germany |
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| Abstract: | We consider the problem of sequencing n jobs with random processing time on a single machine so as to minimize the expected variance of job completion times. Our main result is a new sufficient condition for an optimal sequence to be V-shaped in terms of the mean processing times when n ? 3. We show that this condition is satisfied by a wide variety of problem instances, including those in which the processing times follow different patterns of distributions. This result relaxes a condition proposed before. |
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