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Algorithms and Approximation Schemes for Minimum Lateness/Tardiness Scheduling with Rejection

  • Sudipta Sengupta
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2748)

Abstract

We consider the problem of minimum lateness/tardiness scheduling with rejection for which the objective function is the sum of the maximum lateness/tardiness of the scheduled jobs and the total rejection penalty (sum of rejection costs) of the rejected jobs. If rejection is not considered, the problems are solvable in polynomial time using the Earliest Due Date (EDD) rule. We show that adding the option of rejection makes the problems \(\mathcal{NP}\)-complete. We give pseudo-polynomial time algorithms, based on dynamic programming, for these problems. We also develop a fully polynomial time approximation scheme (FPTAS) for minimum tardiness scheduling with rejection using a geometric rounding technique on the total rejection penalty.

Observe that the usual notion of an approximation algorithm (guaranteed factor bound relative to optimal objective function value) is inappropriate when the optimal objective function value could be negative, as is the case with minimum lateness scheduling with rejection. An alternative notion of approximation, called ε-optimization approximation [7], is suitable for designing approximation algorithms for such problems. We give a polynomial time ε-optimization approximation scheme (PTEOS) for minimum lateness scheduling with rejection and a fully polynomial time ε-optimization approximation scheme (FPTEOS) for a modified problem where the total rejection penalty is the product (and not the sum) of the rejection costs of the rejected jobs.

Keywords

Dynamic Program Polynomial Time Optimal Schedule Maximum Lateness Partition Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sudipta Sengupta
    • 1
  1. 1.Bell LaboratoriesLucent TechnologiesHolmdelUSA

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