Lot-sizing scheduling with batch setup times

  • Authors:

  • Bo Chen;Yinyu Ye;Jiawei Zhang

  • Affiliations:

  • Warwick Business School, University of Warwick, Coventry, UK CV4 7AL;Department of Management Science and Engineering, School of Engineering, Stanford University, Stanford, USA 94305;Department of Information, Operations, and Management Sciences, Stern School of Business, New York University, NY, USA 10012-1126

  • Venue:
  • Journal of Scheduling
  • Year:
  • 2006

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Abstract

This paper is concerned with scheduling independent jobs on m parallel machines in such a way that the makespan is minimized. Each job j is allowed to split arbitrarily into several parts, which can be individually processed on any machine at any time. However, a setup for uninterrupted sj time units is required before any split part of job j can be processed on any machine. The problem is strongly NP-hard if the number m of machines is variable and weakly NP-hard otherwise. We give a polynomial-time $$\frac{5}{3}$$-approximation algorithm for the former case and a fully polynomial-time approximation scheme for the latter.