Minimizing sum of completion times for batch scheduling of jobs with deteriorating processing times

Joseph Y.T. Leung, C. T. Ng, T. C.Edwin Cheng

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

We consider the problem of scheduling n jobs on m ≥ 1 parallel and identical machines, where the jobs are processed in batches and the processing time of each job is a step function of its waiting time; i.e., the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. For each job i, if its waiting time is less than a given threshold D, then it requires a basic processing time pi = ai; otherwise, it requires an extended processing time pi = ai + bi. The objective is to minimize the sum of completion times; i.e., ∑i = 1n Ci, where Ci is the completion time of job i. We first show that the problem is NP-hard in the strong sense even if there is a single machine and bi = b for all 1 ≤ i ≤ n. We then show that the problem is solvable in polynomial time if ai = a for all 1 ≤ i ≤ n. Our algorithm runs in O(n2) time. Finally, we give an approximation algorithm for the special case where bi ≤ D for all 1 ≤ i ≤ n, and show that it has a performance guarantee of 2.

Original languageEnglish (US)
Pages (from-to)1090-1099
Number of pages10
JournalEuropean Journal of Operational Research
Volume187
Issue number3
DOIs
StatePublished - Jun 16 2008

All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

Keywords

  • Batch scheduling
  • Deteriorating processing times
  • Performance guarantee
  • Strong NP-hardness
  • Sum of completion times

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