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The Total Weighted Tardiness of Tasks Minimization on a Single Machine

  • Michael Z. ZgurovskyEmail author
  • Alexander A. Pavlov
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 173)

Abstract

We solve the problem of constructing a schedule for a single machine with various due dates and a fixed start time of the machine that minimizes the sum of weighted tardiness of tasks in relation to their due dates. The problem is NP-hard in the strong sense and is one of the most known intractable combinatorial optimization problems. Unlike other PSC-algorithms in this monograph, in this chapter we present an efficient PSC-algorithm which, in addition to the first and second polynomial components (the first one contains twelve sufficient signs of optimality of a feasible schedule) includes exact subalgorithm for its solving. We have obtained the sufficient conditions that are constructively verified in the process of its execution. If the conditions are true, the exact subalgorithm becomes polynomial. We give statistical studies of the developed algorithm and show the solving of well-known examples of the problem. We present an approximation algorithm (the second polynomial component) based on the exact algorithm. Average statistical estimate of deviation of an approximate solution from the optimum does not exceed 5% of it.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Kyiv Polytechnic InstituteNational Technical University of UkraineKyivUkraine
  2. 2.Faculty of Informatics and Computer ScienceNational Technical University of UkraineKyivUkraine

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