Makespan Minimization with Machine Availability Constraints

  • Authors:

  • Bin Fu;Yumei Huo;Hairong Zhao

  • Affiliations:

  • Department of Computer Science, University of Texas---Pan American, Edinburg, USA TX 78539;Department of Computer Science, College of Staten Island, CUNY, Staten Island, USA 10314;Department of Mathematics, Computer Science & Statistics, Purdue University Calumet, Hammond, USA IN 46323

  • Venue:
  • COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
  • Year:
  • 2009

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Abstract

We investigate the problems of scheduling n jobs to m = m 1 + m 2 identical machines where m 1 machines are always available, m 2 machines have some specified unavailable intervals. The objective is to minimize the makespan. We assume that if a job is interrupted by the unavailable interval, it can be resumed after the machine becomes available. We show that if at least one machine is always available, i.e. m 1 0, then the PTAS for Multiple Subset Sum problem given by Kellerer [3] can be applied to get a PTAS; otherwise, m = m 2 , every machine has some unavailable intervals, we show that if (m *** 1) machines each of which has unavailable intervals with total length bounded by *** (n ) ·P sum /m where P sum is the total processing time of all jobs and *** (n ) can be any non-negative function, we can develop a (1 + *** (n ) + *** ) ***approximation algorithm for any constant 0 *** *** (n ) *** o (1)) ***approximation unless P=NP.