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Approximation Algorithm for Parallel Machines Total Tardiness Minimization Problem for Planning Processes Automation

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Book cover Advances in Computer Science for Engineering and Education II (ICCSEEA 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 938))

Abstract

We present an approximation algorithm to solve the NP-hard scheduling problem of minimizing the total tardiness on identical parallel machines with a common due date and release dates of jobs. The algorithm has an estimate of the maximum possible deviation of its approximate solution from the optimum for each individual problem instance. It is based on the PSC-algorithm for the problem with equal release dates of jobs. Sufficient signs of optimality of a feasible solution and the estimate of the deviation of the obtained functional value from the optimum are known for the PSC-algorithm. The functional value obtained by the PSC-algorithm is the lower bound of the deviation of the functional value obtained by the approximation algorithm from the optimum for each individual problem instance. We give the computational data for test instances with dimensions of up to 40,000 jobs and 30 machines. The research shows that the developed algorithm is a very efficient method for the problem solving which allows to solve problems of any practical dimension. The average frequency of an optimal solution obtaining was 29.7%, and the average deviation from the optimum was 6.12%.

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Authors and Affiliations

  1. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37, Prospekt Peremohy, Kyiv, 03056, Ukraine

    Alexander Anatolievich Pavlov, Elena Borisovna Misura, Oleg Valentinovich Melnikov, Iryna Pavlovna Mukha & Kateryna Igoryvna Lishchuk

Authors
  1. Alexander Anatolievich Pavlov
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  2. Elena Borisovna Misura
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  3. Oleg Valentinovich Melnikov
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  4. Iryna Pavlovna Mukha
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  5. Kateryna Igoryvna Lishchuk
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Corresponding author

Correspondence to Alexander Anatolievich Pavlov .

Editor information

Editors and Affiliations

  1. School of Educational Information Technology, Central China Normal University, Wuhan, Hubei, China

    Zhengbing Hu

  2. Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, Russia

    Sergey Petoukhov

  3. “Igor Sikorsky Kiev Polytechnic Institute”, National Technical University of Ukraine, Kiev, Ukraine

    Ivan Dychka

  4. Halmos College of Natural Sciences and Oceanography, Nova Southeastern University, Ft. Lauderdale, FL, USA

    Matthew He

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Pavlov, A.A., Misura, E.B., Melnikov, O.V., Mukha, I.P., Lishchuk, K.I. (2020). Approximation Algorithm for Parallel Machines Total Tardiness Minimization Problem for Planning Processes Automation. In: Hu, Z., Petoukhov, S., Dychka, I., He, M. (eds) Advances in Computer Science for Engineering and Education II. ICCSEEA 2019. Advances in Intelligent Systems and Computing, vol 938. Springer, Cham. https://doi.org/10.1007/978-3-030-16621-2_43

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