Scheduling jobs with piecewise linear decreasing processing times

Authors

  • T.C. Edwin Cheng,

    Corresponding author
    1. Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China
    • Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China
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  • Qing Ding,

    1. Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, People's Republic of China
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  • Mikhail Y. Kovalyov,

    1. Institute of Engineering Cybernetics, National Academy of Sciences of Belarus, Surganova 6, 220012 Minsk, Belarus
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  • Aleksander Bachman,

    1. Institute of Engineering Cybernetics, Wroclaw University of Technology, Janiszewskiego 11/17, 50-372 Wroclaw, Poland
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  • Adam Janiak

    1. Institute of Engineering Cybernetics, Wroclaw University of Technology, Janiszewskiego 11/17, 50-372 Wroclaw, Poland
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Abstract

We study the problems of scheduling a set of nonpreemptive jobs on a single or multiple machines without idle times where the processing time of a job is a piecewise linear nonincreasing function of its start time. The objectives are the minimization of makespan and minimization of total job completion time. The single machine problems are proved to be NP-hard, and some properties of their optimal solutions are established. A pseudopolynomial time algorithm is constructed for makespan minimization. Several heuristics are derived for both total completion time and makespan minimization. Computational experiments are conducted to evaluate their efficiency. NP-hardness proofs and polynomial time algorithms are presented for some special cases of the parallel machine problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 531–554, 2003

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