Preemptive scheduling with simple linear deterioration on a single machine

  • Authors:

  • C. T. Ng;Shisheng Li;T. C. E. Cheng;Jinjiang Yuan

  • Affiliations:

  • Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China;Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China;Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, Peoples Republic of China

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2010

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Abstract

In this paper we study the problem of scheduling n deteriorating jobs with release dates on a single machine. The processing time of a job is assumed to be the product of its deteriorating rate and its starting time. Precedence relations may be imposed on the set of jobs. Unlike the classical time-dependent scheduling problems, we assume that the execution of a job can be preempted in the sense that the job's deteriorating rate is reduced when it is preempted and each continuously processed part of a job can be regarded as an independent job with a specified deteriorating rate. The objective is to minimize some common regular scheduling performance measures. We first show that minimizing a class of regular symmetric functions is polynomially solvable. Then we construct an O(n^2) algorithm for minimizing the maximum job completion cost with or without precedence constraints. Finally we show that minimizing the total weighted completion time is NP-hard even if there are only two distinct release dates.